Gravity

±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±

±±±±±±±±±±±± ±±±±±±±±±±±±

±±±±±±±±±±±± INTRODUCTION TO MASS INCREASES BY ±±±±±±±±±±±±

±±±±±±±±±±±± GRAVITATIONAL RELATIVITY ±±±±±±±±±±±±

±±±±±±±±±±±± ±±±±±±±±±±±±

±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±

The following proposes that steady state relativistic effects

can be understood to occur pursuent to gravitational fields.

The wider range of distortions in space embraced by the GENERAL

THEORY OF RELATIVITY are put aside and certain specific effects

are studied in detail. These specific effects are understood to

come under the heading of GRAVITATIONAL RELATIVISTIC EFFECTS.

R. S. Livingstone

Ottawa, Canada, June, 1990.

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º ±±±±±±±±±±±±± GRAVITATIONAL RELATIVITY THEORY ±±±±±±±±±±±± º

º CONNECTS CERTAIN SOLAR PLANET MASSES. º

ÌÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍ¹

º ±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±± º

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º ALSO, GRAVITATIONAL AND SPECIAL RELATIVITY THEORIES º

º ARE INTRINSICALLY RELATED º

ÈÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍ¼

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By assuming a mass and spacial effect in general relativity, a

proposed gravitation relativity is evident, in which there is a

direct tie-in between effects seen in Special Relativity and in

Gravitational Relativity. In fact, properties commonly factored

for a star or black hole in Gravitational Relativity, can also

be factored in Special Relativity, and visa versa. This suggests

not necessarily a unified field theory, but definately a connection

betweeen certain properties in gravity, and in electro-magnetism.

ÉÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍ»

º ±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±± º

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º ABSTRACT º

ÈÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍ¼

Several facets are to be discussed in the following.

(Part 1) Arguments demonstrating an increase in mass by the

effects of gravitational relativity are shown through events

which occur in the solar system.

(Part 2) Effects for gravitational and special relativity are shown

to be synonymous for a given mass. Critical limits are uncovered in

the behaviors of both relativities. In specific situations, mass is

locked to a ceiling which is less than, but is determined from, black

hole mass equivalents. In this, it is found that the maximum original

mass which can be gathered before gravitational relativistic effects

are maximized, is that of a black hole's mass divided by a factor

of 1.618034 (a number constant known as the Golden Harmonic Ratio).

The maximum velocity attainable by this mass when moving in special

relativity, is the speed of light divided by the Golden Harmonic Ratio.

(Part 3) It is found that for any visible mass, there is a

maximum special relativistic limit on the mass. This limit can be

known in advance by knowing the maximum velocity the moving mass can

attain and still remain visible in the normal sense, when observed by

a stationary observer. The maximum effect is a derivative of the speed

of light reduced by the relativistic effect of the mass's gravity.

This is shown to define an upper limit velocity at which any given

mass can appear in the same state of the universe as the stationary

observer. Any rest mass reaches this barrier at a plateau that is

predictable, and so the mass cannot visibly expand to infinity.

(Part 4) Innuendos of a unified field theory are harking loudly,

popping out of the framework of relativistic physic. There is a

universality in obvious behaviors working directly between the

one field's venues (gravity) and the other field's venues

(electromagnetism). As to whether these equalities can constitute

segments of a full fledged unified field theory is not to be

addressed at this time, in the scope of the following disclosures.

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º part 1 ±±±±±±±±±±±±±±±± GRAVITATIONAL RELATIVITY ±±±±±±±±±±±±±±±± º

ÈÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍ¼

A little known (entirely unknown) fact is that certain solar

planetary masses can be connected as a direct consequence of

gravitational relativity. This is shown to be true when it is

surmised that relativistic effects of gravity may include an

intrinsic increase in the mass comprising the source of the

gravity.

The relativistic increase for the Sun mass is very small compared

to the mass of the Sun itself. Even though the increase in mass

is small at roughly 4.23 x 10 to the power 27 grms, the increase

is nevertheless nearly 7 times the mass of Mars, and is marginally

less than the mass of Venus.

Such an increase in the Sun mass, when calculated to advanced

accuracy, is found to be exactly equal to the mass difference

between Venus and Mars. Another discrete relativistic potential

includes 1/2 the mass of Jupiter added to the mass of the Sun.

The existence of states makes it possible to infer a more

accurate estimate for the existing mass of the Sun.

The radius of the Sun is considered to be a constant for various

manifestations, shown to correspond to parameters which operate

between solar mass equivalents up to the masses of black holes.

In this, a link between gravitational and special relativity

is shown. The link is the subject of part 2.

ÉÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍ»

º part 2 ±±±±±±±±±±±±±±±±±±±± SPECIAL RELATIVITY ±±±±±±±±±±±±±±±±±± º

ÈÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍ¼

It can be easily demonstrated that a visible mass moving at

velocities nearing the speed of light, can never grow to infinite

quantities and remain visible in the normal sense, and so can never

achieve a velocity equal to the speed of light, in the normal sense.

This is because gravitational relativistic effects have to be

considered for a moving mass, if it is assumed that gravitational

relativity includes an effect that increases the original state of

the mass which is the source of the gravity's relativistic effect.

It is readily shown that such gravity effect has significance to

special relativity.

There is a boxed in limit, where the moving mass (bumped in

value in special relativity) assumes a value equivalent to the

mass of a black hole, when the original rest mass is expanded by

the effect of special relativity, in direct accord with the mass's

radius contracted by the effect of special relativity.

When assuming the mass of a black hole equivalent, the

moving mass effectively drops from sight in the normal

physical view as seen by a stationary observer.

(See Appendix A at the end of this document, for a related

discussion involving elementary particles such as the proton).

One of the finite limits to which a mass can be accelerated

in special relativity, and to which a mass can be accumulated

in gravitational relativity, can be explicitly expressed for

both modes of relativity as factors of a number constant known

as the Golden Harmonic Ratio, 1.61803398875 .

In this, the Golden Ratio's significance is to the existence of

black holes. Specifically, a black hole's mass includes both an

original mass and an augmentive portion from the relativistic

effect of gravity, to comprise the total mass involved. The

relationship between original, gained, and final black hole

mass aggregations, can be expressed in exact terms of the

Golden Harmonic ratio.

In particular, however, in the dynamic behaviors of both

relativities, important boundaries are reached at a certain

critical limit whose mathematical significance is the Golden

Harmonic Ratio. The parameters here include a black hole's

mass aggregate and event horizon.

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º part 3 ±±±±±±±±±±±±±±± THE GOLDEN HARMONIC RATIO ±±±±±±±±±±±±±±±± º

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The effects of gravitational relativity can be generally related

to the effects of special relativity, to the extent that relativity

effects of gravity and of special relativity can be shown to be

equated through a single common factor.

The maximum velocity attainable by a visible moving mass, is

the speed of light reduced by the proportionate effect of the

gravitational relativistic effect in the mass being accelerated.

The critical limit (maximum velocity) possible, is restricted

by bounds achieved in special relativistic effect when the rest

mass has increased, and radius has contracted, to a point where

the moving entity reaches a state where it forms a black hole and

effectively disappears from view, relative to a stationary observer.

The barrier limit is easy to calculate and to mathematically

confirm, when given the original rest mass and radius.

It becomes clear that, generally a visible mass accelerated to

relativistic velocities cannot theoretically achieve an infinite

mass, and the velocity can never theoretically equal the speed of

light. The traditional interpreted statements in special relativity

which say any visible mass continues to expand toward infinity,

and the velocity continues to the speed of light, are in error

about such things.

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º ±±±±±±±±±±±±± GRAVITATIONAL RELATIVITY THEORY ±±±±±±±±±±±±± º

º ±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±± º

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º ±±±±±± GENERAL INTRODUCTION for part 1 The Solar System ±±±±±±± º

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In the following, the existing orbits of planets are not

considered as terms, and all of the events are shown to

occur as within a constant confinement radius which is

the existing radius of the sun.

A general relativistic equation is in common use for gravitational

effects. Such an equation has been around in physics since 1916.

Variations of the equation are also in common use. Given a known mass

for instance, a Schwarzschild radius for that mass confined as a black

hole can be immediately calculated.

Conversely, given a radius, how much mass would be needed to be

confined within that radius as a black hole can also be calculated.

Such effects are a steady state system. It is the amount of

mass within a specified radius which counts. The effects are

constant per given mass and radius, since no outside velocity

or acceleration is involved with the masses sitting stationary.

The same is true for mass aggregates which are not a black hole,

but which have mass sufficiently large, and a radius sufficiently

small, for gravitational relativistic effects to be discernible.

For stars the size of the Sun, for instance, there are discernible

effects, even though they appear to be very slight at first sight.

In a closer look, however, the slight effects can reveal many major

properties in the fundamental relativistic behavior of gravity.

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ÛÄ´ GRAVITATIONAL RELATIVISTIC EFFECT ³

ÀÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÙ

In principle, gravitational relativistic effects are calculated via

the standard equation, for varying mass and radius, until a meeting

point is reached at which the mass and radius correspond to the

formal parameters of a black hole.

In the standard equation, a term for the relativistic effect

results, which has been mainly used to determine the slowing

of time in closer vrs more distant proximities to the field

generating the effect.

The same term can be used to find out how much a gravitational

mass's radius can further contract relativistically per given

increase in mass, when assuming that gravity relativistically

contracts its own confinement radius. The same term can be used

to calculate the gravity's relativistic effect on its own mass.

This term can be called E (for effect). The value of term E

suddenly nose dives toward 0 when the mass is sufficiently large,

due to a sudden relativistic upsurge in pull in the greater power

of the gravity itself, at which point the existing mass becomes

a so called black hole and the existing mass's radius no longer

appears to contract, rather, it will begin to increase given

further increases in mass.

This mass and radius stabilization is considered a physical

boundary called the Schwarzschild radius, or event horizon.

The stabilization is discussed in 'A Comparison Between

Gravitational And Special Relativity' (found directly

under the 'General Introduction for Relativity' Part 2',

below), and is formally described in Equations 3 to 5

in APPENDIX B at the end of this document.

ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ¿

ÛÄ´ GENERAL MASS QUANTA EFFECT ³

ÀÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÙ

In variations of the equations, when a quantity of mass is given

and the radius containing it is also known, then a simple solution

using term E can denote how much of a mass increase may occur in

the mass, due to a relativistic augmentation by the mass's gravity.

The augmentation can be conjectured to occur in two ways.

Either a measured mass is naked (original with no relativistic

augmentation), or is augmented (the measured mass includes

the augmentation).

Hence the augmentation can be conjectured to be in two

modes; either a decrease upon the originating mass, or

an increase.

In keeping with special relativity effects, a mass increase

in gravitational relativistic augmentation can be presumed

with no difficulties.

For instance the Sun (given its mass and radius) is surmised

to have a visible radius which is marginally reduced by

relativistic augmentation (shrunk), and so the Sun's apparent

mass is also surmised to be marginally augmented (expanded) in

a mass increase by an equivalent relative proportion.

The problem is that such a conjecture (relativistic augment-

ation in mass) is hard to prove, since it is not possible to

actually separate a given mass from its gravity and so observe

any change in the apparent mass, when the mass is compared with

vrs without the relativity of the gravity.

In which case, any evident mass augmentation will have to

be learned by some secondary means.

In this solar system such a means is provided mechanically,

by the fact that the amount of solar mass augmentation is a

meaningful quantity in company with the existing mass of some

of the planets.

The mass augmentation has a value which is in a quantum

correspondence to the existing masses of Venus and Mars.

This makes the mass augmentation clearly visible. The fact

that the relativistic mass is involved with these planets

(in relationship with small particles external from the Sun)

is very curious.

ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ¿

³ GRAVITATIONAL RELATIVISTIC EFFECTS ³

ÀÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÙ

The standard equation for gravitational relativistic effect

is described as follows:

EQUATION A

ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ

³ 2G (Mass)

E = ³ 1 Ä ÄÄÄÄÄÄÄ

\³ Cý R

The square root of ((1 - the product of 2 times the

gravitational constant G, times a mass), divided by the

radius of that mass times the speed of light squared),

yields a gravitational relativistic effect factor, termed E.

EQUATION B

The radius of the mass times the reciprocal of the

E factor, gives the originating radius of the mass,

ie., before contraction of the radius by the mass's

gravitational relativistic effect.

ÚÄ Ä¿

³ ÚÄ Ä¿ ³ Where Re is the

³ ³ 1 ³ ³ amount of space

³ R x ³ ÄÄÄ ³ ³ - R = Re by which the Sun's

³ ³ E ³ ³ radius is contracted

³ ÀÄ ÄÙ ³ by the relativity

ÀÄ ÄÙ in the Sun's mass

ÚÄ Ä¿ Ro is the original

ÀÄ Ro ÄÙ radius before effect.

R is the existing radius

(the radius we see) which

includes effect (Ro + Re)

These (Equations A and B) are well known and nothing new

has been so far stated.

The relativistic collapse in the Sun's radius

is very slight, hardly 1« kilometers.

This is learned as the difference between the originating Sun

radius Ro, minus the existing (augmented) radius R. The difference

seems to be a remarkably close approximation of « the Schwarzschild

radius needed for the Sun mass to be a black hole. However this is

not surprising, in that the smaller the mass and/or the larger the

radius, the closer the radius augmentation is to « the Schwarzschild

radius. The 1/2 approximation grows closer, the less the mass

aggregate is a black hole.

In principle, with little mass and a large radius, there is

very little augmentation. Conversely, a very small radius for

the small mass is needed as the event horizon for the small mass

to become a black hole.

The point intended is that as the mass to radius ratio

approaches the primes of a black hole, the rates of

change due to gravitational relativistic effects climbs

up a steepening gradient.

At solar quantities, the effects are so slight as to be

normally thought of as negligible. But this is not so.

If for instance 1/2 the mass of JUPITER is added to that of

the Sun, and this enhanced mass sum is regarded as being within

the confines of the existing Sun radius, the relativistic mass

augmentation effect when applied to the mass of the Sun minus

1/2 the mass of Jupiter, equals the previously noted congress

involving Venus and Mars masses, (at the end of 'General Mass

Quanta Effect', above).

Such state arrays reveal a previously unsuspected property,

of relativistic mass quantal arrangements displaced at long

distance from the source generating the relativistic mass

effect. A first suspicion is that:

'THERE IS AN INCOMPATIBILITY BETWEEN A GRAVITATIONAL

FIELD AND THE RELATIVISTIC EFFECT IT GENERATES'.

The appearance is that some aspect of the relativistic mass

effect generated in a field of gravity, does not stay within

the field generating it.

In supposition, it appears that some relativistic component

is expunged (externalized) from the originating field of

gravity. In the case of our solar system's example, the

masses of Venus and Mars, along with Jupiter, are external

and yet relativistically tied to the Sun mass.

ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ¿

ÛÄ´ ESTIMATED ACCURACY OF SOLAR MASSES ³

ÀÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÙ

Masses in the solar system are traditionally published in two

ways. A mass for each planet is given as a ratio between it and

the mass of the Sun. Since comparative ratios can be inferred to

considerable accuracy, the Sun to planet mass ratios for most of

the planets are well known.

On the other hand estimating the actual mass of a planet or

the Sun in terms of (say) gram units, is not so easy, since

there is no way of actually sitting a planet on a scale. For

that matter, estimating the real mass of the Sun (in say grams)

is also difficult since the Sun cannot be weighed on a scale.

The problem is compounded in that in order to know a real

weight (in grams) requires that the universal gravitational

constant (G) be known to high accuracy, which it is not.

Whereas determining the mass influences of one body on another,

as a ratio, is easier since (G) is not a critical factor for

the accuracy.

For these reasons the real mass of (for instance) the

Sun (in say grams) cannot be stated with great accuracy

by ordinary measuring methods.

The Sun's mass is currently given as somewhere between

1.989 x 10 to 33 grms, and 1.991 x 10 to 33 grms. Whereas

planet masses are currently given in gram figures accurate

to between 4 and 5 significant figures. The greater accuracy

for planet masses is assisted by the fact that the planets

tend to subtlety bounce each other around in orbit, and their

bouncing can be closely watched. Whereas the Sun is hardly

bounced by the less hardy influence of the planets.

The Earth - Moon combination gives the best look at bouncing.

But rigorous real weight analysis for the Earth is not so easy

when tried, because both the Earth and Moon also subtlety bounce

around as a unit.

If the gram weight of the Earth (5.976 ñ .004 x 10 to 27 grms)

is multiplied by the Sun to Earth mass ratio (332,995.9 ñ .4),

then the Sun's gram weight results as (1.9899834 x 10 to 33 grms).

This value is actually deemed low to a very minor degree for the

equations which follow below. In the following, a Sun mass in the

vicinity of (1.990993 x 10 to 33 grms) is explicitly inferred.

Another problem in any advanced accuracy is inherent in the weak

solar gravitational relativistic effects per se. Because the effect

for solar mass quantities is so slight, there is a loss of some

accuracy due to inherent truncation in doing the calculations.

In the equations which follow, accuracy has been maintained

to 13 significant digits, but inherent truncation results at

the 7th significant digit of certain of the terms.

Such truncation is diminished when dealing with larger

masses confined within small radii. The truncation disappears

completely when dealing right at the range of black hole masses.

Hence, black hole limits can provide a tool for comparing

calculations, to determine which calculations produce

exactitudes and which produce close approximations only.

This is actually more straightforward than it sounds.

ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ¿

ÛÄ´ BASIC CONVENTIONS ³

ÀÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÙ

In the following, the existing orbits of planets are not

considered as terms. All of the events are shown to occur

as within a constant confinement radius, which is the

existing radius of the sun.

For the sake of convenience, the mass of the

Sun is shown as a standard term labeled (MM).

In the following, the calculations are accomplished at

an accuracy of 10 to the 13 significant digits. Zeros are

used to fill gaps between available digits and the 13th

significant digit. As already mentioned, some of the terms

are accurate only to the 7th significant digit. In fact,

some terms cut off at the 7th digit. For this reason, the

highest maintained accuracy possible is very important.

For the universal gravitational constant G, a recent

revision having a digital value of 6.6720 x 10 to -8

is used.

The speed of light C of the following value is used:

2.99792458 x 10 to 10 cms/sec.

The radius of the Sun is used as a constant R, having

the value 6.96265 x 10 to 10 cms.

ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ¿

³ MASS CONVENTIONS ³

ÀÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÙ

The following mass aggregates have been adopted as standards for

the involved quantities. The high accuracy given them has been

by the adjusting of repeated pure math experimental results until

a semblance of coherency in the mass standards looked viable.

The term 'aggregate mass' is used for denoting a mass (such as

the Sun, plus or minus another mass (such as 1/2 the mass of

Jupiter). 'Aggregate mass' is also used to denote any apparent

mass, since the mass is assumed to include relativistic

augmentation due to gravity. Hence, the original mass before

augmentation is termed 'original mass', or 'originating mass'.

K has been adopted as a term to explicitly denote the

relativistic mass augmentation in the Sun's mass due

to the Sun's gravity.

In determining aggregate mass values, the value of MM for the

Sun's apparent mass was first determined, based on an assumed

equality that a so called K augmentation factor for the Sun mass

is indeed the mass difference between planets Venus and Mars.

Without doubt the real values for the mass aggregates (given

in grms for instance) will marginally change depending on

future adjustments of the universal gravitational constant,

and perhaps sharper astronomy techniques.

(For that matter, mass MM may not be the true real

mass of the Sun. It may turn out that MM is the mass

of the Sun ñ something else).

It is anticipated that any such changes would nevertheless

prove to continue to be coherent within the realms of the

gravitational relativistic state equations which involve them.

Several tables and basic equations follow. Following these,

a discussion begins on how a mass of MM was inferred for the

Sun, via gravitational relativistic effects.

Table 1 which follows, lists important mass aggregations,

and the highest resolved real mass values possible as used

to explore their relativistic highlights.

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º INFERRING A GRAVITIONAL RELATIVISTIC º

º AUGMENTED MASS VALUE FOR THE SUN º

ÈÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍ¼

TABLE 1 INFERRED VALUES

ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ¿

³ ³

³ MM = Existing Sun mass, presumed to include ³

³ original mass plus mass augmentation K ³

³ ³

³ = 1.9909930 x 10 to 33 grms ³

ÃÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ´

³ ³

³ K = Gain in original mass of the Sun, the ³

³ amount of relativistic augmentation ³

³ due to the Sun's gravity ³

³ ³

³ = 4.226490 x 10 to 27 grms ³

ÃÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ´

³ ³

³ Mbh = Mass of a black hole having an event ³

³ horizon equal to the Sun's radius R ³

³ ³

³ = 4.689536679 x 10 to 38 grms ³

ÀÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÙ

TABLE 1-A ESTABLISHED VALUES

ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ¿

³ ³

³ R = Existing Sun radius ³

³ = 6.96265 x 10 to 10 cms ³

ÃÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ´

³ ³

³ C = Speed of light ³

³ = 2.99792458 x 10 to 10 cms/sec ³

ÃÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ´

³ ³

³ G = Universal gravitational constant ³

³ = 6.6720 x 10 to -8 cms3/grms secý ³

ÃÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ´

³ ³

³ CR = A physical constant for Mass/Radius ³

³ ratio of a black hole ³

³ = 6.735275620 x 10 to 27 grs/cm ³

ÃÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ´

³ ³

³ GH = Golden Harmonic Ratio ³

³ = 1.61803398875 ³

ÀÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÙ

TABLE 2

ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ¿

³ ³

³ Planetary masses - Data is from tables found at the ³

³ back of the following reference: ³

³ ³

³ UNIVERSE by Don Dixon, Houghton Mifflin Co., ³

³ Boston, 1981 ³

³ ³

³ Moon = .0735 x 10 to 27 grms ³

³ ³

³ Venus = 4.8683 x 10 to 27 grms ³

³ Earth = 5.976 x 10 to 27 grms ³

³ Mars = 6.4181 x 10 to 26 grms ³

³ Jupiter = 1.901 x 10 to 30 grms ³

³ ³

³ Sun = 1.9888 x 10 to 33 grms ³

³ ³

ÀÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÙ

TABLE 3

Certain terms are used to generalize certain types of masses:

ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ¿

³ ³

³ Low mass - Masses in the range of those found ³

³ in this solar system ³

³ ³

³ Enhanced mass - Solar mass aggregates other ³

³ than the Sun, added or subtracted ³

³ to the Sun mass ³

³ ³

³ - Specifically the mass of the ³

³ Sun plus 1/2 Jupiter, and mass of ³

³ the Sun minus 1/2 Jupiter, also mass ³

³ of the Sun minus mass of Venus ³

³ ³

³ Higher mass - Mass of a black hole, and in mass ³

³ range of a black hole ³

³ ³

³ - Specifically the mass for a ³

³ black hole whose event horizon ³

³ is the radius of the Sun ³

³ ³

³ Originating mass - Original mass accumulation without ³

³ any relativistic augmentation ³

³ ³

³ Augmented mass - Existing mass assumed to include ³

³ a change from the originating ³

³ mass due to relativistic effect ³

³ of gravity ³

³ ³

³ Existing mass - As physically measured, with ³

³ any assumed augmentation present ³

³ in the measurement ³

³ ³

³ Real mass - A real weight, in terms of a ³

³ physical weight, for instance ³

³ measured in grms as if weighed ³

³ on a scale ³

³ ³

ÀÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÙ

Certain equations are used to generalize mass effects

due to gravitational relativity. Certain term conventions

are adopted for the sake of convenience in bookkeeping:

EQUATION C Determining a relativistic effect factor Em

for a mass aggregate, in particular the Sun:

ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ

³ 2G (MM) Where MM is the mass

Em = ³ 1 Ä ÄÄÄÄÄÄÄ of the Sun, and R is

\³ Cý R the radius of the Sun

EQUATION C-1 Determining how much mass augmentation relativistically

occurs in the mass aggregate of the Sun:

(MM) - ((MM) x Em) = Km Where K is the actual mass

augmentation increased on

the Sun's original mass

due to gravity

EQUATION C-2 Determining a relativistic effect factor for a mass

aggregate, such as the Sun plus X, where X is anything:

ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ

³ 2G (MM+X)

Ex = ³ 1 Ä ÄÄÄÄÄÄÄÄÄÄÄ

\³ Cý R

EQUATION C-3 Determining how much mass augmentation relativistically

occurs in a mass aggregate, such as the combined mass

of the Sun + X , when both are confined in radius R :

(MM+X) - ((MM+X) x Ex) = K+x

EQUATION C-4 For example, determining a relativistic effect factor

for such as the Sun plus 1/2 Jupiter combined:

ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ

³ 2G (MM+1/2j)

E+1/2j = ³ 1 Ä ÄÄÄÄÄÄÄÄÄÄÄ

\³ Cý R

EQUATION C-5 Determining how much mass augmentation relativistically

occurs in a mass aggregate, such as the combined masses

of the Sun and 1/2 Jupiter, when both are confined in

radius R :

(MM+1/2j) - ((MM+1/2j) x E+1/2j) = K+1/2j

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º VERIFYING A MASS OF MM FOR THE SUN º

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An aggregate mass MM (being the mass of the Sun) found to have

intrinsic relativistic consequences, can be easily verified.

If starting with an estimated Sun mass, for instance;

(1.989 x 10 to 33 grms); and assuming that the Sun mass is

already relativistically augmented, the gravitational relativistic

mass increase of a Sun mass of (1.989 x 10 to 33 grms) is found

(using Equations C and C-1), to be slightly less than the mass

difference between Venus and Mars.

That is: Venus mass is 4.8683 x 10 to 27 grms

Mars mass is .64181 x 10 to 27 grms

Venus - Mars is 4.226490 x 10 to 27 grms

whereas the mass augmentation Km of a

Sun mass of (1.989 x 10 to 33 grms) is

(4.218033 x 10 to 27 grms), which is low.

If the Sun's mass is gradually increased, eventually a

mass aggregate will be found, in which the relativistic

mass augmentation K is precisely (Venus - Mars), that is:

K = 4.226490 x 10 to 27 grms.

The point of agreement occurs when the mass aggregate

for the Sun MM is found to be (1.990993 x 10 to 33 gms).

For instance, suppose arbitrary units of Neptune's mass are

systematically added to a base mass of (1.989 x 10 to 33 grms).

A break point will be reached. At + 18N units of Neptune's mass

the relativistic augmentation (Km) of the aggregate mass will be

marginally less than (Venus - Mars). And at + 19N units of

Neptune's mass, the relativistic augmentation (Km) of the

aggregate mass will be marginally more than (Venus - Mars).

And so somewhere between (base + 18N) and (base + 19N) is a solar

mass component whose resulting augmentation (K) is exactly equal

to (Venus - Mars). The search can now be narrowed to (base + X),

where (+ X) falls somewhere between (+ 18N and +19N).

Fine tune fiddling back and forth using smaller and smaller

increments for X, eventually closes in on a result for;

(base + 18N + X)

in which the relativistic mass augmentation

from (base + 18N + X) when using Equation D

below, equals (Venus - Mars) exactly.

EQUATION D

Where b is a base mass

ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ (1.989 x 10 to 33 grms)

³ 2G (b+X)

E = ³ 1 Ä ÄÄÄÄÄÄÄÄ And so (b+X) - ((b+X) x E) = K,

\³ Cý R and K = (Venus - Mars) exactly,

when (b + X) is exactly

(1.990993 x 10 to 33 grms)

EQ D can be written so that (b+X) is standardized as MM, so that:

EQUATION E

Where MM is an inferred Sun

ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ mass, so MM - ((MM) x Em) = K

³ 2G MM where K = (Venus - Mars),

Em = ³ 1 Ä ÄÄÄÄÄ and Em is the relativistic

\³ Cý R effect factor for mass MM

In other words the inferred Sun mass MM presents a solar

mass factor whose relativistic gravitational augmentation (K)

is exactly equal to the mass difference between Venus and Mars.

That is: Equation E determines Em

and: MM - ((MM) x Em) = K

and: K = 4.226490 x 10 to 27 grms

which is precisely (Venus - Mars)

which also is: 4.226490 x 10 to 27 grms

This instantly presents an interesting situation. The inferred

mass of the Sun MM appears to involve a relativistic gravitational

mass amalgamation which is greater than the mass of the Sun alone.

The interesting kink is that the masses of Venus and Mars

are found expunged into space, at long distance orbits around

the Sun. This orbital existence is not explained at this point

and so is noted only as a comment.

The other interesting point of view is that although the mass

of Mars for instance is very small compared to the mass of the

Sun, the mass of Mars is nonetheless highly visible. This is

something like the high visibility of the electron's tiny

binding energy unit in comparison to the mass of the Proton.

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º SPECIFIC MASS QUANTA EFFECT º

ÈÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍ¼

As described under 'A Comparison Between Gravitational And Special

Relativity' (found directly under the 'General Introduction for

Part 2', below), gravitational relativity includes at least two

variable source terms for its effect. These source terms are the

aggregate mass, and the mass's confining radius. It means that

different quantities of mass can be said to occupy the same area.

In which case there can be (in result) different or identical

relativistic mass augmentations, depending on discrete combinations

of how much mass is said to be added or subtracted to the initial

mass aggregate, confined in the same or in different radii.

For instance in mass aggregates which are in the range

of the size of the Sun, here, discrete extra mass in the

same radius (the Sun's radius) can produce a relativistic

factor Ex which when arbitrarily applied to yet another

discretely different mass aggregate, can produce a K

augmentation which is otherwise gained from yet another

different mass aggregate.

For instance, the Sun mass MM, plus 1/2 the mass of Jupiter,

can provide via EQ C-2 an effect factor (E+1/2j) which when

applied to the same mass aggregate, via EQ C-3, results in

K+j .

But if E+1/2j is applied to a different mass aggregate, for

instance to MM-1/2j, a value slightly departed from K+j must

result. The resulting slightly lower value in fact once again

happens to be K exactly (the mass difference between Venus

and Mars).

The formal description for this enhanced mass state is:

EQUATION E-1

ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ (MM+1/2j) is the

³ 2G (MM+1/2j) aggregate of the Sun

E+1/2j = ³ 1 Ä ÄÄÄÄÄÄÄÄÄÄÄ mass plus 1/2 the mass of

\³ Cý R Jupiter, confined in the

existing Sun radius R

EQUATION E-2

(MM-1/2j) - ((MM-1/2j) x E+1/2j) = K

where K equals the mass of (Venus - Mars), and

(E+1/2j) is the relativistic effect of the slightly

denser aggregate of the inferred Sun mass MM plus 1/2

the mass of Jupiter, when confined in the Sun's radius R.

In keeping with state-like mass aggregates, if EQ E-1 is

rewritten so that the initial mass aggregate used in EQ E-1

is now MM-1/2j, and a resulting effect (called E-1/2j) is

used in a rewritten form of EQ E-2, then a relativistic mass

augmentation equal to K once again results; that is:

EQUATION E-3

(MM+1/2j) - ((MM+1/2j) x E-1/2j) = K

where K equals the mass of (Venus - Mars).

EQUATION E-4

The bifurcation of Jupiter mass around the mass of the Sun

to form coherent relativistic states can be generalized as:

E+1/2j of mass M+1/2j applied to M-1/2j yields K

Em of mass MM applied to MM yields K

E-1/2j of mass M-1/2j applied to M+1/2j yields K

EQUATION E-5

Such a bifurcation around the mass of the Sun

can be generalized as:

E+x of mass M+x applied to M-x yields Kx

E of mass M applied to M yields Kx

E-x of mass M-x applied to M+x yields Kx

However, the augmentation quantity Kx only equals known

augmentation value K, when M+x and M-x are specifically

MM+1/2j, and MM-1/2j. That is, when 1/2 quantas of Jupiter's

mass are added, and subtracted, to the inferred mass MM of

the Sun.

(It should be noted that the bifurcation results of EQ E-4

are not perfect exactitudes. The three resulting values of

K happen to look the same for masses in the range of this

solar system. For higher mass densities for example MM

times 1000, confined in the same radius R, the three K

values (shown as Kx in EQ E-5) are noticeably separated).

ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ¿

ÛÄ´ VERIFYING THE COHERENT 1/2j STATES ³

ÀÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÙ

Equations E-1, E-2, E-3, and E-4, were not easily found without a

prior insight and a discovery. In question is how come a unit of 1/2

the mass of Jupiter has been arbitrarily used to arrive at a seeming

non arbitrary result, this result being where K is twice again

calculated, as summarized in Equation E-4.

An original intention was to see if the total mass of the solar

system could be inferred to be in any way involved in some sort

of interphasing between different mass aggregates in this solar

system's gravitational relativity. This thought itself came from

an original impression that the real mass of the Sun was in the

range of base (1.9891 x 10 to 33 grms), and inferred mass MM

would be the real Sun mass (base) plus Jupiter's mass, since

(MM - base) closes in on an excellent approximation of Jupiter's

real mass at (1.901 x 10 to 30 grms), when using EQ D to infer

mass MM.

For a while it was looking good. It seemed that if MM was the

mass of the (Sun + Jupiter), and a mass value just slightly

larger than the total mass of the solar system was substituted

in EQ C-2, then a mass augmentation of K was again found when

the factor Ex of EQ C-2 was substituted in EQ C-3, when

Jupiter's mass was subtracted from the solar total mass

aggregate and the result of this reduction substituted for

MM+X in EQ C-3.

In the exploration, a mass term Mt was adopted for the solar

mass total, plus some little extra, to give mass term Mtx.

And mass term Mtx-j denoted the solar total minus the mass

of Jupiter.

The value of Mtx could be rigorously inferred, as being

exactly the mass aggregate needed in EQ C-2 to result in

a mass augmentation effect equal to K in EQ C-3, when mass

aggregate Mtx gave augmentation effect Etx, which was used

to find the augmenting effect on mass Mtx-j, as in:

EQUATION F

ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ

³ 2G Mtx

Etx = ³ 1 Ä ÄÄÄÄÄÄ

\³ Cý R

and a mass aggregate of (Mtx - Jupiter) was substituted

in EQ C-3, giving:

EQUATION G

(Mtx-j) - ((Mtx-j) x Etx) = K

In other words, the thinking was heading along a line that a

sort of formal relativistic interphasing might be occurring,

whose boundary was spread between the base mass of the Sun,

and the total mass of the solar system. For instance between

the Sun, and (Sun + Jupiter), and (Sun + planets + moons),

and (Sun + planets + moons - Jupiter). The problem was in that

little extra mass bit, (the x of Mtx). What might it represent?

It was suddenly and unexpectedly found that the value

of Mtx as rigorously inferred, turned out to be exactly

(MM + 1/2 Jupiter). This was not a percentage of error

type of equality. The figures that suddenly appeared on

hand were identical to 8 significant digits.

In other words, the rigorously determined value for Mtx,

and MM+1/2j, were identical to 8 significant figures.

Which dramatically changed the picture.

It was now easy to think that MM instead of being

a (Sun mass + Jupiter) aggregate, represented the

real mass of the Sun itself. In other words, MM

could well be the real mass of the Sun.

It was also easy to perceive a formal verification for the

quanta bifurcation factor involving 1/2 the mass of Jupiter.

By using Equations F and G to find a result equal to K,

a mass quanta increment of (+X) added upon MM eventuates in

an interphase involving (MM-X) for the K result, only when

X is exactly 1/2 Jupiter, when using the same inferencing

technique as was used to infer MM in the first place, as

described above under 'Verifying a Mass of MM For The Sun'.

A slightly more accurate inferencing for MM itself was thus

made possible. In order for Equations E-1 to E-4 to yield

results definitely equal to K, the value of MM is adjusted

to the greater accuracy of (1.99099305 x 10 to the 33 grms).

It made the explorations involving solar mass total aggregates

Mt and Mtx not important. This avenue of reasoning was dropped,

and is mentioned above only to reveal how a quantal value of

ñ 1/2 Jupiter as displayed in Equations E-1 to E-4 came to be

an issue.

ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ¿

ÛÄ´ OTHER MASS AGGREGATE STATES ³

ÀÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÙ

In applying such interphasing logic to the solar system, the

study is narrowed to include only mass quantities which currently

exist; these being the Sun, and certain planets.

In the case of a bifurcated Jupiter mass, a theoretical attribute

is identified. This is where mass aggregates and resulting

gravitational relativistic effects can phase in and out (in a

continuation of certain coherent effects), through a range of

mass densities confined within a single constant radius.

A form of harmonic interphasing through a realm of masses

is definitely sensed.

In gist; a higher relativistic effect from an enhanced mass

aggregate is applied to a lower mass aggregate, such that

the resulting augmentation is lower or different than would

be expected for either the originating enhanced mass, or the

reduced mass.

This type of reasoning should only be speculative, except that

the mass augmentation which actually results when +1/2 Jupiter

and -1/2 Jupiter are involved, is already a recognized quantity,

this being mass term K, already independently seen for a mass

aggregate which is other than an effect that is expected

straight across for an enhanced or diminished sum of the Sun

plus or minus 1/2 Jupiter.

ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ¿

ÛÄ´ OTHER MASS EFFECT COHERENCIES ³

ÀÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÙ

Other mass effect coherencies seem to occur. One involves the

mass of the Earth (Me), which, when subtracted from mass MM,

yields an aggregate mass whose relativistic effect factor

(herein called Ee), which when applied to mass aggregate MM,

results in a discrete mass split which is precisely equal to

the mass of the Earth Me minus K.

This formula (as exemplified in EQ H and I below), might at first

seem tautological until further studies show that a relativistic

factor Ex for any mass aggregate (M + X) or (M - X) does not phase

in perfectly to an exact result for (MM - (MM x Ex)) = X - Kx for

any value assumed for mass X. Only certain precise values of ñ X

are seemingly phased in a coherency. For instance when:

1. X equals the mass of Earth

2. X equals the mass of Venus

3. X equals ñ 1/2 the mass of Jupiter

The case of X being equal to ñ 1/2 the mass of Jupiter

has already been demonstrated in Equations E-1 to E-4.

When X equals the mass of Venus, then a mass split resulting

in a discrete relativistic augmentation, also incorporates the

mass of Mars. This is shown further below in Equations Q to S.

A formal description for the interphasing state involving

the Earth is as follows:

EQUATION H

ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ

³ 2G (MM-Me) Where (MM-Me) is mass MM

Ee = ³ 1 Ä ÄÄÄÄÄÄÄÄÄ minus the mass of the Earth Me.

\³ Cý R MM is the mass of the Sun

EQUATION I

MM - ((MM + Me) x Ee) = Me - K Where Me is the mass of Earth,

and K is (Venus - Mars)

This formula (as exemplified in EQ I), might at first seem

exciting until it is recognized that it is rather a sort of

strange tautology.

That is, further exploration shows that a relativistic factor Ex

for any low mass aggregates in the range available for this solar

system, for instance (MM + X) or (MM - X), phases in to a seeming

predictable result where:

when Ex is determined as the relativistic effect factor

for mass MM-X (for instance using EQ H), then:

MM - ((MM+X) x Ex) = Xx = (X - K)

where Xx = (X - K) results for any

reasonable value assumed for mass X.

But for higher masses (much beyond MM), the equality actually

breaks down, demonstrating that there was no tautological

equality to begin with.

A formal description for showing the breakdown is:

EQUATION J

ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ

³ 2G (M-X) Where (M-X) is mass M minus

Ex = ³ 1 Ä ÄÄÄÄÄÄÄ any other mass X, and radius

\³ Cý Rx Rx is the same for any values

of (M-X), then:

EQUATION K

M - ((M) x Ex) = Kx And:

EQUATION L

M - ((M+X) x Ex) = Xx And:

EQUATION M

Xx - X = Kx Where:

Xx + Kx = X And:

Xx = X - Kx Where X is the original arbitrary

mass that was subtracted from M in

EQ J, and was then added to M in

EQ L

-- Continued in RELATIVE.2 --

Item B if you are using the HELP MENU

ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ¿

ÛÄ´ STRANGENESS IN A SEEMING TAUTOLOGY ³

ÀÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÙ

This section covers general ground and seems to ramble, rather

than to leap straight ahead from one event to a next. Read if

interested. This section concludes with information of importance

to the following section 'A Coherent Phase in This Solar System'.

The discussion resumes in earnest in PART 2 a few pages further below.

Do not be fooled by the implied authority of Equations J to M.

Equations J to M are not a perfect tautology. Even though they are

presented above as such. Instead, they are strange, in that their

results can actually vary in several ways, under the microscope

of vigorous scrutiny.

For instance terms X and Xx begin to noticeably separate for larger

values of M, for instance when M begins to assume a mass approaching

that of a black hole having radius Rx. In these higher mass regions,

the value of Kx can begin to rapidly escalate over and above any

amounts of increase given to mass M.

In other words Kx begins to itself take on high value

(pursuant to gravitational relativistic augmentation),

but always is less than the value of M.

The value of Kx is in fact somewhat periodic in two ways.

(Kx is said to be the mass augmentation due to the gravitational

relativistic effect of mass M acting on itself, ie. on mass M).

Firstly: the digital value of Kx is dependent almost entirely upon

the digital value of M. For example a Kx digital value ranging

from (4.21 x 10 to the power 27) up to (4.79 x 10 to the power 37)

is found for mass M values ranged from (1.989 x 10 to the power 33)

up to (1.989 x 10 to the power 38), when the confinement radius

Rx is held constant at (6.96256 x 10 to 10 cms), through greater

and greater magnitudes in the concentrations of mass M.

Secondly: it will be seen that for every increase of M by a factor

of 10, the value of Kx increases by a power of 100 (actually just

slightly more than 100), until the Value of Kx vrs M closes suddenly

in a very rapid crunch toward unity as the value of M approaches a

last iota in becoming the mass of a black hole. The power of just

above 100 in the increases of Kx, is due to the modest increase in

the digital value of Kx identified in the previous paragraph.

At the junction at which the confinement radius Rx becomes the

same as an event horizon of a black hole, Then the augmentation Kx

vanishes from the picture, because when M is the mass of a black

hole having a radius Rx, then Kx can no longer be calculated.

Related events can be closely watched for permutations by

keeping certain parameters constant. For instance Rx is the

same constant radius, in Equations O to O-4 which follow.

Then, given the basic equation:

EQUATION O

ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ

³ 2G (Mh) Where Ex is the relativistic

Ex = ³ 1 Ä ÄÄÄÄÄÄÄ factor of a high mass Mh

\³ Cý Rx having a confinement radius

Rx, and:

EQUATION O-1

M - ((Mh) x Ex) = Kx

But when Mbh is the mass of a black hole of radius Rx, then:

EQUATION O-2

2G (Mbh)

ÄÄÄÄÄÄÄÄ = 1 And therefore:

Cý Rx

EQUATION O-3

ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ

³ 2G (Mbh)

Ex = ³ 1 Ä ÄÄÄÄÄÄÄ

\³ Cý Rx Is no longer valid, since:

EQUATION O-4

ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ

Ex = ³ 1 Ä 1 The square root of 1 - 1 = 0

\³ is impossible.

However, in looking back to Equations J through M, where terms X

and Xx are featured, certain important distinctions can be observed

to occur for high masses M that are not yet a black hole. For instance

if variable amounts of mass M ñ X are confined within the same radius Rx

so as to provide a consistent point of view via a constant Rx, then in

particular:

ITEM A. If X is closer in value to the higher value M, (for

instance if X is 1/100th the value of M), then Xx of

EQ L can be substantially lower than X, and Xx can

also be substantially lower than Kx.

ITEM B. If X is substantially lower than the higher value

M, (for instance if X is 1/100000th the value of M),

then Xx can increase substantially above X. In fact Xx

approaches the value of Kx for the mass M (as will be

found when in using Equation K, above).

These above mentioned 'drifts' are inherent in the gravitational

relativistic arena. It was possible to see them only because

for the instances of ITEMS A and B above, the value of radius

Rx was held constant, so that the consequences of different

masses (M-X) and (M+X) through different values of M and X can

be followed in the varying results.

The above 'drifts' have been discussed here at length because

if their insights are not known, certain confusions may seem

to occur in doing high mass calculation in the denser levels

up to that of a black hole, vrs doing low mass calculations

involving values of mass M that are on par with the mass

aggregates available in this solar system.

In such low mass calculations, conditions similar to ITEM A

above are found. Except in low mass calculations for this solar

system, the value of Xx can be rather close to the value of Kx,

and Xx + Kx can be rather close to the value of X.

In fact in mass regions on par with this solar system, any difference

between X and (Xx + Kx) of Equation M above, in which the Earth mass Me

is X, is hardly discernible, so indiscernible that X and (Xx + Kx) seem

the same, (as indicated in EQ I above, where Xx would be Me - K). But X

and (Xx + Kx) are not truly identical.

Yet there are certain precise values phased in a certainty

for all values of M right up to that of a black hole.

For instance there is a condition in which Xx and Kx can

both turn out to be identical. This is as follows:

EQUATION O-5.

ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ

³ 2G (Mass)

Ex = ³ 1 Ä ÄÄÄÄÄÄÄ

\³ Cý Rx And:

Mass - ((Mass) x Ex) = Kx Then:

EQUATION O-6. (A zero result occurs in using the reciprocal 1/Ex)

Mass - ((Mass - Kx) x (1/Ex)) = 0 This is true for both

low mass and high mass

calculations

ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ¿

ÛÄ´ A COHERENT PHASE IN THIS SOLAR SYSTEM ³

ÀÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÙ

In this solar system there is one precise value of X

which seems phased in a genuine coherent certainty, when

viewed through the scope of Equations J through L.

Specifically, when the mass aggregate equals MM, and X

equals the mass of Venus (Mv), the strange tautology of

Equations J through L become a seeming genuine equality,

wherein the resulting X = (Xx + Kx) mass split in relativistic

augmentations, also incorporates the mass of Mars. Specifically,

Xx is the mass of Mars.

The formal description for this state is as follows:

EQUATION P

ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ

³ 2G (MM-Mv) Where (MM-Mv) is mass MM

Ev = ³ 1 Ä ÄÄÄÄÄÄÄÄÄ minus the mass of Venus Mv.

\³ Cý R MM is the mass of the Sun,

and R is the exiting radius

of the Sun.

EQUATION Q (Determines a value K)

ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ

³ 2G (MM)

Ek = ³ 1 Ä ÄÄÄÄÄÄÄ

\³ Cý R This is the same as EQ E,

so that:

MM - ((MM) x Ek) = K Such that:

EQUATION R

MM - ((MM+Mv) x Ev) = Ma Where Ev is the effect

factor of EQ P above,

and Ma is the mass of Mars,

so that:

EQUATION S

Mv - Ma = K In which also K + Ma = Mv

With Equations P to S there is established a formal second

(albeit obvious) identification for the previously noted

condition; that the relativistic augmentation (K) of the inferred

mass of the Sun MM is identical to the mass difference between

planets Venus and Mars.

ÉÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍ»

ÉÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍ»

º ±±±±±±±±±±±±±±±±±±±±±±±±±±±±± PART 2 ±±±±±±±±±±±±±±±±±±±±±±±±±±±±±± º

º ±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±± º

º ±±±±±±±±± GRAVITATIONAL AND SPECIAL RELATIVITY THEORY ±±±±±±±±± º

ÈÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍ¼

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ÉÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍ»

º ±±±±±±±±±±±±±±± GENERAL INTRODUCTION for part 2 ±±±±±±±±±±±±±±± º

ÈÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍ¼

ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ¿

ÛÄ´ A COMPARISON BETWEEN GRAVITATIONAL AND SPECIAL RELATIVITY ³

ÀÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÙ

It is traditionally thought that gravitational relativistic

effects differ in kind from special relativistic effects, in that

in special relativity, an approaching equality between a velocity

and the speed of light is theorized to lead to an escalating mass

increase which continues toward infinity as the velocity closes in

on the speed of light. In this view of special relativity, there is

only the one ultimate source of the effect, this being the varying

velocity. The velocity of light can never be reached in an onrush

of mobile matter, due to the infinity in mass which would result.

In gravitational relativity, at least two source parameters are

variable. Specifically, there is a given mass and a given radius,

each of which can change independently, and so can ultimately

combine in combinations where various equalities exist. For

instance a radius of a mass can vary depending on ambient mass

density, for example between a gas such as hydrogen, and a solid

such as gold.

But for any mass of sufficient size, gravitational collapse

can theoretically lead to a black hole.

1. In a mathematical convenience, more mass added to the same

radius can produce the collapse. In this sense there are

equalities involved. The equalities are when the mass's

existing radius is normal and when the same radius is the

boundary of a mass's black hole event horizon.

1A. A sort of double flip flop occurs at this boundary. If

extended beyond this equality, any increase in mass in the

black hole results in an increase in radius (rather than

decrease in radius). But conversely a decrease in a black

hole's radius results from a decrease in mass, ie., if the

mass does not decrease the radius does not decrease).

2. This stable equality can exist because both the input terms

for mass, and confining radius, are variable. For instance a

low density gas cloud can have a high mass but large radius,

resulting in very weak relativistic consequences, whereas

the same mass concentrated in a very small area can have

substantial relativistic consequences.

3. Further, mass can be removed or added within the same radius,

dramatically changing the aggregate's relativistic components.

Conversely the same mass can be drawn closer together or spun

farther apart, thus changing the radius, thus again dramatically

effecting the aggregate's relativistic components.

4. A similar though not identical property can occur in less

dynamic realms, for instance in mass aggregates which are the

size of the Sun. In this case extra mass in the same radius

(the Sun's radius) can for instance produce a relativistic

factor E which when imaginarily applied to another mass

aggregate, can produce a Kx augmentation which is otherwise

gained from a different mass aggregate.

In the case of the solar system, the Sun's radius and resident mass

aggregate are not the total quantities involved in the aggregate's

relativistic components. Planet masses in the bodies of Jupiter,

Venus, and Mars, are also involved. It means that the relativistic

components include something which is manifesting in an external-

ization of the effect, occurring at long distances from the field

which is generating the relativistic effect. What these external-

izing influences are is not immediately known. Nonetheless the

evidence of their existence is unmistakable.

The evidence in fact does infer that a mass augmentation is

present in a field of gravity. In truth, the evidence does not

immediately prove whether the mass augmentation is a relativistic

increase, or decrease, on an original mass. The equations herein

shown have assumed that the augmentation is an increase.

The evidence on its own raises questions which are not answered

at all. For instance, how come the particular planet orbits for

Jupiter, Venus, Mars, and also the Earth? And what linkages

might angular momentum and/or planetary spin have, if any? Etc.

The gist of Part 2 is not in the speculation, but in certain

understandable exactitudes which do occur. These exactitudes

are particularly easy to see in high mass ranges closing in

right on black hole masses, and so can be extrapolated back to

less easily seen low mass effects in gravitational relativity.

What is more important, is that a direct tie-in between

gravitational and special relativity becomes obvious.

ÉÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍ»

º ±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±± º

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³ A UNISON BETWEEN GRAVITATIONAL AND SPECIAL RELATIVITY ³

ÈÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍ¼

There is a direct connection between the effects of gravitational

relativity, and special relativity, to the extent that; given a

gravitational mass and its confining radius (so that its mass

augmentation effect on original gravitational mass is known),

the same quantity in mass augmentation can be determined for

special relativity, according to the mass increase gained by

the same original mass if traveling at some portion of the

speed of light.

Specifically, the gravitational relativity equation provides

a term which allows that the exact velocity of the mass if

moving can be perfectly known, in terms of special relativity.

The predictability between the two relativities is, as said,

exact. That is, the gravitational relativity effect factor from

gravity is related to the proportion by which the speed of light

is reduced, so that the same mass travelling at the stated velocity

(predictably reduced below the speed of light) will experience a

special relativity effect on its mass identical to the effect on

its mass experienced by gravitational relativity.

(This assumes that gravitational relativity indeed has

an effect on a gravitational mass, such that there is for

instance an augmentive relativistic gain in the mass itself

when the mass is standing still. This mass gain by gravitational

relativity, and by the instantly predicted velocity in special

relativity, are identical amounts of gain).

ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ¿

³ THE GRAVITY - SPECIAL RELATIVITY CONNECTION IN DETAIL ³

ÀÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÙ

The connection between gravitational and special relativity is

not quite so naive as first suggested above, when it comes to

actually working out a connection between a given gravitational

mass and its special relativistic equivalent.

To begin with, a certain parameter must be determined for the

gravitational effect. To wit, the radius involved is a control

parameter. Given the radius, the amount of mass needed to have

a black hole confined in the radius as an event horizon, is

determined. (A black hole silent partner for the given mass,

so to speak). The ratio of the partner black hole mass, over

the mass in question, supplies an essential term.

Let's call this term Nx. Let's call the black hole silent

partner mass equivalent Mbh. And let's call the original

given mass M. The ratio of Mbh divided by M, is our ratio Nx.

The speed of light C is divided by the square root of Nx, to

give a velocity that is less than C. Lets call this velocity

Vx. If mass M is travelling at velocity (Vx), then mass M will

experience the same gain in rest mass enhancement via special

relativity, as is otherwise gained when the mass is standing

still but is augmented by its own gravitational relativity.

In a further comment, in the scenes of gravitational relativity,

it turns out that ratio Nx (gained as the ratio of a given mass

divided into its black hole silent partner mass) is a different

view of the relativistic effect factor Ex, which is gained by

calculating the given mass's gravitational relativistic effect.

This puzzling statement has an easy explanation.

For a fact, when:

EQUATION T

Mbh

ÄÄÄÄÄ = Nx Then relativistic effect Ex is:

EQUATION T-1

Gravitational relativistic

ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ effect Ex is calculated from

³ 1 ratio (Mbh/M), when the mass

Ex = ³ 1 Ä ÄÄÄÄÄÄÄ of black hole silent partner

\³ Nx Mbh is calculated from the

radius of M, by:

EQUATION T-2

Cý R

Mbh = ÄÄÄÄÄÄÄÄÄ As in:

EQUATION T-3

ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ

³ 1

Ex = ³ 1 Ä ÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ

³ ÚÄ Ä¿

³ ³ CýR ³

³ ³ ÄÄÄ ³

³ ³ 2 G ³

³ ³ ÄÄÄÄÄÄÄÄÄ ³

³ ³ M ³

\³ ÀÄ ÄÙ

ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ¿

ÛÄ´ EXAMPLES OF THE GRAVITY - SPECIAL RELATIVITY CONNECTION ³

ÀÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÙ

In Equations U through X which follow:

(Eg) is the effect (in gravity) for

a mass M in gravitational relativity

(Es) is the effect (in special relativity) for mass M in

motion at a significant velocity in special relativity

(Mbh) is a black hole mass from a given radius Rx, as

calculated in EQ V below or EQ T-2 above. Mbh

is the silent partner mass for any given mass M

(Nx) is the ratio of the black hole mass Mbh,

divided by the given mass M

EQUATION U

ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ

³ 2G M

Eg = ³ 1 Ä ÄÄÄÄÄ

\³ Cý R

EQUATION U-1

ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ

³ Vý

Es = ³ 1 Ä ÄÄ

\³ Cý

EQUATION U-2 Gravity relativity Bare bone version

ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ

³ 1 ³ 1

Eg = ³ 1 Ä ÄÄÄÄÄÄÄ = ³ 1 Ä ÄÄÄÄÄ

³ Mbh \³ Nx

³ ÄÄÄ

\³ M

EQUATION U-3 Special relativity Bare bone version

ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ

³ ÚÄ Ä¿ý ³ 1

Es = ³ ³ C ³ = ³ 1 Ä ÄÄÄÄÄÄÄ

³ 1 Ä ³ ÄÄÄÄÄÄÄÄ ³ \³ Nx

³ ³ ÚÄÄÄÄ ³

³ ³ \³ Nx ³

³ ÀÄ ÄÙ

³ ÄÄÄÄÄÄÄÄÄÄÄÄÄÄ

\³ Cý

As seen in Equations U-2 and U-3, a fundamental statement for both

special and gravitational relativity are indistinguishable when given

in a Bare bones manner containing term 1/Nx. This is not false, but

misleading, in that term Nx is found from the ratio Mbx/M of EQ U-2.

In the Bare bones version of EQ U-3, term Nx cannot reveal what the

velocity that mass M is moving at in order to have a relativistic

effect factor Es in EQ U-3 that is equal to Eg in EQ U-2.

This is by no means a critical shortcoming. Without knowing term Nx,

the velocity of a moving M can nevertheless be determined directly,

if a substitution is made for term Nx in EQ U-3. This substitution

cannot be easily shown in the full equation in a typed manuscript

such as this. However, the factor to be substituted in EQ U-3 is

easily shown. It is Term 1 shown below in EQ U-4. Term 2 of EQ U-4

is taken straight from EQ U-3.

EQUATION U-4 Term 1 Term 2 Term 3

an exact

ÚÄ Ä¿ ÚÄ Ä¿ velocity V

³ C ³ ³ C ³

³ ÄÄÄÄÄÄÄÄÄÄ ³ ³ ÄÄÄÄÄÄÄÄ ³ V

Substitute ³ ÚÄÄÄÄÄ ³ For ³ ÚÄÄÄÄ ³ = ÄÄÄ

³ ³ Mbh ³ ³ \³ Nx ³ C

³ ³ ÄÄÄ ³ ÀÄ ÄÙ

³ \³ M ³ ÄÄÄÄÄÄÄÄÄÄÄÄÄÄ

ÀÄ ÄÙ C

ÄÄÄÄÄÄÄÄÄÄÄÄÄÄ

Term 1 of EQ U-4 gives the exact velocity V (as used in EQ X

below), at which mass M must be moving, in order to have a special

relativistic effect (Es) identical to a gravitational relativistic

effect (Eg).

In this connective equality between relativities, identical augmenting

effects on the moving rest mass (Mass)(1/Es) of special relativity, and

aggregate mass (Mass)(1/Eg) of gravitational relativity, are gained for

an original mass when moving (special relativity) and when standing still

(gravitational relativity).

Inter-combinant mathematics between the two modes of relativity

have so far been shown strictly for the effect of one mode (gravity)

on the other mode (motion). There are other potentials. For example,

would the motion's effect increment upon the gravity effect. If this

is so, than Equations T to X need to be expanded to include modifying

terms giving the velocity needed when other effects on mass are

considered. Such potential views in the mathematics are not herein

pursued.

ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ¿

ÛÄ´ A Support equation for gravitational relativity follows next ³

ÀÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÙ

EQUATION V

(Mbh) can be determined from the gravitational

relativistic effect (Eg). Given a calculated

effect (Eg), as determined in EQ U above, then:

ÚÄÄ ÄÄÄ¿

³ 1 ³

Mbh = M x ³ ÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ ³

³ (1 Ä (Eg)ý) ³

³ ³

ÀÄÄ ÄÄÙ

EQUATION V-1 However:

ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ

1 ³ 1

ÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ also equals ³ 1 Ä ÄÄÄÄÄ

(1 Ä (Eg)ý) \³ Nx

EQUATION V-2 So that EQ V simplifies to:

M x Mbh = M x Nx So that: Nx = Mbh

ÄÄÄ ÄÄÄ

M M

(The result of Equations V is obvious for very high masses,

for instance for masses approaching that of a black hole. However,

in lower mass calculations (such as for gravitational effects for

masses found in the solar system), there is an intrinsic truncation

eroding the accuracy, leading to imprecise seeming solutions for

Equations V to V-2).

The simplification of EQ V into EQ V-2 has been shown, because

soon we want to watch very closely certain effects involving Nx,

when Equations T through U-4 are used to explore particular aspects

of both gravity and special relativity modes in masses which work

backwards starting at the limit of black hole masses.

As seen in Equations V to V-2, term Nx can be made to have an

overly complex look (EQ T-3), or overly simplistic look (EQ V-2).

The general confusing looks vanish when certain exact values are

attached to ratio Nx.

In an exploration which follows after the next section, a

constant number already well known as the Golden Harmonic

Ratio, becomes apparent as a term of fundamental importance

when things are looked at through a certain point of view.

ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ¿

ÛÄ´ Summary equations for the two modes of relativity follow next ³

ÀÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÙ

EQUATION W Basic Gravitational relativity equation

ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ

³ 2G (Mass) EQ W is the

Eg = ³ 1 Ä ÄÄÄÄÄÄÄÄ same as EQ C further above

\³ Cý R

(Gravitational effect Eg is known to slow time in the

vicinity of a (Mass) which is generating effect Eg).

EQUATION W-1

(Mass) - ((Mass) x Eg) = Kx Where Kx is an augmentation

of (Mass) by gravitational

relativistic effect Eg

EQUATION X Basic special relativity equation

ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ

³ Vý Many text books cite

Es = ³ 1 Ä ÄÄÄÄÄ a greek letter for effect

\³ Cý Es, and for ratio Vý/Cý

Effect 1/Es increases the mass. Es decreases the

radius, and slows time for an entity moving at

velocity V relative to the speed of light C

EQUATION X-1 Basic black hole mass calculation

(Mbh) of EQ X-1 is the mass of a black hole mass as gained

when radius R is the event horizon (Schwarzschild radius)

of the black hole, whose mass is calculated as:

Cý R Finding the mass (Mbh) needed for

Mbh = ÄÄÄÄÄÄÄÄÄÄÄÄ a black hole whose Schwarzschild

2G radius is given as R. EQ X-1 is

the same as EQ 5 of APPENDIX B below

ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ¿

³ INTERPRETATIONS ³

ÀÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÙ

It is worth noting that Equations T through X are true for an

existing mass. Specifically, there is a given (existing) gravitational

mass M which has an augmentation (Kx) included. The augmentation (Kx)

is easily found in its exact amount (by Equation W-1). How fast does

the existing (Mass) have to be in motion to experience the same

degree of augmentation as Kx via special relativity? This simple

question has been addressed by Equations T to U-4.

However otherwise the equations of gravitational relativity theory

lead to this, (which is the same as saying the energy equivalent

in forward escaping light is pulled backward (or bent) by powerful

gravity at the same rate of acceleration as the forward velocity C

of the light), from Term 1 of Equation U-4 above it is clear that

at the mass limit of a black hole, the ratio 1/Nx of the black hole

mass Mbh to aggregate mass M, is equal to 1.

And so in Term 2 of Equation U-4 the ratio of the speed of light C

divided by the root of Nx (as in C/ûNx) will also be equal to 1.

Special relativistics then will no longer have effect, as in:

EQUATION X-2 Term 1 Term 2 Term 3

exact

ÚÄ Ä¿ ÚÄ Ä¿ velocity

³ C ³ ³ C ³

³ ÄÄÄÄÄÄÄÄÄÄ ³ ³ ÄÄÄÄÄÄÄÄ ³ C

Substitute ³ ÚÄÄÄÄÄ ³ For ³ ÚÄÄÄÄ ³ = ÄÄÄ = 1

³ ³ Mbh ³ ³ \³ 1 ³ C

³ ³ ÄÄÄ ³ ÀÄ ÄÙ

³ \³ Mbh ³ ÄÄÄÄÄÄÄÄÄÄÄÄÄÄ

ÀÄ ÄÙ C

ÄÄÄÄÄÄÄÄÄÄÄÄÄÄ

However, the situation here is actually more deceptive.

For instance how can the rest mass of a relativistically moving mass

aggregate increase toward infinity as its velocity ratio V/C from

(C/Nx divided by C in EQ U-5) approaches 1, to keep in step with a

stationary gravitational mass aggregate approaching its black hole

mass limit Mbh as defined in EQ X-1 above, according to the aggregate

mass's radius R ?

This is no question to be sneezed at.

It implies an idealized stable situation, where A = B. That is,

the ratio of Mbh/M as A, equals the ratio of velocities V/C as B,

such that masses approaching infinity should be possible, as ratio

Mbh/M approaches 1.

However, the wrinkle is that mass M can never exceed mass

Mbh. Not via any mass increases gained by higher and higher

gravitational relativistic effects on mass M. And therefore

extreme mass enhancements in special relativity as velocity V

over C approaches 1, are not possible, if velocity V is gained

as an Nx factor directly from the ratio of Mbh/M.

ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ¿

³ THE CONUNDRUM ³

ÀÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÙ

In the real world, the situation is in no way idealized. For

instance masses approaching infinity should begin to appear, as

the equivalent mass aggregate M begins to home in on the final

iotas before becoming a black hole, if the A = B relationship

is in all ways exact.

But, the contingency of a mass said to approach infinity in the

special relativity side is not proof that mass infinities can be

achieved by M plus mass augmentation Kx at higher and higher

plateaus of gravitational relativistic mass effect.

How might this conundrum be explored as an intellectual exercise?

If the confining radius of a mass aggregate itself is being

relativistically contracted by effects of the mass's gravity,

then the real world situation is very different than the idealized

version. For instance, increasingly less mass is required to

aggregate in a diminishing radius to form a black hole.

It would now seem that the mass aggregate could bleed away toward

nothing as the gravity increases in tune with a relativistically

diminishing (contracted) confining radius.

What would prevent this is two things.

First, the mass aggregate increases in relativistic proportion

to the decrease in radius. Since both terms are found in the

same equation, as in:

EQUATION Y

ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ

³ 2G (Mass)(1/Eg) Mass is increased by 1/Eg,

Eg = ³ 1 Ä ÄÄÄÄÄÄÄÄÄÄÄÄÄÄ Radius is decreased by Eg

\³ Cý R(Eg)

which results in the ratio portion (Mass)(1/Eg) / R(Eg)

being increased by the square of the reciprocal of Eg.

In a second prevention, if 2G (twice the gravitational constant) is

decreased by Eg while the square of the speed of light is increased

by 1/Eg, as in Equation Y-1:

EQUATION Y-1

ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ

³ 2G(Eg) (Mass) Gravity is decreased by Eg,

Eg = ³ 1 Ä ÄÄÄÄÄÄÄÄÄÄÄÄ Cý is increased by 1/Eg

\³ Cý(1/Eg) R

then the ratio portion (2G)(Eg) / Cý(1/Eg)

is decreased by the square of Eg.

In which case all relativistic augmentations found in Equations

Y and Y-1 internally cancel each other, as in Equation Y-2:

EQUATION Y-2

ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ

³ 2G(Eg) (Mass)(1/Eg)

Eg = ³ 1 Ä ÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ

\³ Cý(1/Eg) R(Eg)

and the net internal effect is again simply

2G (Mass) / CýR, as in Equation W above.

But this type of intellectual exercise does not solve

the above posed conundrum. The conundrum's answer is

introduced immediately below.

ÉÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍ»

ÉÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍ»

º THE GOLDEN HARMONIC RATIO IN RELATIVITY THEORY. º

º A CRITICAL LIMIT IN THE FOUNDATION OF GRAVITATIONAL RELATIVITY º

º ±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±± º

ÈÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍ¼

ÈÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍ¼

ÉÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍ»

º ±±±±±±±±±±±±±±± GENERAL INTRODUCTION for part 3 ±±±±±±±±±±±±±±± º

ÈÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍ¼

TABLE 4

ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ¿

³ KEY TERMS ³

³ ³

³ Mbh Mass of a black hole, having radius Rbh ³

³ ³

³ Mo An original mass (before mass augmentation ³

³ due to gravitational relativity) ³

³ ³

³ Ko Mass augmented upon mass Mo due to ³

³ gravitational relativity ³

³ ³

³ M An existing mass, which includes: Mo + Ko ³

³ ³

³ Mc A Critical Mass Limit, where Mc is an Mo ³

³ which is less than Mbh by precisely the ³

³ Golden Harmonic Ratio ³

³ ³

³ Rbh An event horizon radius for black hole Mbh, ³

³ and for other masses such as Mo, M, and Mc ³

³ which are evaluated with the same Rbh radius ³

³ but are not yet at the black hole mass limit. ³

ÀÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÙ

TABLE 4 CONTINUED

ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ¿

³ ³

³ 1/Ng Ratio Mbh/Mc = 1/Ng when Mc = Mo, as when: ³

³ Mbh/Mo = 1/Nx ³

³ ³

ÃÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ´

³ ³

³ GH Golden Harmonic Ratio 1.61803399, also called ³

³ Golden Ratio, having a digital value equal ³

³ to 1/2 the square root of 5, plus .5, as in: ³

³ ³

³ 1.1603398875 + .5 = 1.61803398875 ³

³ ³

ÃÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ´

³ ³

³ Vc A critical limit velocity in special ³

³ relativity, where the ratio C/Vc is equal ³

³ to the square root of the Golden Harmonic ³

³ ratio GH = 1.61803398875 ³

³ ³

ÀÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÙ

ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ¿

ÛÄ´ FUNCTIONAL INTERPHASE BETWEEN ³

³ GRAVITATIONAL AND SPECIAL RELATIVITY ³

ÀÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÙ

The thing about speculations is that many words can be used

to discuss a point which has no convincing answer. Whereas

a simple equation can state it all for a self evident truth.

However, the simple equation may be obvious to only

the soul who wrote it. For others, the simple equation

may need elaborate support such as explanation and

interpretation.

The following sets forth a question which begs an answer.

The answer being self evident is then quickly stated. But

the stating is accompanied by explanation and interpretation.

ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ¿

³ QUESTION ³

ÀÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÙ

One important question which comes immediately to mind (already

asked further above in 'The Conundrum') is how can the rest mass of

a relativistically moving mass aggregate increase toward infinity as

its velocity ratio V/C from EQ U-4 approaches 1, to keep in step with

a stationary gravitational mass aggregate which is approaching its

black hole mass limit?

ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ¿

³ ANSWER ³

ÀÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÙ

The answer is that a gravitational mass can only increase to a

certain limit, reached before the black hole mass. At this reached

limit, the increase in gravitational relativistic augmentation on

the mass, raises the overall mass in a final bump to the black hole

limit. The final range closing in on the black hole limit is bypassed

by the bump.

ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ¿

³ INTERPRETATION ³

ÀÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÙ

The problem is that the conundrum is only apparent and not real;

that: as a mass aggregate rapidly approaches its black hole limit,

the ensuing special relativity mass increase counterpart will rapidly

begin to climb toward infinity, and such an infinite mass is not

possible in the sense of real events.

For instance, assuming the conundrum is real, in the following

thoughts let Rbh be a given radius. Let's say a mass aggregate M

of radius Rbh is at 99% of the Mbh black hole mass limit for radius

Rbh. The gravitational relativistic effect (Eg) is roughly about

Eg = .09950, which translates into a special relativistic mass

enhancement effect of roughly (10.049 x M) on the mass travelling

at roughly (root 99%) of the speed of light).

Effect Es = 10.049 is reciprocally equivalent to effect Eg = .09950.

The problem here is that the special relativistic enhancement

on the mass will be roughly 10 times the black hole limit for

the mass in question.

The problem here is also that if mass M is increased by a

gravitational relativistic effect Eg of 10.049, then the

resulting augmented mass will exceed its own black hole limit

by a factor of roughly 10 times.

How, then, does an aggregate mass M of radius Rbh increase

only to a black hole mass Mbh of radius Rbh, in keeping with

a committed tie-in to special relativity, without the moving

mass M impossibly increasing to infinity as the aggregate

mass M closes in on Mbh, and without the stationary mass

increasing wildly above its own black hole limit due to

its own gravitational relativity?

The question is a thought balloon which seems to go in

several directions. But actually has a unique answer.

ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ¿

³ EXPLANATION ³

ÀÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÙ

In a fundamental point of view, events are explored from

the outlook of an original mass, which is augmented to

become an apparent mass.

Specifically, let an original mass Mo (before mass augmentation) be

used in an Mbh/Mo ratio, to give ratio term 1/Ng (instead of 1/Nx).

And let velocity (C divided by the root of Ng) be the velocity the

original mass is travelling in special relativity, to have the same

enhancing effect on Mo as would be found when the gravitational

relativity effect augments mass Mo.

ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ¿

³ THE GOLDEN HARMONIC RATIO - A CRITICAL LIMIT ³

ÀÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÙ

When ratio Ng is equal to the Golden Harmonic Ratio,

then several striking things happen. The Golden Harmonic

Ratio is 1.6180339. It is typically given as a number quantity

from (1/2 of root 5, plus .5).

Let the Golden Harmonic Ratio be GH. And so let Ng = GH.

ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ¿

³ THE CRITICAL LIMIT in gravitational relativity

ÀÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÙ

When Mbh/Mo is GH, a vital event occurs. The gravitational

effect Eg precisely turns out to be 1/GH (the reciprocal of

the Golden Harmonic Ratio).

And so mass (Mo x 1/Eg) = (Mo x 1/GH), which

precisely turns out to be mass Mbh. Effectively,

mass Mo leaps uphill to become mass Mbh in one

final single bump.

This is a box, where one thing specifically yields another. In

interpretation, a mass augmentation (Eg) on an original mass Mo,

raises the quantity of the original mass Mo to that of a black

hole mass Mbh, when ratio Ng = Mbh/Mo is precisely the Golden

Harmonic ratio GH.

In which case, in special relativity, when the original mass

Mo is moving at a velocity V which is root GH less than the

speed of light, the special relativistic effect Es increases

mass Mo to mass Mbh in a final single bump. In which case mass

Mbh becomes a black hole and disappears from sight, relative

to a stationary observer watching the mass move.

There is a locked in equality here. Explicitly, Mbh/GH is a

critical limit preceding mass Mbh, at which an original mass

Mo is raised to the black hole limit Mbh by the mass effect

of its own gravitational relativity. Let Mc be the critical

mass limit.

Effectively, it establishes that if gravitational relativity

includes a mass augmentation effect, the original mass cannot

exceed the critical mass limit Mc. And so the original mass can

never be the same as a black hole mass, or even a fraction less

than a black hole mass, since the black hole mass includes an

original mass Mo at the critical mass limit Mc, raised to Mbh

through a quanta bump equal to the Golden Ratio GH.

In this locked in state, Mbh - Mc = Ko, where Ko is the

actual mass augmentation, the same as is otherwise said to

be Kx, except in this instance, Ko is fundamentally related

to the Golden Ratio GH. In exactitude, Ko = Mbh - (Mbh/GH).

It means that when the critical mass limit Mc is reached prior

to a black hole, the original mass Mo is augmented by effect 1/Eg

to become a black hole equivalent, and no more mass can confine

in the same radius Rbh. (More original mass added would serve to

increase the confining radius to greater than Rbh).

As already said, the Mc critical mass limit

(for radius Rbh) is simply (Mbh/GH), where

(GH) is the Golden Harmonic Ratio.

ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ¿

³ THE CRITICAL LIMIT in special relativity

ÀÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÙ

It also means that in special relativity, when the critical

mass Mc is a rest mass in motion at a velocity equal to C

divided by the square root of GH, the original rest mass

Mc expands via 1/Es in a single bump to a mass value where

it also becomes a synonymous black hole of mass Mbh.

In consequence there never is a condition where the original

mass Mo in special relativity expands toward infinity as

mass Mo closes in on mass Mbh in gravitational relativity,

because the convergence in gravitational relativity for an

original mass Mo closes off completely at the critical mass

limit Mc, when Mc is less than mass Mbh by a ratio equal

to GH. This is a simple and elegant exclusion clause here

in the realms of the two modes of relativity, gravitational

and special.

EQUATION Z

In gravitational relativity, the critical limit is:

Mo = Mc = Mbh/GH

Where: Eg is the gravitational relativistic effect of Mc

Such that: Eg = 1/GH

And Mbh = Mc + Ko, where Ko = (Mc x 1/Eg) - Mc

And also: Mc x 1/Eg = Mk, and Mk - Mc = Ko

And so: Mbh = Mc x 1/Eg = Mk

Only when: Mc = Mbh/GH

So that: Mbh = Mk

Where Mk an apparent mass equals its own black hole silent partner

mass equivalent. This physical condition occurs because the Golden

Ratio GH constantly defines Mo as Mbh/GH.

EQUATION Z-1

In special relativity, there is a companion critical

velocity limit Vc for velocity V, where Vc is the speed

of light divided by the square root of the Golden Harmonic,

such that a critical velocity limit Vc constantly exists

for mass Mc, when C is the speed of light, as in:

Vc = (C / root GH) ;

where Vc is actually:

Vc = (C / root (Mbh/Mc)) or also (C / root GH)

when: Mc = Mbh/GH or also GH = Mbh/Mc

so that when: Mc is travelling at velocity Vc

the special relativity effect is: Es

and the special relativity effect 1/Es increases

rest mass Mc to black hole mass Mbh in a bump

because Eg is equivalent to 1/GH .

-- Continued in RELATIVE.3 --

Item C if you are using the HELP MENU

ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ¿

³ A TEST CASE: ³

ÛÄ´ GOLDEN HARMONIC RATIO IN THE TWO MODES OF RELATIVITY ³

ÀÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÙ

Let's look at the critical limit situation in more detail.

An apparent mass aggregate Mk contains an original mass, plus

an augmentation in mass due to gravitational relativity. And

so let the originating mass be Mo, the augmenting mass be Ko,

and the resulting mass be Mk. And therefore:

ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ¿

³ For Gravity relativity ³

ÀÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÙ

EQUATION Z-2

ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ

³ 2G (Mo) Mo is an original mass

Eg = ³ 1 Ä ÄÄÄÄÄÄÄ before augmentation

\³ Cý R

EQUATION Z-3

(Mo x 1/Eg) - Mo = Ko Ko is the mass augmentation

on Mo, due to effect 1/Eg

EQUATION Z-4

Mo + Ko = Mk Mk is the measured (apparent)

mass, consisting of original

plus augmentive masses

EQUATION Z-5

When Mo = Mc = Mk/GH then: Where Mc is a critical mass

value for original mass Mo

ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ

³ 2G Mk

Eg = ³ 1 Ä ÄÄÄÄÄÄ Mk is black hole mass with

³ GH horizon radius Rbh, and GH is

³ ÄÄÄÄÄÄÄÄÄÄÄÄ the Golden Harmonic Ratio equal

\³ Cý Rbh to the number 1.61803398875

EQUATION Z-5-1

ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ Mass Mbh is the same as mass

³ 2G Mbh aggregate Mk.

Eg = ³ 1 Ä ÄÄÄÄÄÄ

³ Ng Ng is ratio Nx when the value

³ ÄÄÄÄÄÄÄÄÄÄÄÄ of Nx is GH, which is the

\³ Cý Rbh Golden Harmonic Ratio

EQUATION Z-6

With digits substituted for GH, then:

ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ

³ 2G Mbh

Eg = .61803398875 = ³ 1 Ä ÄÄÄÄÄÄ = 1

³ 1.61803398875 ÄÄÄÄÄÄÄÄÄÄÄÄÄ

³ ÄÄÄÄÄÄÄÄÄÄÄÄÄ 1.61803398875

\³ Cý Rbh

EQUATION Z-7

because:

ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ When and only when Nx = GH.

1 ³ 1 The Golden Ratio contains

ÄÄÄ = ³ 1 Ä ÄÄÄ this self appreciating

Nx \³ Nx mathematical property

and so:

ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ

1 ³ 1 GH is the Golden Ratio

ÄÄÄ = ³ 1 Ä ÄÄÄ 1.61803398875

GH \³ GH

ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ¿

³ For Special relativity ³

ÀÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÙ

EQUATION Z-8

ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ

³ ÚÄ Ä¿ý ³ (Vc)ý

Es = ³ ³ C ³ = ³ 1 Ä ÄÄÄÄÄÄ

³ 1 Ä ³ ÄÄÄÄÄÄÄÄ ³ \³ cý

³ ³ ÚÄÄÄÄ ³

³ ³ \³ Nx ³

³ ÀÄ ÄÙ

³ ÄÄÄÄÄÄÄÄÄÄÄÄÄÄ

\³ Cý

EQUATION Z-9

ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ

³ ÚÄ Ä¿ý ³ (Vc)ý

Es = ³ ³ C ³ = ³ 1 Ä ÄÄÄÄÄÄ

³ 1 Ä ³ ÄÄÄÄÄÄÄÄ ³ \³ cý

³ ³ ÚÄÄÄÄ ³

³ ³ \³ GH ³

³ ÀÄ ÄÙ

³ ÄÄÄÄÄÄÄÄÄÄÄÄÄÄ

\³ Cý

EQUATION Z-9-A And so:

(Mc x 1/Es) = (Mc x GH) = Mbh, because (Es = 1/GH)

when 1/Es is the special relativitistic effect on

mass Mc which is moving at velocity Vc of EQ Z-9

EQUATION Z-10 As in:

ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ

³ ÚÄ Ä¿ý

.61803398875 = ³ ³ C ³

³ 1 Ä ³ ÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ ³

³ ³ ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄ ³

³ ³ \³ 1.61803398875 ³

³ ÀÄ ÄÙ

³ ÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ

\³ Cý

ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ¿

ÛÄ´ FOR SPECIAL RELATIVITY EFFECT ON BOTH MASS AND RADIUS ³

ÀÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÙ

There is yet another factor to consider. In special relativity

the radius of a mass contracts in reciprocal proportion to the

enhancement of mass. In this regard, when the radius is contracted,

less mass will be required to form a black hole in the relativist-

ically reduced radius.

How does this effect the status of the critical limit Mc,

where the original mass Mo is the black hole mass divided

by the Golden Ratio?

Specifically, what mass will now form the black hole,

when the original mass's radius is concomitantly reduced

by special relativity's effect?

The new mass is easy to find.

EQ Z-9 is abruptly rewritten to accommodate both a reduction in

radius, and expansion in mass, upon original (critical) mass Mc.

The correct velocity for mass Mc can be labelled as (Vbh), as in

'Velocity for black hole', and is easy to find. It turns out to be:

Vbh = (C / GH) Given as:

EQUATION Z-11

ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ

³ ÚÄ Ä¿ý ³ (Vbh)ý

Es = ³ ³ C ³ = ³ 1 Ä ÄÄÄÄÄÄ

³ 1 Ä ³ ÄÄÄÄ ³ \³ cý

³ ³ GH ³

³ ÀÄ ÄÙ

³ ÄÄÄÄÄÄÄÄÄÄÄ

\³ Cý

Es turns out to be the reciprocal of the square root

of the Golden Harmonic. That is; Es = (1/ûGH).

It means that when a mass Mc is physically moving at velocity

Vbh relative to a stationary observer, its radius Rbh contracts

by (1/ûGH), as its rest mass Mc expands by (ûGH), with the result

that a new black hole is formed, having a lesser mass equal to

(Mc x ûGH), and a lesser radius equal to (Rbh x 1/ûGH).

As already said, this occurs when velocity Vbh is equal

to the speed of light divided by the Golden Harmonic Ratio.

The new mass can be labelled as Mbh-, which is less than the

gravitational black hole mass Mbh, by a factor of ûGH. As already

indicated, Mbh/Mc = GH, but the special relativistic mass result

Mbh- is not the same as Mbh. There is a series:

EQUATION Z-12

Mc x ûGH = Mbh- x ûGH = Mbh

It means that a visible mass cannot expand to infinity,

because velocities can approach but can never reach the speed

of light, due to built in limiting factors. This statement

is true specifically for visible masses.

For instance, the maximum velocity possible for mass Mc is Vbh

which is C/GH, but this is only when the original mass Mo is at

the critical mass limit Mc which is a black hole mass Mbh divided

by GH. Whereupon the mass becomes a new black hole of mass Mbh-

and disappears from view, relative to a stationary observer.

The ratio C/GH is (C / 1.61803398875)

(The preceding does not take into account any effect that

gravity might have to relativistically reduce the radius of the

mass causing the gravity's relativistic effect. It is realized

that if a reduction in gravitational radius is also needed as a

key term, than the parameters of the critical mass limit Mc regards

the black hole final limit Mbh, will adjust accordingly, as will

the exact factors related to the Golden Harmonic Ratio).

(The question of such possible adjusting is not addressed in

this disclosure, whose prime intention is to simply show that

certain critical limits and equalities do synonymously exist

in the domains of gravitational and special relativity. And

that the Golden Harmonic Ratio is a fundamental primary term).

ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ¿

³ A REMARK ³

ÀÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÙ

The Golden Ratio was not a term pulled with a sleazy wink from

a magician's hat to fit an idea. The Golden Ratio turned out

to be a resulting term that provided a theory; whose gist is

as follows:

How can a limiting velocity (thus a universal barrier to infinite

expansion of visible mass relative to a stationary observer), be

determined for any visible mass, in special relativity?

The answer to this is straight forward and demonstrates that

a visible mass can never expand to infinity. A discussion

regards this answer begins further below under:

'Special Relativistic Effects on any Mass and Radius'.

ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ¿

ÛÄ´ SUPPLEMENTAL REMARKS ³

ÀÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÙ

The following remarks are included to complete the discussion

regards relativity theories and the Golden Harmonic Ratio. These

supplemental remarks cover the subject of how the Golden Ratio

was found to be a constant in critical limit situations.

The remarks discuss the issue from firstly; effects on the critical

mass only; and secondly for effects on the critical mass and radius.

ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ¿

³ Golden Harmonic Relativistic Effects on Mass Only ³

ÀÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÙ

How was the Golden Harmonic found to be the critical

ratio factor Ng for Nx in Equations Z-5 and Z-5-1 ?

A value of (square root of 2) was first tried for Nx, yielding

a mass augmentation result (1/Eg x Mo), which was greater

than mass Mbh, when root 2 for Nx was ratio (Mbh/Mo = Nx).

In intuitional trial and error, an Nx value arbitrarily

selected as 1.8 was next tried. It yielded an (1/Eg x Mo)

value which was slightly less than mass Mbh.

So the two Nx values were averaged as in 1/2(û2 + 1.8)

to yield a value of 1.608. Since this number was close to a

known number (1.61803398875), this known number was tried to

see how close the Es result (1/Es x Mo) came to Mbh, using

this familiar number as Nx for a point of reference.

It turned out that 1.61803398875 happened to be the very

term wanted, because the result was perfect. This fast

found number was given the label GH.

When GH was Nx, then (1/Es x Mo) = Mbh.

And so this particular Nx was

labelled Ng (for Golden Ratio).

And Mo was understood to be

the same value as mass Mc.

Equations Z-6 and Z-7 show why Ng is a constant. The

set of Equations Z to Z-10 followed as a consequence

of knowing this.

ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ¿

³ Golden Harmonic Relativistic Effects on Mass and Radius ³

ÀÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÙ

But Equations Z to Z-10 consider only the special relativistic

effect on mass, and left unanswered another question which was:

'What modifications would occur in the parameters of

mass when the radius of the mass is also conjointly

changed by special relativity effects'.

The answer to this was also quickly forthcoming, but

in hindsight seems to reflect a very fortuitous guess.

Trial and error was started again. A velocity was needed,

to determine at what rate mass Mc would be travelling to

relativistically increase to mass Mbh-, when radius Rbh

of mass Mc was conjointly contracted to radius Rbh-.

In this thought balloon, Mbh- and Rbh- would be the

parameters forming a new black hole when mass Mo was

travelling at sufficient high velocity.

At this point the rate of joint contraction on mass Mbh

and radius Rbh was not known. And neither was the velocity.

The intention was to find what term Nx is

divided into C to yield the significant velocity.

In a remarkably lucky guess, the first Nx

term tried was GH itself, (in EQ Z-11).

To begin, radius Rbh was modified by (Es x Rbh) as gained

from (EQ Z-11) with Nx equal to GH in the ratio C/GH, to give

contracted radius Rbh-. Then, using EQ 5 of APPENDIX B below

to find the mass of a black hole formed in radius (Es x Rbh-),

a new mass Mbh- was the result. It turned out that the ratios

of masses (Mbh/Mbh-) and (Mbh-/Mc) both equaled the square

root of ratio GH.

It had thus been found that when (C/GH = Vbh), then

EQ Z-11 yielded the square root of GH as the Es value.

The result is that with Es equaling the reciprocal of the

square root of the Golden Ratio, when Rbh is multiplied by

Es to yield radius Rbh-, and mass Mc is multiplied by the

reciprocal of Es to yield mass Mbh-, then radius Rbh- and

mass Mbh- are the correct parameters to form a new black

hole from the special relativity effects on both mass Mc

and radius Rbh, when Mc is travelling at a (C/GH) velocity.

ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ¿

³ How was this verified ? ³

ÀÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÙ

The 'dual effect' event was easily

verified by the following:

A. Radius Rbh- was found from radius Rbh,

by using the Es effect of EQ Z-11 in:

Rbh x Es = Rbh-

B. Using radius Rbh- to find mass Mbh- in:

Cý Rbh- Finding mass Mbh- needed for a

Mbh- = ÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ black hole whose Schwarzschild

2G radius is given as Rbh-

C. Mbh- turned out to be mass Mbh / (1/ûGH)

when effect Es (of EQ Z-11) was 1/GH.

D. It meant mass Mbh- and radius Rbh- form a new black hole,

which is less than a black hole of mass Mbh and radius Rbh,

by a factor of the square root of the Golden Ratio for

both Mbh- and Rbh-.

E. This is true when mass Mc is travelling in special

relativity, at a reduced velocity Vbh, as gained

from EQ Z-11.

F. The synonymous special relativistic 'dual effect' event

for a gravitational relativistic event at the critical

mass limit Mc, is gained by using term Nb = GH (as used

in EQ Z-5-1), to find velocity Vbh in EQ Z-11.

ÉÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍ»

º ±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±± º

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º SPECIAL RELATIVISTIC EFFECTS ON ANY MASS AND RADIUS º

ÈÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍ¼

Only certain critical limit cases

(for masses Mo and Mc = black hole mass Mbh/GH)

have so far been considered.

ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ¿

³ QUESTIONS ³

ÀÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÙ

What if instead of Mc there is given any general mass Mo,

having a radius said to be Ro. Would there still be critical

limits involving Golden Harmonic factors that would limit a

general test case to a state that is less than infinite mass,

at a velocity which can never tightly approach the speed of light?

For that matter are other, more general, limits possible,

besides those already shown to be related to the Golden Ratio?

And if general limits are in the fabrics of physics, how to

determine them, given a general mass quantity that to begin

with is not known to be related to anything else, especially

when it is NOT RELATED to the Golden Ratio ?

ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ¿

³ ANSWER ³

ÀÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÙ

This questioning also came to a quick answer, although

the finding of the answer was not all that straightforward.

The answer demonstrates that any visible mass travelling at a

relativistic velocity in special relativity, reaches a limiting

barrier, beyond which the mass does not visibly increase any further

toward infinity, and its velocity closes no further toward equaling

the speed of light.

The first insight is that any entity (in its most general

sense) comprises a mass and a radius. With mass is some

gravity. For instance a typical Sun sized star is an

ideal test case entity.

For example, the ratio of the Sun's existing mass M over

the Sun's existing radius R is its (mass/radius) ratio,

ie., M/R

(Note that Mo would be the Sun's original mass before any

mass augmentation effect due to gravitational relativity.

The Sun's original mass Mo is less than its existing

mass M, since the existing mass as physically measured

is assumed to include a mass augmentation upon mass Mo).

The Sun's black hole Mbh mass (silent partner mass)

is easily found by:

EQUATION Z-13

Cý R Finding mass Mbh needed for a

Mbh = ÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ black hole whose Schwarzschild

2G radius is given as R when

R is the radius of the Sun

so that another ratio is found, this being (Mbh/R)

which is the Sun's (black hole mass/radius) ratio.

But actually, term Mbh of EQ Z-13 is worthless. What

we really want to find is what (Mbh-/R-) ratio forms a

black hole out of the original Mo/R parameters, when Mo is

travelling at increasingly faster velocities approaching the

speed of light.

We need a comparative term, to study any differences between

the Sun when standing still, and when moving at a relativistic

velocity. The comparative term we want to know is found as:

EQUATION Z-14

Mbh Cý Where ratio Cý/2G is a constant,

ÄÄÄ = ÄÄÄÄ when C is the speed of light, and

R 2G G is the universal gravitational

constant.

R is the original radius of original mass Mo

Mass Mbh is instantly found from EQ Z-13.

The logical argument formed in advance, was that

any mass result M+, and radius result R-, ensuing

from special relativistic effects on original states

Mo and Ro, should also equal the black hole constant

ratio Cý/2G, if mass M+ and R- were relativistically

altered sufficiently to form a new black hole.

Ratio Cý/2G can be labeled ratio CR (for 'constant ratio') and

has the value of (6.735275620 x 10 to 27 grs/cm), given a speed

of light whose digital value is 2.99792458, and a gravitational

constant whose digital value is 6.6720 x 10 to -8.

Ratio Cý/2G is known as a constant

for the given values of C and G.

What we can do is follow special relativistic changes upon

both Mo and Ro through successively greater velocities, until

the combined ratios (1/Es x Mo) / (Es x Ro) equals the ratio

Cý/2G, as in:

EQUATION Z-14A

((1/Es x Mo) / (Es x Ro)) = (M+/R-) = (Cý/2G)

where Es is the special relativistic effect.

ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ¿

³ Finding a significant Velocity value, which results in ratio CR ³

ÀÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÙ

It was useful that a good test model was available in the

solar system's Sun, where given the Sun's existing mass as M,

and existing radius as R. The Sun has to be accelerated to such

an extent that through the parameters of special relativity, the

Sun's modified mass M+ and radius R- reach a point where they

transfigure into conditions which form a new black hole.

It was assumed that such a transfiguration should

occur, and that the transfigurating velocity in

special relativity could be inferred.

How could the velocity needed for the transfiguration, be

determined for an arbitrary general case such as the Sun ?

At this point, some intuitively lucky guesswork again prevailed;

a 'seeing around corners' so to speak. To make a long story short,

it is easy to predetermine the prerequisite velocity. How, is

outlined as follows:

1. Given an existing Sun mass M of 1.99099305 x 10 to 33 gms

(mass MM from Part 1 above)

1A. Given a Sun radius R of 6.96265 x 10 to 10 cms

1B. Given constant ratio CR = Cý/2G

= 6.735275620 x 10 to 27 grms/cms

2. Given the black hole radius parameter

of EQ 4 of APPENDIX B, as:

EQUATION Z-14-1

2G M Finding the Schwarzschild

R' = ÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ radius R' of a black hole's

Cý event horizon, when given

mass M

3. And given Equation 5 of APPENDIX B, rewritten as:

EQUATION Z-14-2

Cý R Finding mass Mbh needed for a

Mbh = ÄÄÄÄÄÄÄÄÄÄÄÄÄ black hole whose Schwarzschild

2G radius is given as R

Mass Mbh is the black hole silent

partner mass for any given mass M.

4. Given Equation Z-8 above for special relativistic effect

on both an original rest mass and its original radius, based

on a term Nx to determine a velocity, so that:

EQUATION Z-15

ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ

³ ÚÄ Ä¿ý ³ (Vx)ý

Es = ³ ³ C ³ = ³ 1 Ä ÄÄÄÄÄÄ

³ 1 Ä ³ ÄÄÄÄ ³ \³ Cý

³ ³ Nx ³

³ ÀÄ ÄÙ

³ ÄÄÄÄÄÄÄÄÄÄÄ

\³ Cý

5. Given that (1/Es x M) = M+

6. Given that (Es x R) = R-

7. Given that (1/Es x M+) / (Es x R-) = Cý/2G = M+/R-

8. Then it should be possible to find a velocity for EQ Z-15-1

below such that the resulting (M+/R-) ratio = Cý/2G

9. A first arbitrary value for Nx was tried, being 1.0001, which

produced results that were too low for the above Item 7 to be

correct.

10. A second arbitrary value for Nx was tried in EQ Z-15, being

1.00001, which was of the right magnitude for a mass M+, but

Item 7 was still not correct.

11. However, it was noticed that 1/1.00001 by itself was in the

magnitude range of gravitational relativistic effect Eg from

the Sun's mass, as determined in EQ C of Part 1 further above.

(MM in EQ C is the same value as Sun mass Mo given in EQ Z-2,

and immediately above in Item 1. And Eg of EQ Z-2 is the same

as Eg used immediately below in Item 12).

12. And so Eg was determined for the Sun's mass M = MM = Mo in

EQ Z-2, and conveniently labelled Egs (for 'effect gravity Sun

mass'), and was substituted as term 1/Nx in EQ Z-15 immediately

above, to give:

EQUATION Z-15-1

ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ

³ ÚÄ Ä¿ý ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ

³ ³ C x Egs ³ ³ (Vx)ý

Ess = ³ À Ù = ³ 1 Ä ÄÄÄÄÄÄ

³ 1 Ä ÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ \³ Cý

\³ Cý

where velocity Vx is (C x Egs),

and special effect Ess conveniently

means an Es effect related to the

gravitational mass via term Egs.

13. Then; Sun mass M in (M x 1/Ess) = M+

14. And; Sun radius R in (R x Ess) = R-

15. And; ratio (M+/R-) = 6.73527458 x 10 to 27 grms/cms

As found in:

EQUATION Z-15-2

(M x 1/Ess) / (R x Ess) = CR = (M+/R-)

16. Which turned out to be an excellent approximation of ratio

CR (being Cý/2G as created in Item 1B immediately above)

Well, this was very good for a first found attempt. How

about for other masses, and how did the ratio result of

Item 15 favorably equate in truth to Item 1B above, in

that the CR result in Item 15 is marginally below the

CR constant in Item 1B ?

17. The mass of the Sun was arbitrarily raised by a factor

of 1000, so that now M = 1.99099305 x 10 to 36 grms

18. A new Egs effect factor was determined using the

larger mass of Item 17, in EQ Z-2 above

19. The new Egs factor was substituted in EQ Z-15-1

to give a new Ess factor

20. The new Ess factor was substituted in the

terms of Items 13, 14, and 15

21. The result M+/R- = 6.735275620 x 10 to 27 gms/cms = CR,

which is exactly the constant of Item 1B

Two things were instantly made clear.

It is clearly evident that Equations Z-15, Z-15-1,

and Z-15-2, are correct for any mass, to yield (M+/R-)

ratios equal to Cý/2G.

It is clearly evident that ratio (M+/R-) closes

in on ratio Cý/2G, the closer that given original

mass M is to the black hole silent partner mass Mbh

as determined in EQ Z-14-2

(It is also clear from preceding explorations, that

when relativistic effects are to act upon an original

mass, the original mass M can never approach its black

hole silent partner equivalent Mbh any closer than by

Mbh divided by factors of the Golden Ratio).

ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ¿

³ Finding that terms M+ and R- are properties of a black hole ³

ÀÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÙ

At this point we are still not finished. The final question is;

are terms M+ and R- (as determined by Equations Z-15-1 and Z-15-2),

in fact the terms of a new black hole whose mass is M+ and whose

radius is R- ?

This final question was very easy to test by a double check:

22. The value of M+ from Equation Z-15-1 and Item 13 for the

Sun mass arbitrarily increased by a factor of 1000, as in

Item 17, yielded an Ess value in Item 19, which as applied

to Item 13, was:

3.055623494 x 10 to 27 grms

23. The value of R- from the same Ess in Item 19, applied

to Item 14, was:

4.536746031 x 10 to 9 cms

24. Looking to Equations Z-14-1 and Z-14-2, it was found in

EQ Z-14-2 (given mass M+ of Item 22), and found in EQ Z-14-1

(given radius R- of Item 23), that (M+/R-) = CR. This is shown

in the following three equations:

EQUATION Z-15-3

2G M+ Finding the Schwarzschild

R' = ÄÄÄÄÄÄÄÄÄÄÄÄÄÄ radius R' of a black hole's

Cý event horizon, when given

mass M+

R' was 4.536746031 x 10 to 9 cms,

exactly the same as R- in Item 23

EQUATION Z-15-4

Cý R- Finding mass M' needed for a

M' = ÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ black hole whose Schwarzschild

2G radius is given as R-

M' was 3.055623493 x 10 to 27 grms,

exactly the same as M+ in Item 22

EQUATION Z-15-5

And so: M' of EQ Z-15-4, divided by R' of EQ Z-15-3, = CR

as in: (M'/R') = CR

where: CR is the constant of Item 1B

proving: that M+ of Item 22 and R- of Item 23 are the

correct parameters of a new black hole created

by relativistic effect Ess of Item 19, on higher

mass M of Item 17, using EQ Z-15-1 to determine

Ess, after using EQ Z-16 to determine Egs.

ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ¿

ÛÄ´ SUMMARY EQUATIONS ³

ÀÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÙ

The delineations of Items 1 to 23, and Equations Z-14 to Z-15-5,

once understood, resolve into a quick series of steps, used to

determine a relativistic barrier for any given mass M and its

radius R, as in:

EQUATION Z-16

ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ

³ 2G M M is any mass, R is its

Egs = ³ 1 Ä ÄÄÄÄÄÄ radius, and Egs is the

\³ Cý R gravitational relativistic

effect of mass M

EQUATION Z-16-1

ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ

³ ÚÄ Ä¿ý ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ

³ ³ C x Egs ³ ³ (Vx)ý

Ess = ³ ÀÄ ÄÙ = ³ 1 Ä ÄÄÄÄÄÄ

³ 1 Ä ÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ \³ Cý

\³ Cý

Ess is the special relativistic effect ensuing from

velocity Vx, determined as the direct consequence of

the speed of light reduced by the mass's gravitational

relativistic effect Egs.

EQUATION Z-16-2

(M x 1/Ess) = M+

EQUATION Z-16-3

(R x Ess) = R-

EQUATION Z-16-4

(M+/R-) = Cý = CR

ÄÄÄÄ

and mass M+ and radius R- are a relativistic transfiguration of

M and R into the parameters of a black hole, when ratio (M+/R-) = CR.

CR is a physical constant in black holes,

whose value is given as the speed of light squared

divided by twice the gravitational constant, and

whose value is 6.735275620 x 10 to 27 gms/cms.

EQUATION Z-16-5

And ultimately, Ess can be determined directly

from Egs, by:

Essý = 1 - (Egs)ý

Ess is not the same value as Egs. Ess can be higher

or lower than Egs. The exact relationship between the

value of Egs and Ess is known by:

EQUATION Z-16-6

ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ

Ess = \³ 1 - (Egs)ý

ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ

Egs = \³ 1 - (Ess)ý

Why this relationship occurs is explained

further below, beginning with EQ Z-17),

and explicitly in EQ Z-19.

In a nutshell, Equations Z-16 to Z-16-6 fully show that

fundamental terms in both gravitational (stationary) and

special (moving) modes of relativity are synonymous.

ÉÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍ»

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º ±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±± º

º UNIFIED EFFECTS IN FIELD BEHAVIOR º

º ±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±± º

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º ±±±±±±± GENERAL INTRODUCTION for part 4 Unified Fields ±±±±±±± º

ÈÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍ¼

'The best information seems to come after you think you

have it wrapped up and have stopped thinking about it'.

'For example, the following floated into

consciousness as an afterthought'.

In a broad sense, relativity synonymy evokes innuendoes

of unified behavior between the fields of gravity and

electromagnetism (a unified field theory).

But wait, this is not a fully fledged unified field theory. What

is under review here are only parts of what appear to be a unified

field theory environment. What is shown are exactitudes whereby

gravitational effects of an assumed mass changing character on a

body, result explicitly in equivalent special relativistic effects

synonymous to the body moving at characteristic velocities.

Certain rules of behavior define these two modes of relativity in

their unified behavior. These rules are easy to understand, once

clearly seen, but can be very confusing until their characteristics

are shown in an obvious way. This next section (Part 4) explores

the rules.

To do the job, a particular environment is arbitrarily created. Exact

test cases are followed to the nth degree. The created environment is

in violation of certain conditions already outlined in Part 2 above;

to wit: that certain critical limits exist in the rate of mass

expansion, where the maximum expansion oscillates between a black hole

mass equivalent Mbh, and plateaus below this, articulated as functions

of the Golden Harmonic Ratio 1.61803398875.

For the test cases, it is desirable to see what happens

mathematically for events which are right at the brink of

a black hole mass, compared to masses well below the brink.

The phenomenology is thus most easily watched in detail.

For this, such masses are arbitrarily created, and assumed to exist

in violation of the statements in Part 2 above (which delineate that

a mass of black hole equivalent includes an original mass Mo, a mass

augmentation unit Ko, and resultant mass aggregate which is that of a

black hole or less. If the mass is that of a black hole, the original

mass is at a critical mass limit Mc, and the ratio Mbh/Mc = Ng is a

function of the Golden Ratio. For masses other than than Mc, ratio Ng

is given the general label Nx).

In the following, the cases for Mc and Ng parameters are ignored by

conveniently looking the other way. In the test cases which follow,

the existence of discrete portions denoted by terms such as Mo, Mc,

and Ng, are expeditiously put aside, and a mass value is assumed which

can be anything less than Mbh, even if less than Mbh by a few parts in

a thousand. This is called a HIGH mass, for convenience.

ÉÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍ»

º ±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±± º

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º TEST CASE º

ÈÍÍÍÍÍÍÍÍÍÍÍ¼

In a test case, a HIGH mass value is studied which hangs right

below the mass of a black hole Mbh. This is in a deliberately

selected HIGH mass range which as already said ignores properties

such as a critical mass factor (Mc) outlined in Part 2 above.

The intention this time is to follow test case examples in

excruciating digital detail, so that the effects and their

changes are unmistakable.

The sole intention of the following, is to observe how certain

properties are universally united in a general way through various

transformations between gravity and electromagnetic field behaviors.

And so a new study model is created, based on the arbitrary

criteria that any job needed to do a certain job is good enough

for the purpose intended.

A HIGH mass gravitational event and a LOW mass event are thus

arbitrarily created from the same Mbh term, which is the mass

of a black hole confined in the Sun's radius. Mbh for the Sun's

radius is (4.689536679 x 10 to 38 grms).

The Sun's radius (6.96265 x 10 to 10 cms) has been chosen as an

easily recognized radius for use as a constant to investigate

the effects of different mass densities confined in a fixed

(unchanged) area. Otherwise, the Sun's radius has no physical

significance when tied to the following arbitrary mass aggregates.

To supply the study, a small ratio Nx has been selected for a

control in the study. Nx is meaningless other than its value

is the charge to mass ratio of the hydrogen atom, ie.:

((Proton + electron) / electron) = 1.000544617 = Nx.

(The interpretation is that the negative electron charge

of the lightweight electron influences the heavy proton

by only 1.000544617 of the effect the proton has on the

electron, since both particles have the same quantity of

charge (opposite) despite widely divergent rest masses.

This is mentioned only to satisfy curious minds. As said,

the real value for the above ratio Nx has no intrinsic

significance in the following).

MASS1 In our study model, Mbh is arbitrarily reduced by the

small ratio Nx to give a HIGH Mass1 term, which is very

slightly below Mbh.

MASS2 Mass1 is then arbitrarily reduced by a factor of 100,000 to

give a LOW Mass2 term having the same digits but much lower

magnitude then Mass1.

The intention is to be able to follow certain relativistic field

effects in detail by following the digital results of both the

HIGH mass term (Mass1), and LOW mass term (Mass2), to more openly

follow the unifying effects between the two fields (being gravity

and electromagnetism).

In the study model, as already said, the value of Nx has no

significance except that it provides a convenient low value

Nx ratio to arrive at a HIGH mass term for the study model.

Nx is given to 13 significant digits as gained from the

ratio (P 938.2796 mev + E .5110034 mev) / (P 9382796 mev)

= 1.000544617404

TABLE 4-A

ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ¿

³ ARBITRARY STUDY MODEL DATA ³

ÃÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ´

³ ³

³ Nx = 1.000544617404 = (P + E) / E ³

³ Mbh = 4.689536679 x 10 to 38 grms ³

ÃÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ´

³ ³

³ HIGH mass1 = Mbh / Nx ³

³ = 4.686984066 x 10 to 38 grms ³

³ Nx = 1.000544617404 ³

³ ³

³ LOW mass2 = Mass1 / 100,000 ³

³ = 4.686984066 x 10 to 33 grms ³

³ Nx = 100054.4617404 ³

ÃÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ´

³ ³

³ In the following, Equations Z-17-1 and Z-17-3 ³

³ are the same as EQ Z-15-1 above, except, the real ³

³ digit value of each Egs ratio is substituted for ³

³ the algebraic term Egs. ³

ÀÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÙ

EQUATION Z-17 HIGH gravitational Mass1 results:

ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ

³ 2G (4.686984066 x 10 to 38 grms)

Egs = ³ 1 Ä ÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ

\³ Cý R

Mass1 has been given in

terms of a real weight.

Radius R is the radius of the Sun.

Egs is the gravitational relativistic effect of Mass1

ÚÄÄÄÄÄÄÄÄÄÄÄÄ¿

HIGH gravity field effect Egs = ³ .023330687 ³

Egs is closing toward 0 ÀÄÄÄÄÄÄÄÄÄÄÄÄÙ

EQUATION Z-17-1 Electromagnetic field effect results

(Ess is special relativistic effect)

ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ

³ ÚÄ Ä¿ý

³ ³ C x .023330687 ³ Vý

Ess = ³ À Ù = ÄÄÄÄ

³ 1 Ä ÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ Cý

\³ Cý

.023330687 is effect Egs

of EQ Z-17

Ess = 1 - (Egs)ý

As in: 1 - (.023330687)ý = .999727802

ÚÄÄÄÄÄÄÄÄÄÄÄÄ¿

LOW special field effect Ess = ³ .999727802 ³

Ess is closing toward 1 ÀÄÄÄÄÄÄÄÄÄÄÄÄÙ

V velocity is starting to

close toward 0

EQUATION Z-17-2 LOW gravitational Mass2 results:

ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ

³ 2G (4.686984066 x 10 to 33 grms)

Egs = ³ 1 Ä ÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ

\³ Cý R

Mass2 has been given in

terms of a real weight.

ÚÄÄÄÄÄÄÄÄÄÄÄÄ¿

LOW gravity field effect Egs = ³ .999995002 ³

Egs is closing toward 1 ÀÄÄÄÄÄÄÄÄÄÄÄÄÙ

EQUATION Z-17-3 Electromagnetic field effect results

(Ess is special relativistic effect)

ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ

³ ÚÄ Ä¿ý

³ ³ C x .999995002 ³ Vý

Ess = ³ À Ù = ÄÄÄÄ

³ 1 Ä ÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ Cý

\³ Cý

.999995002 is effect Egs

of EQ Z-17-2

Ess = 1 - (Egs)ý

As in: 1 - (.999995002)ý = .003161416

ÚÄÄÄÄÄÄÄÄÄÄÄÄ¿

HIGH special field effect Ess = ³ .003161416 ³

Ess is closing toward 0 ÀÄÄÄÄÄÄÄÄÄÄÄÄÙ

V velocity is closing toward 1

ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ¿

ÛÄ´ COMPARING M+ AND R- RESULTS FOR HIGH AND LOW MASSES ³

ÀÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÙ

As delineated in Items 22 to 24 above, and in Equations Z-15-3

to Z-15-5 which immediately follow Items 22 to 24, two terms

M+ and R- represent the enhanced mass and reduced radius on

an object due to special relativistic results ensuing from the

proper ratio of the speed of light divided by the proportionate

relativistic effect of the object's gravity.

And so the synonymity of related behaviors, (the resulting

effects of Ess from Equations Z-17-1, and Z-17-3), when applied

to the HIGH mass of EQ Z-17, and LOW mass of EQ Z-17-2, will yield

appropriate M+ and R- terms for each of the masses. These are

listed in the following:

TABLE 5

ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ¿

³ ³

³ HIGH MASS GRAVITY ³

³ ³

³ MASS1 = (4.686984066 x 10 to 38 grms) ³

³ ³

³ RADIUS R = 6.96265 x 10 to 10 cms ³

³ ³

³ Ess EFFECT = .999727802 ; from EQ Z-17-1 ³

³ ³

³ M+ = (Mass1 x 1/Ess) ³

³ = 4.688260199 x 10 to 38 grms ³

³ ³

³ R- = (radius R x Ess) ³

³ = 6.9607547839 x 10 to 10 cms ³

³ ³

³ CR = ratio (M+/R-) ³

³ = 6.735275620 x 10 to 27 grms/cm ³

³ ³

ÀÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÙ

TABLE 6

ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ¿

³ ³

³ LOW MASS GRAVITY ³

³ ³

³ MASS2 = (4.686984066 x 10 to 33 grms) ³

³ ³

³ RADIUS R = 6.96265 x 10 to 10 cms ³

³ ³

³ Ess EFFECT = .003161416 ; from EQ Z-17-3 ³

³ ³

³ M+ = (Mass1 x 1/Ess) ³

³ = 1.482558107 x 10 to 36 grms ³

³ ³

³ R- = (radius R x Ess) ³

³ = 2.201183848 x 10 to 8 cms ³

³ ³

³ CR = ratio (M+/R-) ³

³ = 6.735276152 x 10 to 27 grms/cm ³

³ ³

ÀÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÙ

ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ¿

³ It is seen that results M+ , though higher than an ³

³ originating mass, are lower than the ceiling mass Mbh ³

³ in LOW mass results, and close in on ceiling mass Mbh ³

³ in HIGH mass results. (Ceiling mass means a black ³

³ hole mass equivalent Mbh formed in radius R. ³

ÃÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ´

³ In HIGH mass situations, M+ can look like the high ³

³ mass itself, but in low mass situations, M+ is far ³

³ removed from the low mass itself. ³

ÃÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ´

³ Also, it is obvious that M+ of LOW mass results can ³

³ gain substantially over the LOW mass itself, yet still ³

³ remain substantially below the final mass Mbh, whereas ³

³ M+ hardly gains over its originating HIGH mass, and ³

³ can also look very much like final mass Mbh, when ³

³ the HIGH mass itself looks closely like Mbh. ³

ÃÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ´

³ In real situations, the HIGH mass will be fixed at a ³

³ maximum ceiling of critical limit Mc. In this current ³

³ test case situation M+ looks neither like Mc, or Mbh. ³

³ Yet M+ will be explicitly Mc x ûGH, and Mbh/ûGH, when ³

³ GH the Golden Ratio 1.618034 is term Nx. ³

ÃÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ´

³ (Ratio CR in the LOW mass situation, is seen to be ³

³ marginally more than CR = Cý/2G . This shift might ³

³ be due to intrinsic truncations in the digital ³

³ accuracy of the equations for lower mass densities. ³

³ It is hard to tell, in the scope of a digital ³

³ accuracy limited to 13 significant figures). ³

ÀÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÙ

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º FIRST INTERPRETATION º

ÈÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍ¼

Thus M+ can approach but never equal or exceed Mbh. As the Egs

effect approaches 0 (greatest power in gravity field strength),

the Ess effect approaches 1 (the least power, no effect), in

velocity related relativistics.

At the point where the gravity effect has its greatest value;

at Egs = 0 ; the special relativistic effect ceases to exist

(comes to a standstill), because there is no velocity, as when:

EQUATION Z-17-4

(C/0) / C = 0/C = 0 .

This closes right in on a clear insight regards the question

of how maximum potential relativistic gravity effect can

contain light - effectively cancel the velocity of light.

The velocity of light is not cancelled. The ability to have

a velocity related to any special relativistic effect is

cancelled. It appears this amounts to the same thing as a

counteracting of the velocity of light.

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º DIRECT INTERPRETATION º

ÈÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍ¼

A first interpretation of the consequences of Equations Z-17 to

Z-17-3, is that a HIGH gravitational mass density results in a

LOW special relativistic synonymity. And a LOW gravitational

mass density results in a HIGH special relativistic synonymity.

It has the immediate interpretation that things run faster in

LOW gravitational events, and slower in HIGH gravitational events.

It adds another picture to the experimentally

confirmed property that proximity to gravity,

relativistically causes time to slow.

Intuitively, it answers a question as to how gravity at

its highest can confine light. A see saw (or yin yang)

characteristic in the works is summarized in the following:

TABLE 7

ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ¿

³ HIGH mass gravity Effect Egs approaches 1 ³

³ Effect Ess approaches 0 ³

³ ³

³ LOW mass gravity Effect Egs approaches 0 ³

³ Effect Ess approaches 1 ³

ÃÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ´

³ You can see at a glance how gravity can confine ³

³ light. As gravity effect Egs closes in on 1, ³

³ special effect Ess closes down toward 0 velocity. ³

³ When Egs is right at 1, Ess is closed down right ³

³ to 0 and the velocity of light C in a V/C ratio ³

³ is vanished when 0/C = 0 . ³

³ ³

³ Conversely, when Egs is low and closing down to 0, ³

³ effect Ess intensifies with a velocity approaching ³

³ 1, which is equivalent to approaching the full ³

³ speed of light. ³

ÃÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ´

³ In another sense, it is clearly seen that events ³

³ are free to move more rapidly in activities of a ³

³ HIGH velocity, in a LOW gravity field density. ³

³ ³

³ And in a HIGH gravity field density, events are ³

³ constrained to low velocity activity approaching ³

³ 0 velocity, when the gravity field approaches the ³

³ density of a black hole, re: special relativity. ³

ÃÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ´

³ ³

³ Notes: ³

³ ³

³ In real events, as summarized above in Part 2, ³

³ if a mass augmentation is assumed for gravity ³

³ effect Egs, then when a mass's density (without ³

³ augmentation) reaches a critical mass factor Mc, ³

³ the mass augmentation amount Ko is sufficient to ³

³ jump the mass amalgamation in one whole bump to a ³

³ black hole quantity Mbh, such that effect Egs = 1. ³

³ And thus effect Ess = 0; which is the equivalent ³

³ of a 0 velocity for light. ³

³ ³

³ The proportionate bump of mass Mc to Mbh is a ³

³ function of the Golden Ratio 1.61803398875. ³

³ ³

³ It means there never is a situation where effects ³

³ Egs and Ess slowly converge to 1 and 0, as is ³

³ fictitiously indicated in Equations Z-17 and ³

³ Z-17-1. As show in Part 2 further above, effects ³

³ Egs and Ess will jump in a final leap to 1 and 0 ³

³ in a single bump via Golden Ratio functions, when ³

³ the gravity mass density reaches Mc before ³

³ reaching black hole mass Mbh. ³

³ ³

ÀÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÙ

-- Continued in RELATIVE.4 --

Item D if you are using the HELP MENU

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º PURE MATH CONNECTORS º

ÈÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍ¼

Terms Nx, Egs, and Ess, can be shown to be mathematically

connected by direct steps which bypass the physical dynamic

terms. This does not mean the physical dynamic terms do not

exist, it only means that it is possible to quickly work back

and forth between Ess, Egs, and Nx, when a few connector rules

are known. These rules include the following:

Given an Nx term:

then: Egs = û(1 - 1/Nx)

and: Nx = root 1/(1 - (Egs)ý)

and: Ess = root 1 - (Egs)ý

and: Ess = û(1/Nx) = 1/ûNx

These connector rules can be more readily shown in a table,

as follows:

TABLE 8

ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ¿

³ FOR EXAMPLE, GIVEN THAT Nx = û3 = 1.732050807 ³

ÃÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ´

³ ³

³ Then: for GRAVITY relativity ³

³ ³

³ ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ ³

³ ³ 1 ³

³ 1. Egs = ³ 1 - ÄÄÄ = .650115167 ³

³ \³ û3 ³

³ ³

³ 1 ³

³ So that: Nx = ÄÄÄÄÄÄÄÄÄÄÄ = 1.732050807 ³

³ 1 - (Egs)ý ³

³ ³

ÀÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÙ

Cont.

ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ¿

³ ³

³ Then: for SPECIAL relativity ³

³ ³

³ ÚÄÄÄÄÄÄÄÄÄ ³

³ ³ 1 ³

³ 2. Ess = ³ ÄÄÄÄ = .759835685 ³

³ \³ û3 ³

³ ³

ÃÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ´

³ ³

³ ÚÄÄÄÄÄÄÄÄÄÄÄÄÄ ³

³ ³ 2G M ³

³ Ess = ³ ÄÄÄÄÄÄ = .759835685 ³

³ \³ Cý R ³

³ ³

³ 2G M ³

³ And: Essý = ÄÄÄÄÄÄ = .577350269 ³

³ Cý R ³

ÀÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÙ

Cont.

ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ¿

³ ³

³ Essý Cý R ³

³ So that: M = ÄÄÄÄÄÄÄÄÄÄÄ ³

³ 2G ³

³ ³

³ ÚÄÄÄÄÄÄÄÄÄÄÄÄ ³

³ And: Ess = \³ 1 - (Egs)ý = .759835685 ³

³ ³

³ ÚÄÄÄÄÄÄÄÄÄÄÄÄÄ ³

³ And: Egs = \³ 1 - (Ess)ý = .650115167 ³

³ ³

³ 1 ³

³ And: Ess = ÄÄÄÄÄ = .759835685 ³

³ ûNx ³

³ ³

³ 1 ³

³ So that: Nx = ÄÄÄÄÄÄÄ = 1.732050807 ³

³ (Ess)ý ³

³ ³

³ And: Vx = C / 1/Egs = Velocity ³

³ ³

ÀÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÙ

ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ¿

³ ³

³ NOTE: There are specific similar distinctions ³

³ between the Nx terms for the two relativities, ³

³ and first given Egs and Ess terms, shown in ³

³ TABLE 8 as 1, and 2. ³

³ ³

ÀÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÙ

ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ¿

³ ³

³ These above shown pure math permutations are ³

³ true when given any value for Nx, or Egs, or Ess. ³

³ ³

³ With these rules it is possible to freely move back ³

³ and forth to arrive at key terms for gravitational ³

³ and special relativites. ³

³ ³

³ For instance, given a special effect (Ess) for a ³

³ body moving at a high velocity, then equivalent ³

³ gravitational effect (Egs) in relativity is directly ³

³ known by a single step calculation, for instance ³

³ by: ³

³ ³

³ ÚÄÄÄÄÄÄÄÄÄÄÄÄÄ ³

³ Egs = \³ 1 - (Ess)ý ³

³ ³

³ And what portion the given moving body's mass ³

³ is to a black hole silent partner equivalent, ³

³ is directly known by a single step calculation, ³

³ for instance by: ³

³ ³

³ 1 ³

³ Nx = ÄÄÄÄÄÄ because: Nx = Mbh/M ³

³ (Ess)ý ³

³ ³

ÀÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÙ

When dealing with real events which occur at the critical

mass limit Mc, where then Mbh/Mc = GH (the Golden Harmonic

Ratio 1.618034), then pure math connectors can appear slightly

confusing, in that certain pure math factors exactly occur through

functions of the Golden Ratio, rather than through relativistic

field dynamics.

For instance:

TABLE 9

ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ¿

³ GIVEN THAT Nx = 1.61803398875 = The Golden Ratio ³

ÃÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ´

³ Then also: ³

³ ³

³ Egs = 1/GH = GH - 1 = .6180339 ³

³ ³

³ ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄ ³

³ And: Egs = \³ 1 - (Ess)ý = .6180339 ³

³ ³

³ And: Nx = Egs + 1 = 1.6180339 ³

³ ³

ÀÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÙ

ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ¿

³ ³

³ And: Ess = ûEgs = .7861514 ³

³ ³

³ And: Nx = (Ess x 1/Egs)ý = 1.6180339 ³

³ ³

³ And: Nx = Essý + 1 = 1.6180339 ³

³ ³

³ Etcetera ³

³ ³

³ BUT THESE ARE TRUE ONLY WHEN NX = THE GOLDEN RATIO ³

³ ³

ÀÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÙ

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º WHY Egs AND Ess ARE INTRINSICALLY RELATED º

ÈÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍ¼

In a closer look at the preceding, some

further facets are learned. In particular:

EQUATION Z-18

For example: Taking data for Ess and Egs from EQ Z-17-3 ;

and: M+ from table 6

then: in EQ Z-18 ;

ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ

Ess = \³ 1 - (Egs)ý

where: M+ = ûNx ; when: Nx = Mbh

ÄÄÄ ÄÄÄ

M M

and so: in EQ Z-18-1 ;

EQUATION Z-18-1

ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ

Ess of .003161416 = \³ 1 - (.999995002)ý

because: (M+/M) = ûNx

as when: in EQ Z-18-2 ;

EQUATION Z-18-2

(1.482558107 x 10 to 36 grms)

ÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ = 316. 313878376 = û100054.469653

(4.686984066 x 10 to 33 grms)

where: û100054.469653 = ûNx x 100,000

because: Nx is ratio 1.000544617404

and: Mbh / 1.000544617404 gave Mass1 for our study model

and: Mass1 / 100,000 gave Mass2 for our study model

NOTE: The true value of û(Nx x 100,000) = 316.313865868 =

û100054.4617404, is slightly departed from the actual Nx

value for Mass2 shown immediately above. The departure

is due to intrinsic truncation in accuracy, where a few

digits are clipped from the tail end of the HIGH special

relativity Ess term .003161416, and the LOW Egs term

.999995002.

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º ±±±±±±±±±±±±±±±±±±±±± SPECIFIC CONCLUSIONS ±±±±±±±±±±±±±±±±±±±±± º

º ±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±± º

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It is now clear, according to the above derivations which begin

with EQ T and continue through EQ Z-18-2, that a fundamental

barrier exists in physics, which limits special relativistic

effects on a visible moving mass entity to a pre-determinant

black hole gravitational mass equivalent, gained by a

pre-determinant limit in velocity.

The pre-determination on the entity is as seen by a stationary

observer watching the mass entity move at relativistic velocities.

At its pre-determinant limit in velocity, the mass entity

transfigures into a black hole and disappears from view.

(This does not mean that the black hole cannot keep acceler-

ating. What it means is that the possibility of such further

acceleration is not addressed in any way, in the scope of this

disclosure. This exploration ends with the original radius R

transfigured into an event horizon R- = R'. And so as an event

horizon radius R- will thereafter behave in dissimilar ways

than in the physical form of a radius R. Such dissimilarity

in behavior of radii is discussed further above at the start

of Part 2, as Items 1 and 1A under: 'A Comparison Between

Gravitational and Special Relativity').

In outlook, a visible mass is any mass of radius R.

The visible mass has to be capable of radiating light to be

seen in the universe. Its black hole M+ and R- equivalent at

the relativistic limiting barrier does not radiate light, and

so no longer physically exists in terms of basic electromagnetic

radiation.

Generally, a visible mass accelerated to relativistic

velocities cannot achieve a theoretical infinite visible mass,

and the velocity of the visible mass can never theoretically

equal the speed of light.

The interpreted statements in special relativity which say a

mass (obviously visible) continues to expand toward infinity,

and the velocity continues to the speed of light, are wrong, when

they do not take into consideration the black hole barrier effect.

The maximum velocity attainable by a visible moving mass, is

the speed of light reduced by the proportionate ratio of the

gravitational relativistic effect of the mass being accelerated.

The velocity barrier limit (maximum velocity) possible, is

restricted by the bounds achieved in special relativistic

effect when the mass has increased, and its radius has

contracted, to a point where the moving entity forms a

black hole and effectively disappears from view.

As already said, this point is easily calculated, as

being the velocity resulting when the speed of light

is divided by the proportionate effect of the mass's

gravitational relativistic effect.

This point will vary from mass to mass, and from radius to

radius per given mass, but will inevitably appear somewhere

before the speed of light is reached, when the visible mass

is being accelerated to relativistic velocities.

A further limiting factor is reached, when the original

mass factors and augmented mass factors are summed, to

reach an absolute prior limit at which the total mass

transforms into a black hole equivalent in single bumps,

which are proportionate factors of the Golden Harmonic

Ratio 1.618034.

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º ±±±±±±±±±±±±±±±±± GENERAL CONCLUSIONS ±±±±±±±±±±±±±±±±± º

º ±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±± º

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The fundamental point of view adapted for much of the

preceding, is to consider that gravitational relativistic

effects are steady state. Ie., the gravitational source is

simply sitting there doing its relativistic thing.

And so there are no gravitational accelerations of a kind

which involve motions of points of center, when understanding

certain of the effect's basic properties, such as the effect

on the original mass of the gravity causing the effect.

Throughout the gravitational relativity explorations of Part 1,

the perspective was entirely from the perception of different

mass aggregates being squeezed within the same unchanged radius.

In practice, the only radius used was the radius of the

Sun, as it is presently measured empirically in this solar

system. That the Sun's radius can be presumed to be reduced

slightly by the relativistic effect of gravity has been taken

into consideration, but has not been explored through any of

the possible permutating effects that changes to the radius

might have. In short, the studies involved variable densities.

The very nature of gravitational relativity implies permuting

effects due to gravity on all of the parameters involved, for

instance on all of the terms in EQ W. The sheer magnitude of the

job of trying to explore all possible combinations of permutations

involving just R vrs M for this solar system, for instance, has

not been explored here.

Which leaves wide open a very important question. In the

circumstances so far described, there is no proof that the radius

of a mass aggregate is the bottom line through which important

gravitational relativistic manifestations are to be observed.

This in no way suggests that a proof should not be forthcoming.

It so happens that a constant radius (in this case the radius

of the Sun) is very convenient for displaying many important

manifestations of gravitational relativity and black hole

correspondences. It appears to hold together a thread of logic

though many physically dissimilar events, including standing stark

still (gravity relativity) and in motion (special relativity).

Such stark realism between the relativities would be a hard

(if not impossible) task to monitor if the confinement radius

was allowed to be mutable.

So, the Sun radius is freely used as a constant

for exploring different stark manifestations.

ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ¿

ÛÄ´ MASS DENSITIES IN A CONSTANT RADIUS ³

ÀÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÙ

It is clear (as shown in many of the preceding demonstrations)

that the existing Sun radius might in some way be of fundamental

importance. Not necessarily in core physics of the universe as

a whole, but at least in core physics of the solar system.

This is seen in the interphased mass congress states involving

« units of Jupiter's mass, as discussed in Part 1.

In the various relativistic explorations, the Sun's radius has

been willfully maintained as a constant value through different

discrete changes in mass aggregates studied. (This applies to the

corresponding planet masses explored, and is not meant to apply

to any special relativistic effects explored).

Dynamically, a change in mass within the same radius usually

translates into a change in density of the aggregate.

In other words, density pressure may be a part of the cause

and effect, or at least may have originally been a part of

the cause and effect, prevailing at the time of this solar

system's formation.

This may be a clue regarding the unusual solar characteristics

observed; where different discrete units of mass (including

mass particles said to be a part of total mass aggregates)

are seen externalized as planets orbiting far from the major

field of the Sun.

The mystery is that the particles are orbiting well

beyond the significant radius of the inducing effect.

The external factors include planet masses which are a

part of the mass aggregate inducing significant effects.

One particular planet is Jupiter. Other planets are

clearly related to the induced effects, but their masses

do not seem to be included in the mass aggregates. These

planets are Venus and Mars.

It may be that concomitant to gravity relativistic

effects gained with the Sun's mass, special relativistic

effects are also gained. But rather than being produced

in the form of increased mass per se, the special effects

become produced in the form of velocity which can translate

directly into angular momentum, resulting in at least some

of the induced influences being flung into orbit thus carrying

away discrete units of relativistic effect in the form of

discrete quantities of angular momentum. This is only a

thought, probably ridiculous.

(In a casual thought, if a gravitational body also

induces a synonymous relativistic effect (motion) the

motion has no real way to go forth in itself, since

ideally all of the effect of motion is equidistantly

applied to a sphere (the gravitational body). In this

scenario, the motion portion is thrown off (externalized)

in order to be expressed).

ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ¿

³ A QUESTION REGARDING RELATIVISTIC ³

³ MASS EFFECT AND QUASARS ³

ÀÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÙ

These following remark are purely conjectural.

Let's suppose that certain relativistic effects induced by

gravity seem to be incompatible with the basic gravity itself.

In other words there are two aspects to gravity: the original

(naked) gravity for any material, and the relativistic effects

caused by that gravity. In this supposition, some relativistic

nature cannot exist within the naked nature, and so is

externalized at long distance.

The externalizing is guessed as either by a throwing off

(forcibly casting forth) or by a remake (as if in leaping

from here to there, where 'there' is a predetermined position

in some kind of latent underscore pattern involving the gravity

field). (In high energy physics, many sub atomic particle

interactions are depictable as occurring simultaneously in two

places at once, where an event at one place directly effects

the event in another place even though nothing but thought

can transfer between the two places). A third form of ejection

might be by the simple virtue of an outthrow of discrete bits

by angular momentum.

In the workings of gravitational relativity, several things are

at issue. There is an original mass, plus the original mass's

augmentation due to the relativity of the mass's gravity. There

can also be more mass added into the conglomerate at any time.

Which results in a hike in the augmentation effect due to

strengthened relativity.

It can be supposed that if an increase in mass takes place within

a given radius, resulting in a hiked relativistic mass augmentation

due to the added mass, which in turn causes jitters so that

something of the hike has to be expunged or externalized from the

gravity field which is generating the effect in order to satisfy

an esoteric yearn to solve the jitters, then where added mass is

accreting into a large black hole some of the relativistic gain

is transferred to an external position outside the black hole.

Since very high energy effects are involved with the black

hole anyway, it is not difficult to picture that the expunging

can appear highly energetic. What the mechanism is that could

transfer the effect to an external place is not here conjectured

but can be supposed. For instance:

A long arm recurrence (here and also there) is one mode.

An intense radiating away (or bleeding away) of some of

the change upon the event horizon boundary, in alternative

to allowing a change to go ahead in the relativistic regions

of the boundary size itself, is another mode. This is made more

viable if it is suggested that the black hole yearns to maintain

some form of internal density which has no further relativistic

influence inside the black hole.

And finally, a conversion of units of intrinsic spin

as energy, (conversion from spin to propagational energies),

is another, if possible.

ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ¿

³ A QUESTION REGARDING RELATIVISTIC ³

³ EFFECT ON THE GRAVITATIONAL CONSTANT ³

ÀÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÙ

There is also the prospect that the gravitational constant itself

is modified by the relativistic effect of gravity. In retrospect,

it is not readily apparent as to whether the gravitational constant

would weaken, or strengthen, relativistically, given larger and

larger masses. The present day mode of thought is to consider that

the gravitational constant might grow relativistically stronger.

On the other hand, Equations Y to Y-2 above suggests that

the gravitational constant relativistically weakens through

increasing mass aggregates.

On yet another hand, it has not been proven that a mass

relativistically increases (as opposed to decreases) by

gravitational relativity. A stable picture should ensue,

albeit not exactly the same as the picture described in

Equations T through Z-11-4, if a mass decreases by its

gravitational effect, such that the mass's confining

radius might increase, or decrease, and the gravitational

constant also might increase, or decrease, etc.

Such possibilities are not considered in the above shown mass

congresses involving the Sun and certain planet masses. If the

gravitational constant is in fact modified by relativity, then

the apparent mass of the Sun is still valid, but the original

mass should not be precisely that as determined by the apparent

mass MM, minus the apparent mass times the effect; as shown in

EQ W-1.

In fact all of the parameters of Equation 1 below in APPENDIX B

(except for the speed of light) might be in states of modification.

These parameters include G and M, where a mutable value of G therefore

is internally influencing the value of M.

In any case, the resulting gravitational relativistic mass

congresses between the Sun and planets as viewed herein are

in their resultant apparent states (involving the masses as

seen in the domain of the solar system and empirically measured).

And finally, the direct tie-ins between gravitational and

special relativity are balanced correctly anyhow, according

to the parameter choices selected for the preceding, to

infer then portray their handshake nature.

In a casual thought, if a gravitational body also induces

a synonymous relativistic effect (motion) the motion has no

real way to go forth in itself, since ideally all of the

effect of motion is equidistantly applied to a sphere (the

gravitational body). In this scenario, the motion portion

is thrown off (externalized) in order to be expressed.

It is not hard to speculate that the special relativistic

mass gain for the stationary object (gravity source) can be

(at least in part) thrown off in the form of energy, since

e=mCý. In which case a lot of energy will be visible per

small quantities of involved gain in mass.

In this speculation, there is a pure (rather than nuclear)

conversion of mass to energy.

In unstated allusions are hints that gravity and special relativistic

effects work hand in hand, with perhaps the special relativity effects

being more and more suppressed the higher the gravity. But as already

said, any special relativity associated seems to be incompatible within

the naked gravity itself and so ends up externalized (for instance) as

certain planets, as if a velocity is induced in a gravity mass at rest

which can leave its source, via angular momentum in the velocity.

ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ¿

³ A QUESTION REGARDS THE GRAVITATIONAL ³

³ CONSTANT AND THE GOLDEN HARMONIC RATIO ³

ÀÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÙ

Whereas in another conjectural possibility, going in the other direction,

it may be possible that the apparent quantum jump in relativistic effects

seemingly embodied in operators involving the golden section ratio (the

golden harmonic), do not actually occur in the physical universe.

For instance if the universal gravitational constant did change in

value under increasing relativistic influence, it may result in a

situation where such things as mass and space increase smoothly toward

infinity after all, with the quantum leap from a plateau straight to black

hole parameters smoothed out or voided by relativistic changes in the power

of the universal gravitational constant.

Ho hum, speculations can be rather boring.

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ÉÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍ APPENDIX A ÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍ»

º ±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±± º

º ELEMENTARY PARTICLE MASSES º

º ±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±± º

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In high energy physics experiments, particles such as the

electron or Proton are being accelerated to velocities said

to be virtually at the speed of light.

How is this possible?

This is possible because the Mass/Radius ratio of the proton

(as an example) is extremely small, compared to the Mass/Radius

ratio of the Sun for instance. The Mass/Radius ratio of the Sun is:

(Mass 1.991 x 10 to 33 grms) / (Radius 6.963 x 10 to 10 cms)

= (2.859 x 10 to 22 grms/cms)

which itself is very small compared to the ratio of a black hole

having the Sun's radius, in which the Mass/Radius ratio is then:

Mass = (Cý x R) / 2G = (4.689 x 10 to 38 cms)

And:

(Mass 4.689 x 10 to 38 grms) / (Radius 6.963 x 10 to 10 cms)

= (6.735 x 10 to 27 grms/cms) = CR

Note that value (6.735 x 10 to 27 grms/cms) = CR is actually

a physical constant for every black hole, and is equal to the

ratio of the speed of light divided by twice the universal

gravitational constant, as in: (Cý/2G) = CR = (Mbh/Rbh)

when Mbh and Rbh are the Mass and Radius (event horizon) of

a black hole, C is the speed of light, and G is the universal

gravitational constant.

When, otherwise, a normal M and R are transfigured by special

relativity into a new black hole having mass M+ and radius R-,

then: CR = (M+/R-), where, CR still has the constant value:

(6.735 x 10 to 27 grms/cms).

In the large scale world of normal events the magnitude of

the Sun's mass at (10 to +33 grms) is well above the magnitude

of the Sun's radius at (10 to +10 cms).

In the world of the very small, the situation is

quite reversed. For example the mass of the proton is:

1.672 x 10 to -24 grms

whereas its radius is reverse in magnitude,

in the much larger range said to be about:

1.32 x 10 to -13 cms.

This produces a Mass/Radius ratio (proton Mass/proton Radius) of:

= 1.239 x 10 to -11 grms/cm.

Clearly, a proton will have to accelerate to an extremely

high velocity, virtually to the speed of light, in order

for special relativistic effects to transfigure the proton's

effected mass M and radius R into the (M+/R-) = CR parameters

of a new black hole.

The Mass/Radius ratio of the proton will have to grow by a

magnitude of (5.435 x 10 to the 38), in order for the accelerated

proton to take on the look of a black hole having mass M+, and

radius R-, and a (M+/R-) ratio equal to CR.

A calculation to determine what velocity the proton needs to

move in order for the transfiguration, is impossible to complete

with devices having mediocre accuracies good to only (say) 13

significant figures.

The calculation to determine the proton's velocity first requires

knowing what the gravitational relativistic effect Eg is for the

proton's mass and radius. Effect Eg is too small by many magnitudes

to be mechanically calculated by a device of 13 significant figures.

Given a device with greater accuracy, the resulting Eg effect for

the proton is divided into the speed of light, to give the velocity

at which the proton must travel to relativistically transform into

a black hole. The velocity will be the same as the speed of light

to many significant figures, before the digits begin to deviate.

(Unless there is (previously unsuspected) a gate in the velocity

of light, at which a particle (for instance a proton) might in fact

make a quantum leap to black hole magnetudes at a point that is at

some measurable factor less than a total 100 percent of the speed

of light).

ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ¿

³ Proton Comparative Mass Density ³

ÀÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÙ

To give a comparison on just how nebulous is the mass

density of the Proton (how little in the way of gravity

that Proton matter presents), the mass density of a Proton

is on par with about 1 gram of matter wisping in a shell

whose width is equivalent to 10 times the full diameter

of the orbit of the Moon around Earth.

If the on par Proton mass were gathered together for the protion

which occupied the actual orbit of the Moon, it would be a moon

weighing about .48 grams circling the Earth.

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ÉÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍ APPENDIX B ÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍ»

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º BASIC EQUATIONS º

º ±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±± º

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Advanced details of a black hole, such as a paradigm model

of a charge membrane for instance, are not considered.

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º ±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±± º

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º RELATIVISTIC MECHANICS º

ÈÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍ¼

EQUATION 1

ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ

³ 2G M Finding gravitational relativistic

Eg = ³ 1 Ä ÄÄÄÄÄ effect Eg, for a given mass M and

\³ Cý R a given radius R

EQUATION 2

(1 Ä (Eg)ý) x Cý R Finding mass M for a given

M = ÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ radius R and a given

2G relativistic effect Eg

EQUATION 3

2G M Finding radius R for a given

R = ÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ mass M and a given gravitational

Cý (1 Ä (Eg)ý) relativistic effect Eg

EQUATION 4

2G M Finding the Schwarzschild

R' = ÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ radius R' of a black hole's

Cý event horizon. When effect

E = 1, then factor (1 Ä (E)ý)

is 0, which drops from EQ 3

leaving EQ 4

EQUATION 5

Cý R' Finding mass M' needed for a

M' = ÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ black hole whose Schwarzschild

2G radius is given as R'

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º GRAVITATIONAL MECHANICS º

ÈÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍ¼

EQUATION 6

Vý R Finding the mass M for

M = ÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ sustaining a body orbiting the

G mass at a given velocity V at

a given orbiting distance R

EQUATION 7

G M Finding the orbit R of a

R = ÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ body around a given mass M

Vý at a given orbital velocity V

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ÉÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍ APPENDIX C ÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍ»

º ±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±± º

º PURE MASS CONGRESS º

º ±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±± º

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ÈÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍ¼

This information is presented as a separate tableau and

has no self evident bearing on any of the explorations

and conclusions of the above statements. The following

shows that generally:

(« THE SUM OF THE MASSES OF MERCURY, VENUS, EARTH, MARS),

PLUS THE MASS OF THE MOON, EQUALS THE MASS OF THE EARTH.

(« the sum of masses N1 to N4) + N5 = N3

TABLE 10

Masses + N1 Mercury = .33020 x 10 to 27 grms

+ N2 Venus = 4.8683 x 10 to 27 grms

+ N3 Earth = 5.9760 x 10 to 27 grms

+ N4 Mars = .64181 x 10 to 27 grms

ÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍ

= 11.81631 x 10 to 27 grms

ÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ

« = 5.908155 x 10 to 27 grms

ÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ

+ N5 Moon = .07350 x 10 to 27 grms

ÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍ

Equals N3x Earth = 5.981655 x 10 to 27 grms

ÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ ÄÄÄÄÄÄÄÄÄÄÄÄÄÄ ÄÄÄÄÄÄÄÄÄÄÄÄ ÄÄÄÄÄÄÄÄ ÄÄÄÄ

Inequality N3x - N3 = .005655 x 10 to 27 grms

There is an extra (+ .005655 x 10 to 27 grms) in the N3x

result, which is unexplained. There is no other Moon in

the inner region of the solar system for instance.

The aggregate mass of the asteroids seems to be too

small by a factor of 10 to be this inequality. So the

extra (.005655 x 10 to 27) does not meaningfully represent

the mass of the asteroids. What the mass inequality may

represent is not clear at all.

ÉÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍ»

º ±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±± º

ÌÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍËÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍ¼

º GENERAL MASS CONGRESS (summary)

ÈÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍ¼

The Sun's mass plus « the mass of Jupiter added, can be shown

to induce a gravitational relativity mass increase effect which

is exactly equal to the mass difference between the planets Venus

and Mars.

ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ

³ 2G x (Sun mass + 1/2 Jupiter mass)

(Sun effect ratio) = ³ 1 Ä ÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ

\³ Cý x R

C = Speed of light

G = Gravitational constant

R = Radius of the Sun

K (Mass augmentation) = Sun mass - [Sun mass x (Sun effect ratio)]

K (also equals) = Venus mass - Mars mass

The same result is handled (in a slightly different way)

in the section beginning with TABLE 1 of file RELATIVE.1 .

See TABLE 11 next below.

TABLE 11

ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ¿

³ K = 4.226490 x 10 to 27 grms ³

³ = (Venus mass - Mars mass) ³

ÃÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ´

³ C = 2.99792458 x 10 to 10 cms/sec ³

³ G = 6.6720 x 10 to -8 cms3/grms secý ³

³ R = 6.96265 x 10 to 10 cms ³

ÃÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ´

³ ³

³ Planetary masses Data is from Table 1 in ³

³ the file RELATIVE.1 ³

³ ³

³ Moon = .0735 x 10 to 27 grms ³

³ ³

³ Venus = 4.8683 x 10 to 27 grms ³

³ Earth = 5.976 x 10 to 27 grms ³

³ Mars = 6.4181 x 10 to 26 grms ³

³ Jupiter = 1.901 x 10 to 30 grms ³

³ ³

³ Sun = 1.9888 x 10 to 33 grms ³

³ ³

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ÉÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍ APPENDIX D ÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍ»

º ±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±± º

º FOOTNOTES º

º ±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±± º

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ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ¿

±±±±±±±±±±±±±±±±±±±±±±±±±±±±± Footnote 1 ±±±±±±±±±±±±±±±±±±±±±±±±±±±±±

ÀÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÙ

ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ¿

ÛÄ´ RELATIVITY EQUIVALENCE PRINCIPLE ³

ÀÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÙ

EQUATION Z-21

1 - Egý = 1 - Esý

One minus the square of gravity's relativity effect,

equals one minus the square of special relativity's effect.

ÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ

EQUATION Z-22

1 1

ÄÄÄÄÄÄÄÄÄÄ = ÄÄÄÄÄÄÄ = Nx

1 - (Eg)ý (Es)ý

The reciprocal of one minus the square of gravity's relativity

effect, equals the reciprocal of the square of special relativity's

effect.

This equality is equal to the ratio of a gravitational mass divided

into the mass equivalent of a silent black hole partner for the

gravitational mass.

ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ¿

±±±±±±±±±±±±±±±±±±±±±±±±±±±±± Footnote 2 ±±±±±±±±±±±±±±±±±±±±±±±±±±±±±

ÀÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÙ

There is recent speculation that events in electroweak theory and

gravitational theory may converge to similar kind at very small

distances of the order of (10 to -28 cms) to (10 to -33 cms), said

to be possible at the time of a so called big bang. Whether or not

the unified field behaviors as disclosed in the above equations are

favorable or distasteful to such a big bang outlook is not in any

way considered to be of our concern, here.

ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ¿

±±±±±±±±±±±±±±±±±±±±±±±±±±±±± Footnote 3 ±±±±±±±±±±±±±±±±±±±±±±±±±±±±±

ÀÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÙ

In use of the Sun's radius as a constant confinement delineator for

various mass aggregates and equivalent black hole masses, it is

acknowledged that the amount of extra mass poured into the existing

size of the Sun has to be very large to make a black hole.

For example the amount of mass is about 235,000 times the mass of

the Sun, poured into the space occupied by the Sun, to make a black

hole. This is of course physically unrealistic, (that that mass can

pour into the Sun and the Sun stay the same size). But having a

constant radius makes it far easier to keep track of various effects.

The physical universe is actually quite different. For instance the

radius of the Sun will dramatically expand with any appreciable amount

of mass poured into it.

But this is iffy. For example if the extra mass is iron, the Sun's area

will expand according to high material density. If the matter is helium

or hydrogen, the enlargement of the Sun's radius will be substantially

more.

In either case, since the radius is expanding (with more matter

poured in), a black hole mass plateau will be eventually reached

at a much different enlargement in mass than the factor of 235,000

times mentioned above. As you can see, pinning down parameters into

'look and see' constants, with this sort of thing going on, is like

trying to pin down the behavior of silly putty.

And so events herein have been scrutinized in detail from the point of

view of a single unchanged basic radius (the Sun radius), used as a

convenient point of reference to compare significant related events

that involve that single radius.

ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ¿

±±±±±±±±±±±±±±±±±±±±±±±±±±±±± Footnote 4 ±±±±±±±±±±±±±±±±±±±±±±±±±±±±±

ÀÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÙ

The Golden Harmonic Ratio 1.61803398875, cited in this disclosure, is

an absolute number value gained as (« of û5) plus .5. This number is

also known as the Golden Section. The number can functionally permutate

through a bewildering array of directions on its own, with many

particular permutations appearing in the construction of 5 sided

geometrical figures. A particularly well known physical manifestation

of the Golden Section is the proportion of a Golden Rectangle. Other

well known manifestations include spirals and progressions occurring

in nature, some based on the Fibonnaci number series. These are said

to include galaxy spirals and Bode's Law for the solar system, however

some researchers think the astronomy occurrences appear to be as much

a case of co-incidence as anything.

ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ¿

±±±±±±±±±±±±±±±±±±±±±±±±±±±±± Footnote 5 ±±±±±±±±±±±±±±±±±±±±±±±±±±±±±

ÀÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÙ

The Constant Ratio CR cited above as being M+/R- = Cý/2G

also gives instant readout on such curiosity questions as:

1. How much mass is contained in a black hole whose radius

is 1 cm? The answer is:

6.735275620 x 10 to 27 grms In that:

Cý R Finding mass M needed for a

M = ÄÄÄÄÄÄÄÄÄÄÄ black hole whose Schwarzschild

2G radius is given as R = 1 cm

Note that the mass has the same

digital value as ratio CR

2. What confinement radius is needed for a black hole whose

mass is 1 grm? The answer is:

1.484720234 x 10 to -28 cms Note that this is the digital

reciprocal of the value of the

mass M of question 1, in that:

2G M Finding the Schwarzschild radius

R = ÄÄÄÄÄÄÄÄÄÄ R event horizon of a black hole

Cý whose mass is 1 grm

ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ¿

±±±±±±±±±±±±±±±±±±±±±±±±±±±±± Footnote 6 ±±±±±±±±±±±±±±±±±±±±±±±±±±±±±

ÀÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÙ

In the most unusual circumstance of a velocity ratio V/C being

equal to a mass proportional ratio M1/M2, then gravitational

relativistic effect Egs is equal to ratio M2/M1.

For instance, let the ratio of one mass M1 divided

by a smaller mass M2 be called Rn.

ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄ

³ (C/Rn)ý ³ Vý

Then: Ess = ³ 1 - ÄÄÄÄÄÄÄ = ³ 1 - ÄÄÄÄ

\³ Cý \³ Cý

And: Egs = 1/Rn

ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ¿

±±±±±±±±±±±±±±±±±±±±±±±±±±±±± Footnote 7 ±±±±±±±±±±±±±±±±±±±±±±±±±±±±±

ÀÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÙ

In case there is a concern over what has been done above, (in the

conjecturing of major effects as seen wrapping around changes in

the rest state of masses through two different synonymous modes of

relativity), there are no rules that exclude a direct synonymous

tie-in between both gravitational and special relativistic effects.

For example, it has been experimentally confirmed that time slows

in the proximity of a gravitational field. A main question which

can be asked is:

At what velocity does a mass have to be moving, to induce a

slowing of time (time dilation), that is equivalent to the

field effect from the gravity generating a relativistic

effect of equal magnetude on the flow of time?

The time dilation effect of a velocity in special relativity is

straight forward. That is, at a given velocity, events in time

for the moving object will seem slowed by a specific amount as

seen by a stationary observer.

In the case of gravity effect, the situation is more ambiguous.

The effect of time dilation depends on where the object is in the

vacinity of the field generating the effect. Closer to the field

means a greater time dilation. But in large scale objects such as

the Earth or more so the Sun, closeness empirically means close

to the surface, for example, rather than close to a mathematical

data point or to a fixed velocity.

In our explorations above, real time positions moving here or there

in the embraces of a varying gravity field are not at all in the

picture. The basic 'need to know' speaks through simple statements

consisting of 'how much mass' in 'how much radius' to result in 'how

much effect' in the gravity will effect time.

The main point of view has been in terms of gravity as a mass source

extending in a boundry termed the gravity body's radius. In this view,

events can be measured from the radius and extending outward from the

radius, according to a mass total located at the radius, where the

radius itself is measured from a single point of center.

In questioning a mass augmentation effect in the gravity, the issue

can be more clear cut. Specifically, given a finite mass and a finite

radius, what gravity relativity effect is generated, and how much

does the effect increase the original mass generating the effect?.

From this steady stateness, it is easy to ask across to special

relativity wishing to know what velocity is required to generate

an identical effect.

However, in closer introspect, a greater question has also been asked.

And that is, given a mass enhancement and space contraction in special

relativity, at what velocity does a mass have to be moving in order

for it to transfigure into a black hole? Looking at things from another

point of view the question can be put in yet another way; to wit:

At what velocity does the mass have to be moving in order

for special relativistic effect (increasing the mass's mass

and collapsing its radius) to cause the mass's flow of time

to come to a standstill? The answer is found in an M+/R- ratio,

which is calculated through special relativity using the mass's

gravitational effect to state the equivalent relative velocity.

This type of thinking is out in the open in the material of Part 4.

It is summarized in the relationships enclosed in TABLE 8 under

'Pure Math Connectors' above.

ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ¿

±±±±±±±±±±±±±±±±±±±±±±±±±±±±±± FINISHED ±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±

ÀÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÙ

ÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ

Planetary Data is from the following reference source:

UNIVERSE by Don Dixon, Houghton Mifflin Co.,

Boston, 1981 (References found at

the back of the book)

ÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ

Signed: Rhae. S. Livingstone

Address: 78072, Cityview, Nepean, Ont, Canada K2G 3J0

Phone number: Area code: 613 820-9450

Rhae S. Livingstone. Canada.

Peace Power and Plenty everyone.

ALL DONE

STORY FIVE

THE EXPERIMENTS

THE FIRST PART - A TACTICAL TEST - BEGINS AS FOLLOWS......

The two cadets have been taken to the secret place, and are now

aboard and alone in their separate spacecraft experiencing outer space

in real time.

Of course Earth's astronomical thinkers are very interested in a

recent nearby event. They have sent the two space craft, each containing

a cadet occupant, in great haste to observe the supernova and ensuent

new neutron star at close quarters.

All very secret, of course.

But on the way there is an unexpected change in plans.

Sluggo is commanding the first craft, Nancy the second.

The two craft are even now separated by a only small distance and

are orbiting in toward the unexpected object at different angles of attack.

Their glide paths are diverging increasingly at very high accelarations like

two moths willy nilly around a lightbulb, even though only a few hundred

meters separate them. Both were theoretically travelling at the same velocity

at one point. Sluggo is now arriving in a little closer in to whatever it is

that is effecting their intership communcations so radically.

Nancy, really puzzled, calls across to Sluggo, saying; Sluggo,

you are looking egg shaped.

Sluggo calls across to Nancy, saying; I'm having trouble

unscrambling the math for the relativistic changes I see in you around

this FAR OUT OBJECT!. One thing I can say is that your lights are rapidly

changing frequency, blue shifting like a soprano sliding from lower C to

a high screech right off the register!. Wow ! what an effect !

Sluggo, Be careful! Nancy exclaims in alarm; read the clues

as doppler shifts by gravity, not like red shifted distances in the

universe, that object is far closer to you then you think!

Righto; acknowledges Sluggo.

Fortunately the two caroom off and away on their first trajectories.

And having sailed on the outswing back into space, are now hoving in new

arcs closing fantastically fast back toward the object. Nancy is trailing

as before, offset a short distance outward and behind Sluggo.

That super high pitched screech from you the last time in was

quite a blast; says Sluggo, as things begin to rev up again this time

in earnest. By now they are closer than ever before to the strange object.

I know what you mean; says Nancy. You're time is slowing right down.

I can see every muscle on your face move as you writhe to make a smile toward

me. Far out; Nancy adds; I think you just blinked, but it took so long that

I'm not sure if you actually winked, or fell asleep for at least 10 seconds.

And you're ear and grin are travelling sideways across the screen as your

light bends.

Nancy, we have a problem; Sluggo says. I have only been talking

to you for a few seconds. And I'm staring straight at you, I think.

Oh ! says Nancy. Nancy starts to rapidly readjust some control

settings in her spacecraft.

Sluggo interrupts eventually; you're too dazzling. You're

turning into a high frequency hot spot with no velocity on the graph.

I'm frantically shifting the callibrations of my scopes into the X ray

range to try and keep you in electromagnetic focus. There, I think I've

got some of my computer humming intelligent again. Oops. Nope.

How far are you from the surface of the horizon; Nancy asks,

desparately worried. Nancy has been furiously updating the time factors

in her computer, just to carry on a semblence of the conversation.

About 10 times the width of my spacecraft; says Sluggo.

That explains it; says Nancy. I'm just on the outside of about

1.618 times the width of the object further out than you and holding

fast, but you look so SMALL!, far farther in than you actually are.

Are you still in a curving trajectory, right now?, I can't tell anymore.

Let's talk about it later; says Sluggo in a way that is getting

really weird. You're sounding like a bee to me.

I'll repeat; says Nancy; these hour long pauses between each word

from you are starting to wear me down. Notwithstanding, your voice

sounds like a series of long strong earthquakes.

Roger; says Sluggo, by the end of the next day. And a few days

later his mouth muscles have moved enough to start forming the next

word, Nancy.

Anyway, it is too late. Nancy has managed to get away in the

nick of time. But the last thing Nancy remembers about Sluggo and his

spacecraft is an entity so far red shifted that it seemed to have faded

into nothing, or nearly so, like the last slow hissing redshifting coal

of a campfire, finally dimming out in the dark of night. She caught the

last of him receding far away near the infinite wavelength end of the

spectrum. But even then she wasn't sure if it was a residue of Sluggo's

last word, or static from the background radiation of the universe.

THE FIRST PART - THE TACTICAL PART - FINISHES AS FOLLOWS.....

Thank god; the supervisor says admiring Nancy exiting the

simulator with tears from the lonely feeling in her eyes; that the

stimulator, er, simulator didn't break down with all the neat stuff

you had going on. But, you beat the no win experiment.

But; the supervisor continues talking non stop; how am I going

to explain the success of this experiment to Sluggo. He thinks he lost

a contest, and won't come out until his 'garbles are collected from

the residue of that fatal mistake', quote. We have to, quote, 'wait

till all systems are slow again and we've turned off the event horizon'.

Turn it off!. Can you believe that guy?

The assistant's are in there now; the superivisor continues.

What an idea you had, Nancy, setting up a gain spot in your computer,

thrusting against the turbo of gravity, to stand station keeping in

one position at length from the object so as to read all of the effects

as constants, rather than accelarations changing willy nilly back and

forth through the continuums. Don't forget, the only way either of

you were expected to really see what was happening was to monitor the

black hole from both ships simultaneously, or at least to try to.

That's an idea none of us had; the supervisor continues talking non

stop in the excitement of the new situation here at simulator headquarters;

till you entered the simulator a week ago. I guess you know, the whole of the

experiment was supposed to be a three body problem to make it impossible to

calculate the effects fast enough between the two of you, once you got

inside a time event barrier some distance away from the event horizon,

due partly to the time it takes for electronics to process the

information. All theoretical of course.

Indeed, what happened is; says the supervisor continuing;

once you had your own effects in hand by standing still in steady

state, all of the changing effects you saw came only from Sluggo's

no win plunge into the pit. And THAT will be a piece of pleasure

to resolve in academy land in week's to come, that's for sure!.

Nancy is standing looking sidways at the supervisor during this

time. Watching her private thoughts carefully she speaks not. Thoughts

leak. For sure Nancy is busy keeping lesser judgements from getting loose

that might spoil friendships. Uh huh, she keeps saying. Yes, uh huh.

In times of excitement the supervisor tends to talk non stop, can't

control the hyper side of his career.

At this moment, Nancy and the supervisor are standing around

waiting to see what happens when Sluggo makes exit. To wit, did Sluggo

grow a beard, (Nancy wants to know), or did growth relativistically slow

down? Did Sluggo's psychological perception of time shut off the flow of

hormones whispering grow! grow! to his beard pores.

The supervisor is still motor mouthing at a mile a minute, saying;

but, what made it so hard for Sluggo is that in the last fleeting seconds,

Sluggo had realized that you were still out there, Nancy, standing still,

whole sound and perfect, free of the no win equations which all of us have

had to endure, up until now, in gravitational relativity. And, for the life

of him, Sluggo didn't have time to figure out what you had done to be there.

Who would have thought that counter thrusting at a standstill again the pull

of gravity would change the fundamental point of view so fantastically. What

a new field to ponder, steady state effects of gravitational relativity!

This breakthrough, the idea of a gain spot to monitor constant

effects of gravitational relativity, is a surprise, an insight in the

field that was unsuspected by all of us.

And now, that grunting wreck just now exiting the simulator, is,

you guessed it, Sluggo, looking for Nancy for some serious questions to

some serious answers, you see, Sluggo is the one who had studied hard,

knew every page of the textbooks.

Notwithstanding, there are other things Nancy is aware of.

First is obvious; relativitistic effects pursuant to Earth's gravity

are actually so slight as to be hardly calculable. Even though effects on

time can be suitably inferred from phase shifts in frequencies, in fact

everyone believes any models of relativistic effects of gravity (except

for time) are futile at the Earth. Such effects are so minisculely felt;

given the Earth's puny gravity relativistically speaking, that they show

up more or less as zero in equations. It isn't until more massive power

fields the size of the Sun or a black hole are felt, that the effects

become obvious.

For that matter, it isn't until in the proximity of really giant

local gravity that the effects become starkly highlighted. Close in,

such as two or so times the radii further away from black holes, and

the effects become fully a geometry. At this level, effects can be

calculated exactly. Certain effects can be not just pointed out, but

data casted, factually calculated, by ordinary techniques of plain two

dimensional geometry.

Nancy has already seen; while couped up in the simulator for a

week; that via geometry, bits and pieces of gravitational relativity

information can be added and subtracted, to come up with other bits and

pieces of information, producing the same results as are otherwise

factored in the transformations of gravitational relativity equations.

This is not modelling information, this is the actual datas, the details

and decimals right to the last digit in accuracy. This rigorous geometry

is best seen in steady state effects, ie. those that are found when

standing still, (station keeping) at a fixed point, (a gain spot) a

constant distance from the event horizon of the field of the mass

which is causing the effect.

But it wasn't just the standing still in a (gain spot) which

counts for so much. It is also that something else seems very relevant

about the exact position that she had chosen to stand still in, precisely

1.61803398875 times further out than the black hole's event horizon. This

number happens in fact to be the famous Golden Ratio Constant of nature.

Even so, it was the incredible thing Nancy had done which nobody

has yet realized, which was to calculate the Gravitational Relativistic

effects for the gain spot in the emergancy via Special Relativity, using

sudden new interfaces she'd uncovered between the two relativities on the

spur of the moment.

And even as the trio walk away from the simulators in a cluster

toward the outer door, Nancy is seriously thinking about some remarkable

new twists and turns regards the theories of high energy gravity, and the

two kinds of relativities. Notwithstanding that Sluggo is muttering strange

arguments about how the black hole coulda got ahold of his beard, because

he has none.

- FINISHED -

-- Continue with STORY.6 --

Item F if using the SHORT STORY menu.

STORY SIX

THE SECOND EXPERIMENT

NEW, IMPROVISED, MECHANICAL MODELS FOR GRAVITATIONAL RELATIVITY,

STARRING NANCY AND SLUGGO, RELATIVITISIC SPACE CADETS

Nancy and Sluggo have just been rounded up to take their turn

at trying to describe effects in another routine experiment. It is

part of Nancy's and Sluggo's space training at the Academy.

The experiment is being conducted by the space agency, whose

theoretical lobbyists have continued to sniff the wind for a long time.

It is because, the lobbyists hope, a blockbuster of a breakthrough

of an idea will happen, before the turn of the century, to resolve a long

standing dispute, posed once upon a time by one of the Agency's genius

whizz kids. The prize for intellectual victory is world fame, with enough

prize money tossed in for a trip to the old country.

So they really want to do it to us this time; says Sluggo, as if

continuing a previous conversation, as the two cadets enter the room.

You know what the joke is, don't you?; Sluggo continues, shooting

off his mouth a bit to get rid of a bit of the nervous static. They are

going to try and pick our brains. The answer that wins has to be guaranteed,

mind you, an answer which the physicists of the world can really sink their

teeth into. At least until they have combed through the good stuff. And

then the short circuits and irreconciliable difficulties will make it

plain that the answer is no universal field theory. And start they

will all over again, looking for a theory that's really got it.

Nancy stays silent.

They enter the room and settle in, Sluggo settling down in the

Farstar consul to the left, and Nancy easing into the Farstar consul

to the right.

You know what it all means, don't you? Sluggo asks. At the moment

Sluggo is pushing a couple of buttons in front of him, getting ready. A

small handfull wants to keep at it, trying to make the whole of creation

fall out to some lowest common denomonator in images and likenesses. You

know what I mean, empirical, room temperature, and, oh, roughly human

sized. The bottom line is, is they hope to find a description which

includes a three way space with a time universe, in which we are seen

to fit as humans, nonanomously. Ho Hum.

Nancy gives Sluggo a weird look, because now is not the time to

be philosophizing like a bad science fiction writer, or even worse, an

eager physicist.

Nancy and Sluggo don't know it, but the upcoming experiments, such

as today's, are actually rigged. The cadets aren't actually expected to

come out of the test with anything like an answer. It is the speed of

their thought time that is being tested. This is what the two cadets

have not been told.

Your tendencies to go into hyperventilated intellectualistic-

ifipicationalizingmentestedlyesnessierefesses won't help you this time;

Nancy reminds Sluggo at the start of the experiment, grinning because of

the very long word.

Roger, Nancy; says Sluggo, busy setting the speed of an overhead

casablanca fan, then getting comfortable in the body slot in front of

his Farstar area. Sluggo's Farstar unit is now fully turned on, but not

in stereoscopic mode, whereas Nancy has chosen to function her's in the

glory of full color and 3 Dimensions.

In quick time she has everything ready, as does Sluggo.

Let's get started. Is your Farstar equipment ready?; asks the

supervisor. The supervisor's voice has a slightly hollow ring as if

coming in via long distance telephone rather than from some remote

connection somewhere else in the academy via the two Farstar units.

Yes; reply the two recruits.

In a brief pause before the main event Sluggo inquires of Nancy;

what was that long word again?

Intellectualistic ... ifipicationalizing ... mentestedly ... ah

... esnessierefesses; replies Nancy, feeling somewhat self conscious in

the pauses, having to rethink the word to say it, rather than merely

inventing it over again on the spur of the moment like the last time.

This long word of Nancy's is a bit of a coup, as Sluggo acknowledges

with a long open stare. Each time Nancy practices her long word the word

grows longer. Nancy's word has 62 characters in it today, not one

portion repeated, not bad for an 'Eeble's stultifyer, the longest yet.

Sluggo on the other hand does not have a long word. Instead,

Sluggo has opted for a long prank. It is a plan to use his Farstar unit

in a series of sucker punches based on puny motives, an activity that is

quite uncharacteristic of Sluggo, but nonetheless has Sluggo going for

it at a full 110 percent in this week's games in the lunchroom.

There is a challenge manifesting itself at the academy these days,

headquartered through the lunchroom, an exaggerated excess level which

has source in the kind of thing which occurs in probably everybody's

ordinary work-a-day experience.

The source is a character named Preebe Eebles.

The game is to see who can come up with the ultimate long

word to stultify Preebe Eebles. Or, rather, to do something about

the stultifying absurdities in Preebe Eeble's artificial intelligence

programs. You have to experience Eebles first hand to appreciate why

the long words are interesting, and why the game.

Nancy has said that Eebles is like a walking talking illusion that

interfers with reality.

Oh oh, clango the bell has just rung. It is time to get serious.

Today's experiment begins in earnest, with a concept;

Or rather it begins with a concept test. The test is stated in

simple terms to Nancy and Sluggo as:

"If an ordinary pocket watch is cloned in all aspects in a second

pocket watch which is dispatched at a location in space for awhile while

the first watch is left on earth; and there is no relative motion of any

kind between the two watches such that they remain constant models to

one another; how might the pocket watches model gravitational

relativistic effects on space and time and mass?"

SPACE! and MASS!; the two recruits exclaim simultaneously.

Sluggo is the first to make a try, faking it, mulling it fast.

Time speeds up in the watch in space; Sluggo utters at last, remembering

the first page of the text book.

Right concept wrong idea; counters Nancy quickly. What is the real

rest state time of the second watch?; continues Nancy, intuiting into

the problem. To know that, you have to find a place in the universe

where space is totally free of gravity, or, is, at least, most free of

gravity. But can you?

The first watch on Earth could be egg shaped, sort of; suggests

Sluggo shortly after, trying another way into the problem. A space effect.

How do you know?; Nancy replies fast; everything around the first

watch, including the lab, the measuring equipment, even your eyeballs and

the shape of your brain, might be warped as well. Meybe that's what is

squeezing your intelligence; Nancy adds.

A few chuckles like distant echoes are heard trickling in from

remote sources through the two cadets' Farstar units.

Well, use the second watch, the one in space, to compare the first

watch; says Sluggo, still thinking fast, perhaps missing part of Nancy's

logic. As everyone knows, Sluggo tends to be too hasty, too lazy, if

there is a lot of peer theory already around a subject. Sluggo tends

to figure that all such peer theory is valid.

Can't; Nancy counters; information has to be exchanged between

the two watches in order for them to be compared, and information itself

changes when travelling either way in or out of gravity from one watch

to the other. Can't weigh the watches where they sit for the same reason.

Nancy is focused deep into the 3 Dimensional recesses of her Farstar unit

as she talks.

I guess there's no easy answer; Sluggo says after blinking his

lips through a long silence.

I think there is; says Nancy.

Know what it is?; asks Sluggo.

Not yet; answers Nancy. But I imagine you have to mechanically

bring the second watch home to another place on Earth.

You go ahead and try; says Sluggo, who finishes off the talk

by saying; Me, I've got to figure out some co-ordinates.

A lot of time passes, a LOT of time.

What are you DOING!; exclaims Nancy suddenly. Nancy has just made

a quick glance across to Sluggo's screen to moniter Sluggo's progress.

Sluggo has been unusually quite for a long time.

Sluggo's screen is filled with dots, some in clusters, some

random. Only a few have labels. And Sluggo is sitting there diligently

putting labels on the dots the long slow hard way, one after the other.

A label here. A label there. Every label different by one digit plus the

next letter of the alphabet in series. The labels are nothing more

elegant than small one-word prompt boxes hanging here and there around

Sluggo's screen. The problem is there are so many of them.

Sluggo's project has hardly started and already it is obvious that

the labels are going to take up far more room in the screen then are the

dots.

What are you DOING!; Nancy once again exclaims, laughing in

disbelief.

Trying to see how many data points I will need to tell me the

exact de-accelaration in time the second watch has at any exact location

in orbit as it accelarates in the curvatures of space toward the Earth;

Sluggo answers directly as if all in one word, while swiftly placing

another label underneath a dot.

Okay, then, put a third watch out there, one that gets its time

signaled via synchronous pulse from the second watch, and watch your

whole scheme blow to bits as the third watch starts to simultaneously

circle to Earth on a different trajectory. Empirical accelaration/de-

accelaration combos are no way to start out looking for simple answers;

says Nancy; especially in multi-body situations around the relativistic

effects of gravity.

Oops; says Sluggo.

Then Sluggo hastily reconciders, talking like a guy would explaining

how to dope a moron. Nope, not oops; says Sluggo; see, because the Earth is

stationary, see, I only need to give continuously changing co-ordinates for

only one watch, and the heck with the third watch. I'll put more co-ordinates

in, than anyone else ever did before. Then WATCH my predictions. Ah, ahem.

Sluggo waits with one hand swiveled for the response to the pun.

But none comes.

I wouldn't waste the time; says Nancy, staring deeply into

her Farstar. Nancy is typing fast as she speaks slowly. That's what

everybody tries to do, but not with such ZEAL, such VIGOR, Sluggo.

Do you have any IDEA how many DOTS you've got in your window?

All of this conversation is being recorded in Nancy's Farstar.

No, not, uh, really, uh, uh; Sluggo mutters. I lost count after

the first 6 primary co-ordinate systems. That was before starting to

fill the spaces between the super clusters. (Sluggo pauses to explain

some rationale, here). I thought I had it, until I realized that I had

to identify EXACTLY where the watch is going to go to next, before I can

identify its relativistic rates of change. Believe me, there is lots of

places an object could go to next, depending on whether or not space

contracts or expands, and mass increases or decreases, or such things

remain unchanged, in the relativity of gravity.

You've got to know what you are starting with, in order to know

what your endpoints are; says Nancy, contradicting her friend Sluggo.

For instance, you are not dealing with mass in gravitational relativity,

you deal with mass weight. The number of atoms don't grow.

Huh?; says Sluggo.

Right now; says Nancy; I am not using ANY co-ordinate system,

and I know EXACTLY where my object is going to next. And, I also know

EXACTLY what's going to happen to it at the endpoint of it's journey.

Sluggo smirks.

But not for long. Sluggo looks again at his dot filled screen.

The smirk quickly fades.

Meanwhile, abandoning the conversation, Nancy is right at work anew,

typing at a furious pace into the keyboard panel of her Farstar, frequently

pausing to try out a next or new thought amongst the screen's 3-D images.

Meybe you're right; says Sluggo eventually. Yes, you're right!;

Sluggo finally exclaims, hitting a handy key that lets the dots and

labels go, dismissing the whole mess in the screen with a lightning

quick finger strike to Sluggo's special killer button that utterly

erases the entire screen and circuit contents in a single flash. It's

why Sluggo calls this particular button 'the sting'. It's a button that

Sluggo has installed himself. It is installed in such a way that Sluggo

will hypothetically never feel 'the sting' of loosing a half hour's work

to a wrong keystroke.

Sluggo could have done the same erasure by giving his ridiculously

unambiguous quick-speak command "Fuck it", but choses instead the physical

hit on the killer button which is installed off to the left side of his

main keyboard, because Sluggo wanted to practice hitting the sting while

looking over his shoulder in the other direction, in this case, toward

Nancy.

As usual, with Sluggo, the cross handed strike to the sting is

perfect. The data escapes to eternity in a paff of white, vanishing

in a flash into the red shifting time waves trailing from the planet.

Next, Sluggo, covering his eyes while looking away, says; 'erased'?

The machine answers; certainly, sir. You pray to big cow in blue heaven and

down I come playing blue flute fast'. In evidence is a hindu-moslem accent

thick enough to fool a guru. This is a Sluggo special effect.

Good. Sluggo's personalized impromtu prompt in his Farstar is

right on cue. This is Sluggo's secret doing. Who know's what Sluggo's

Farstar will say next. It might be a German winding the 'eins's' through

adnoids as big as Einstein's. Which is just the way Sluggo has things set

up.

This might all seem droll to the ordinary minded, but it is

carefully rigged to bait Preebe Eebles, who is scheduled to check

out, as in, to calibrate, actually, to muck around, with Sluggo's

personalized language programming in Sluggo's Farstar unit, in

another couple of days.

Sluggo sits there admiring the skills it took to get his Farstar

to respond so rationally irrational. Just like the religions that Sluggo

has plunked into some of the engram modes temporarily.

In fact Sluggo has a nifty little booby trap set up for Eeebles,

if everything goes according to plan. The plan is that Sluggo expects

Eeebles to be playing around with the Farstar unit's conjugations and

the like, as Sluggo has thus far implimented them. Sluggo hasn't

implimented conjugations and the like, Sluggo has implimented useful

words. Conjugations and the like are what Eeebles sees, whether they

are useful or not.

So, Sluggo has set up, for whenever Eebles reaches a certain

number of intructions above a preset limit, that the impromptu promts

will come in, one of them including the killer command, the shockingly

unsophisticated "Fuck it".

Sluggo can already picture it, the fastideous Eeebles slowly leafing

through page upon page of word theory manuals, spending half a day at a time

fooling around with some of the most pointless scientifically definitional

word combinations possible, trying to figure out Sluggo's rationale. And

then, Eebles giving the command to, "proceed to personification of processible

conjugations", or something equally ridiculous; wherein the machine will say

"Fuck-It", in a voice like a fog horn - another Sluggo special effect.

And, instantly responding to its own spoken command, Farstar will

wipe the screen clean, right to the last vestige, in front of Eeebles'

face.

Blink blink blink blink blink will be Eebles' eyelids clamping

nakedly together.

If Eebles is alert enough after the shock of the sting, he

might catch sight of a dinky little thing, a dot smaller than a period,

cavorting amongst the scintillating space curls which will begin to

pervade the 3-D space in the Farstar screen within a few seconds after

the mighty wipe. Sluggo doesn't care that this is all built on illusions

imbedded in the modern mind.

Sluggo figures that a turkey is a turkey, and a stupid turkey is

priceless. If Eebles sits around too long in a stupor, then after about

30 seconds the Farstar will abruptly state: "Put your finger on the

killer button, NOW, Eebles". The button will be lit by this time,

pulsing in colored lights synchronized to Eeble's heavy breathing.

Another Sluggo masterpiece special effect.

If Eebles is humble enough to obey, hitting the killer button will

automatically initiate a zoom sequence. This is logically in reverse of

the killer button's usual purpose. It is intended to demonstrate to Eeble's

that it is impossible for rigid lineal thinkers such as Eebles to know

everything in advance.

On the other hand, Eebles might not take the whole loss personally,

and if deft enough, Eeebles might notice and try to capture the cavorting

dot immediately after the wipe, freeze the anomalous dot in a frame, zoom

it, zoom it again, then again, until suddenly out spreads a panoramic

picture contained in the miniscule dot. One of Farstar's program riffs

is secretly copywrited by the original autocad manufacturers in just

such a dot.

The panoramic picture contains, (besides moving mountains custom

made by Sluggo for Eebles), a homing pigeon towing a banner. The pigeon

is aiming out of the screen as if to hit Eebles in the forehead right

between the eyes. Slow physical wave propigations will be moving

backward along the banner's length in an apparent wind.

Sluggo had contemplated then decided against the idea of having

the homing pigeon travelling in simulation at near the speed of light,

so that major special relativistic effects would be in progress on the

banner's propigational contents, but decided that the science of it

would only confuse Eeebles.

Sluggo chose instead a chugalug speed, and cleverly scaled the

image, in 3-D, so as to make the banner seem several hundred meters

long. In this scale, the giant banner is easy to read. Preebe Eebles

will behold; "Restarter fee. I supply the intelligence. 10 bucks. Zoom

again".

At this point Sluggo's motives should be registering on Eeebles'

vigorously scintillating brain cells.

And if Eebles zooms again, the scintillating representations of

curled space that each sometimes looks like a donut, sometimes like a

coffee cup, randomly at play in the space of the 3-D screen, will

instantly coalesce into the message, both written and spoken: "Slip

10 bucks under the door to the corridor NOW and then I'll tell you

what 'Farstarter' you must speak to Farstar to resume smart input.

Regards. Sluggo".

The gist here is that Eebles has assuredly insisted it is

impossible for a spoken language computer to stall beyond the skills

of a sharp programmer, especially a lineal thinking specialist, such

as Eeebles.

Trouble is, the space agency keeps giving the interferring Eeebles

grant money to continue lineally thinking, and to publish preposterous

papers that impress politicians who simply see the accumulating stack of

them, with no regard to their content.

On the fateful day, Sluggo plans to be lurking in the next room,

watching through the one way glass. Sluggo thinks he might video record

the look on Eeble's face when a machine, A MACHINE!, gives itself its

own willful command to trash its own intelligence.

Yes, Sluggo is anticipating a big win in the lunch room, showing

the video tapes of Eeble's, er, feeble, responses.

Sluggo might even invite the supervisor in for a special session

viewing the tape, as a surprise for the authorities who only yesterday

surprised Sluggo with the dictum that Eebles was due to visit Sluggo's

machine day after tomorrow.

As you might expect, by the way, Eebles has quite a few degrees,

including two PhD's. And is working on a third. And is 'quote' concidering

an offer for a fourth. Eebles has found a niche, that is to say, he thinks

he's arrived at a level no one else can occupy. Partly right, the niche

is more like one that nobody else wants.

What has sluggo really going haywire is that Eeble's has been

insisting with certain success, that artificial intelligence, using

Eeble's, um, concepts, such as 'willability separates', (it means

independent will), is the way to go.

Whereas Sluggo and the rest at the academy, the on hand users,

figure the best all around co-creative computers are those that perform

most effectly. For instance, the Farstar units, recently installed, can

do almost anything, with the intelligence being provided by the user.

Eeebles, seeking to gain a point in his career at someone else's

expense, has sight unseen dared to criticize the way Sluggo has set up

his Farstar unit, this criticism being made to the powers that be in the

space academy. The result was that Sluggo had found himself futilely

trying to invent answers where there were no questions. Sluggo's

invented answers were in response to inane questions supposed by

the powers that be, based on Eeeble's inane innuendos.

So what if Eeble's couldn't get my Farstar machine to turn on,

it's MY MACHINE; Sluggo had shouted red faced.

Not to mention yesterday, Eebles and the supervisor peering over

Sluggo's shoulder as Sluggo demonstrated that his Farstar unit could

indeed be easily turned on, the ever alert Eebles peering ever closer

to see if Sluggo makes a mistake.

Why the forced fake laugh, Eebles? Sluggo had said, their heads

almost bumping, so eager was Eebles in the body shuffle. Sluggo

shouting; back off, Eebles, that wasn't me pleading, all I said was

"speak to me", that's my command for Farstar to switch to voice mode!

Eeebles is likeable enough. But holy cow!

But enough of this.

Yet the distracting reveries continue to assail Sluggo. You have

to have experienced Eebles close up, to appreciate the effect the video

tape could have on the group of other Farstar users which includes, of

course, Sluggo and Nancy and the rest of the bunch from the lunchroom.

Problem is, Eeebles is the type who wears his emotions on his face

like the twisted grins of bible thumpers on T.V. At times his face

motors as fast as a cartoon, as he contemplates a dilemma. The slicky

little mustache doesn't help because it can sometimes appear to move as

if attached to its own muscles. A cord of black string loops deep over

the back of Eebles' shoulders from his eyeglasses. Eeebles doesn't need

glasses for eyesight, he wears them for image. Everyday he smells like

a bottle of musky crotch cologne got splashed on the bathroom floor.

Eebles is, after all, the one who went around pretaking orders

amongst the staffers and cadets for pink flamingos. But you don't

understand!, Eeebles kept insisting, this way we're all guaranteed

flamingo delivery! What do you mean 'who in their right mind wants a

pink flamngo? Haven't you heard?, EVERYBODY in their right mind wants

pink flamingos and I know where to get them. I know where there's a

whole warehouse full of used ones.

Good for you, Eeebles, was the most enthusiastic response.

T I M E I S W A I S ... T I N G ... says Nancy's Farstar Unit.

Ho oh.

Oh, my Farstar has caught something from my private thoughts.

Nancy reacts quickly for the benefit of no one in particular. She is

very engrossed in the circumstances within her screen, but is concerned

about Sluggo's progress.

This is because, so far in this exam, Sluggo seems to have

accomplished, well, nothing. And privately, Nancy thinks the reason

why is because like most people in the world, Sluggo is stymied by

the scientific notion of gravitational curvature of space.

Most people have been trained to think the physics of gravity is

a stainless steel marble dropped on a cobwebb, which says how exactly.

Whereas, that image is as far from the truth as you can get.

Yet, the mistake is so ingrained in the mass conciousness that text

books and popular science magazines, even fabulous science fiction movie

epics on the giant screen, have used the concept of the gravity well, in

psychedelic, vortexing, and plain graph versions.

The square tablecloth cobwebb with the marble in it, a deep sinkhole

poking the center down, has become the central image of gravity and curved

space concepts. A few seconds of logical thought will prove that the image

physically portrays the impossible.

Nancy, on the other hand, hasn't even had to think about the

word 'curvature' as applied to space, during this experiment currently

underway. Everything she has so far entered in her Farstar 3-D screen

since today's test began, has been in perfectly straight lines drawn in

ordinary flat plane perspectives, the solid lines indicating lengths,

and dotted lines indicating distances. Curvatures of space don't even

exist in the diagrams Nancy has been drawing.

But Nancy has been momentarily busy entering some dotted lines that

bend at 90 degree angles and change color as they approach a particular sphere

she has been working around, over left of center, some distance in, into her

screen. Lines also bend toward the sphere's centerpoint P. At this point she

knows exactly what these bent lines are, and they have nothing to do with

curved space, well, at least, with curved space per se.

Other lines also bend, this time in curves toward centerpoint P of

the sphere, sometimes arriving in front of an observer beyond the sphere,

sometimes behind the observer so they can't be seen depending on where

they are aimed. Certain aimings take the bending staight to the observer

and in looking back up the line, the light's source appears displaced to

significant other locations at the source end. At this point Nancy knows

exactly what these curving lines are, and they have everything to do with

curved space, well, at least, with curved space per se.

But these curved lines are of no real use and had only taken a

moment to set up, and were only intended to illustrate the bending of

light by gravitational relativity if needed.

Good enough to leave well enough alone.

Nancy removes all of the lines that bend in curves, and abandons all

curved space ideas, and gets back to the mainstream; insights to demonstrate

a relativisitic presence of Space contraction and Mass weight expansion in a

field of gravity, using a sphere of gravity, to wit the Earth, for the models.

The slow purr of an overhead casablanca fan in the room has been

growing very subtly slower then faster then slow again, during this time,

in line current surges in the ohm-watts, ahem, thinks Sluggo. The blades slice

the air like the snipes of an idling helicopter. This is because that is what

the fan is, made from the rotor of an old chopper.

Sluggo begins to stare up at the fan, wondering what power

surges might be effecting the fan's overall outward behavior. If it

was a helicopter it would be gas and explosions, and relativistic

changes in the rates of its carnot heat cycles, perhaps.

But this is electricity, in the fan inself. At the least, the current's

outer thermodynamic states must be the result of deep inner mutabilities

amongst several forces, ie. the speed at which electrons flow through

the lattices, or the magnetic properties, or something, when supposing

the fan was removed to outer space, free of denser gravity; Sluggo is

thinking. Because surely at the moment, no matter what its speed, the

overhead casablanca fan is rotating more slowly than it would in outer

space free of Earth's gravity. Or would it? Sluggo doesn't know the

answer to that one exactly, and can't think of an easy solution

because of the number of possible mutabilities.

Another fan, in the ceiling next to it, is turned off.

Say, yes, Sluggo suddenly forgets the fan and sets to work on a

new line of thought.

First thing Sluggo does is switch on the keystroke clicks. The

clicks have been recently reintroduced as audio clues to the user. In

Farstar, the clicks can be switched on or off.

Immediately right into it, Sluggo soon enough begins to grunt

a little as he struggles to get a thought free, or to remember an

equation.

As a matter of fact at this point Sluggo becomes quite masculine,

stabbing at certain keys with a hard forfinger, then slamming the space

bar with the hammer of his fist, and all around making a center of

attention of himself.

In and around the grunts, in his furious typing, Sluggo is at

times working so fast that the key clicks seem to blend into rudimentary

vibrations that almost make a music.

The minutes pass.

It couldn't be hard to imagine that at times the talented Sluggo

is playing melodies with the tones of the clicks. Sluggo has several

things going at once in this, ah, surge.

Meanwhile, Nancy has all along remained hard at work, typing

text manually into her Farstar's keyboard, the text being displayed in

a single strip; the convenient read row, found on top of the keyboard

itself. Rapid image editing otherwise keeps events leaping around in

the remoter corners of her three dimensional Farstar unit's screen.

The reason why she's been typing, oddly enough, is that this

is one of those interludes when the effort to speak words is enough

to override the concentration of pure thought at a text writing level.

Nancy has become extra aware during this test, that words spoken aloud

carry their own meaning. This includes extra information imparted by

inflections, pauses, tones, and emotions, including the vibratory strength

of confidence in consciousness in which a thought is expressed vocally,

and so on. And these, if not heard when later read, in Farstar's printout

version for instance, can be far removed from their intended meanings

when lacking the extra juice of human voice.

In Nancy's typewritten text, she is paying particular attention

to how the written descriptions might correctly convey their intended

meanings a day later. Especially when someone else is doing the reading

cold turkey.

Several things have gone on in Nancy's screen during the whole of

this exam. At one point, lines made of strings connected at right angles

seemed to form a balance, a mechanical scale akin to the kind assigned

to the libra birth sign, or used to symbolize justice. This scale had

been erected in outer space free of gravity.

And for awhile, Nancy had in there something that looked like a

straight arrow with a watch at each end, the arrow not touching the

Earth's surface while pointing straight to the Earth's center, then

straight away from the Earth's center, simply by switching the

observer's point of view without switching the arrow.

And then the whole straight arrow was moving in and out by a notch

in a manner which seemed to cause the whole universe as well to shift in

and out, until Nancy got THAT logic straightened out. And then there was

the balance again, the scale. And all along, the second pocket watch has

been marching around the Earth by lengths repeated far out in space,

even as the orientations changed, the length of the watch's chain

shortening by a certain unit when one end ends in gravity.

And then certain other lines were entered. These were those seen

to bend in a bias toward Earth's center when converted to light rays that

were also doppler shifted by gravity. But these are now all deleted.

Meanwhile off in the distance, a third watch that has been moved

around many times seems to have a rocket thruster attached.

In fact, several thrusters have been introduced in each of the

different mechanical assemblies which Nancy has so far erected.

The first major problem to overcome was not merely how to clone

a second watch in free space identical to a first watch in a laboratory

on the surface of the Earth, but how to calibrate two cloned watches in

free space so that each had IDENTICAL MASSES. The third watch is essential

to Nancy's insights. (Free space has come to mean, in Nancy's Farstar, far

enough out in space that no relativistic effects are felt out there due to

Earth's gravity).

Of special interest is that Nancy has found ways in which straight

lines bent at right angles attaching both watches in a single link managed

by pulleys, can mechanically be made to model things when SPACE contracts

and MASS expands, in gravitational relativity. The third watch at this

point is being used to identify certain basic constants.

In fact it happened that things had begun to whizz around willy

nilly in confusion until Nancy had also put in point source thrusters

around certain data points locking them to fixed points in free space, to

satisify any questions of inertia, whereupon a raft of seeming properties

began to unfold, catalogue style.

Some of the data points moved in pairs, the points being where

lengths connect, the lengths changing angles as the points shift to

alternate positions in precise moves albiet like cross eyed windshield

wipers.

For a few minutes (so Sluggo had noticed) Nancy had been sitting there

with her arms held up, palms toward her face, vigorously swinging her elbows

then forearms back and forth in different ways, saying; huh huh, okay, this

works, huh huh, yes, so does that, as she tried various move combinations.

She had also been folding her left palm to shorten the length of

her arm to her elbow by a unit, while windshield wiping.

In the reveries, her's are quick fleeting private thoughts of

the kind that drift along with no weight, no lasting memory.

Don't you dare wave your elbows at me Sluggo, I'm busy; exclaims

Nancy as her friend turns back to pound another round on his keyboard.

But the winshield wiping investigations are seen to be misleading

and abandoned. Instead, one of the incomplete models involving pulleys

is suddenly realized to have a lot more going for it. From that moment

Nancy begins to progress rapidly.

In short order Nancy is hard at work, testing design images via

special effects, and recording notes as time goes on. And then a pause

to take stock of things.

Wow.

In and around the special effects of Nancy's legacy, a surprisingly

lengthy file growing in the form of a typewritten travelogue accompanying

ongoing imagery is now being observed by Nancy to have been entered into

her Farstar. Nancy has been very busy. Other than some minor grammar

difficulties such as deciding between semi-colons, colons, periods, and

such trivial constraints in english, things have been going so good there

is scarcely a spelling mistake to speak of. No, not that, things have been

going so well there is scarcely a writer's mistake to speak of; thinks Nancy.

Not like Sluggo's latest aborted attempt, just completed.

Sluggo's latest had started following the attempt at defining the

dots, back when Sluggo had decided it was time to get extra masculine

and ACHIEVE something, in this test.

From that moment, Sluggo had regressed, in rapidly typing his

ideas as already said, to banging important keys with a hard forfinger,

and finishing each sentence, ie. a thought, with a closed fist banged

hard on the space bar.

'Flourish', is what Sluggo was calling it.

If anybody was watching they were supposed to notice. They were

supposed to presume that these flourishes signified important thoughts.

Sluggo frequently pounded the space bar so hard that the keyboard jumped

a skip from the surface it sat on.

At this point Nancy wasn't noticing, she was busy re-editing

a growing list of item numbers which preceded each new sentence in

her text. This, Sluggo noticed. As far as Sluggo could ascertain,

the growing list was supposed to be points favoring the existence of

mechanically demonstratable Space and Mass properties in the relativity

of gravity. At this moment Nancy is up to point 267, at least this is

what Sluggo can see, peering across, in Nancy's list.

It kind of clangs on Sluggo's brainpan that Nancy's model is

being built entirely of stationary reference points, with a reference

watch moved beyond any significant effect of Earth's gravity, and held

in straight line station keeping with respect to the identical watch in

the lab on Earth. A third watch happens to be lined up above the original

lab on the Earth. But wait a minute, there is another lab on the other

side of the Earth, 180 degrees around the Earth from the first Lab!

As Sluggo watches, now momentarily sucked in, Nancy does a trial,

pushing a couple of buttons. The fixed watch (the one out in free space

above the original lab, clones, and moves deliberately to the right at 90

degrees. Nancy changes her mind - no - tries another image.

This time the watch in the original lab is cloned, by swinging in an

arc out into space, to stand at the end of a line at a right angle between

the watch in the lab and the end of its chain which sticks into space. The

fulcrum of the swing is attached to the end of the chain, and it is clear

to Sluggo that the distance between the fixed watch and new one attached

by thin string on the arc, is longer than the distance between the watch

in the lab to the end of its chain.

As Sluggo watches, Nancy carefully types in the words "CHAIN of

CLOCK 2 expands back to original rest state length in free space". And then

she carefully types "CHAIN of CLOCK 1 contracted in gravitational space".

And then in the Copyrighter mode of her Faster keyboard types: ....

.... But in either case, the distance to Earth, and to the cloned

watch, must be the same if given in a system of units such as centimeters.

ERGO, the system of units can actually change in size in gravitational

relativity per measureable interval, even though the total count of

intervals per se remains the same. Wise, wise, nods Sluggo privately,

even though puzzled at what this is leading to. Oops.

In startled haste, Sluggo turns to his own Farstar and picks

up his own pieces of scattered aptitudes.

Boy, talk about getting carried away up a long creek, Sluggo is

thinking, regards Nancy's enterprise.

What actually has Sluggo so busy is it is in Sluggo's mind to

once and for all, point out that the question posed by the hair brain

genius's two pocket watches is tautological.

Oddly enough, the approach Sluggo is taking has something to do

with the chirality factor in fundamental physics (all one handedness),

and 10 dimensional string theory. At least, this is supposed to be

presumed in Sluggo's assumed premises, a nod being given by gestalt

name dropping of a few ranking researchers here and there in Sluggo's

description yet to be written.

To start the ball rolling, Sluggo had begun to explore an oddball

notion of when one object was rotated within a mechanical assembly that

was otherwise ordinarily interractive and symmetrical to the backdrop of

space, then at least one major break in symmetry could be expected, with

several previously concealed or impossible mechanical activities

suddenly possible.

This notion was part of Sluggo's idea surge. The question of

curled space in the upper multiplex of extra dimensions could come

later, if at all. The truth is, Sluggo has only vague veiled knowledge

of this theoretical side to physics.

But instead of a breakthrough in creative outpouring, what took

place was a kind of dichotomey in Sluggo's thinking here.

Sluggo had planned to swing things around into a 'tautology' which

would say that all concepts about the two pocket watches would crash in

simple cancellations of the kind which say A equals B therefore B equals

A therefore only A really exists.

The problem was, there kept insurging into Sluggo's consciousness

this independent idea of a break in symmetry in which further activities

could be seen to proliferate because of a mechanical break in symmetry.

Sluggo's ideas are often not very simple.

And yet he almost had the key insight for the answer to the test.

Unfortunately, Sluggo hadn't seen a symmetry break as applicable

to the question of relativistic effects in gravity. In fact Sluggo had

been tuned into the idea of a pulley system between the Earth and the

second watch in space, as a means to prove his tautology.

Both recruits have long since lost track of time, so absorbed have

they been in their projects.

Nancy, at this point, silent for so long, her Farstar temporarily

shut down on standby, has been in a deep contemplation, for suddenly she

exclaims fully aloud to herself; hey wait a minute, because the watch

has rotated 180 degrees around the Earth out in free space, there IS a

break in symmetry with the freespace scale, that's how come the extra

Space and Mass effects can be shown to happen.

This is something that has taken quite a while to work its way up

through the many sub-interpretive levels of intuition, into something

that Nancy suddenly realizes is quite clear in her mind. Which is why

the sudden exclamation. She actually had had the answer first, and had

had to work it back into some kind of recognizable question.

So now Nancy is muttering to herself as follows: So, how come the

mechanics behaves differently after the 180 degree rotation around the

Earth?

Hmmm?

How come?

Hmmm.

Hmmmmmm mmmmm.

Ahah,

I know,

The gravity on one side of the Earth does not read the gravity on

the other side of the Earth!

What does this mean?

Hmmm,

Mmmmmmmm mmmm.

Ahah, So that's what it is!

As far as the view in free space is concerned, the two sides of

the Earth are two different sources of gravity, and the difference is

revealed when a model is connected by lengths in space to one side

of the Earth, and also to the other side of the Earth.

How can I say this non intuitionally?

Ahah!

It is like a closed string, whose two ends are joined in a loop, but

end A is separate from end B because of C which intervenes, C containing the

break in symmetry. C in this case is the Earth, a sphere having equal forces

with equal reference points on opposite sides of its surface, these being

connected to the ends of the string closed in a loop. Force A at side A is

supposed to be equal to force B at side B, when item A at side A can connect

to item B at side B, but the two forces are actually NOT THE SAME THING, Hence

the symmetry break enclosed in the closed string!

Oh heck, I don't have to get into this now; Nancy mutters after a

pause.

Nancy begins to earnestly type versions of the comments preceding

the idea of the closed string.

These comments might seem witless to the uninformed but they tie

in specifically to behaviors in the detailed mechanical model which

Nancy has been developing in her Farstar.

Whereupon the sometimes single mindely serious Nancy is very busy

again, typing faster than the eye can follow in quick brief flurishes.

But watch out Sluggo being in a dual minded state the whole of

this time, has begun rethinking, amongst other things, about the

ingenious trap all set and waiting in Farstar for Eebles the day after

tomorrow, a gross misuse of the Farstar device, incidently. Mind you,

Sluggo has become deft at ignoring the twinges of guilt. As said before,

going for the jugular vein is highly uncharacteristic of the good

natured but independently spirited Sluggo. And Eebles is a likeable

enough person.

But lately, holy cow, Eebles must be getting ready to publish

another paper. Probably needs to boast about the successes of his

artificial intelligence program, the one in particularly written for

Farstar. Trouble is, Nancy and most of the others in the lunch room

have been circumventing Eeble's programs use as much as possible.

Sluggo in particular has refuted it altogether and has implimented

his whole independent regime so that his Farstar tends to function like

a video game rather than a hard core office product. Bringing new

meaning to the phrase 'personal computer'. Ahem.

Eeebles it seems, has probably already drafted his paper on how

a sophisticated type like Sluggo finds Eeble's program a successful

advance in the field. WRONG!

Well, its a matter of principle, rather than degree, is what has

Eebles up in the air.

Well, its a matter of degree, rather than principle, is what has

Sluggo going.

Yessiree, this time Sluggo is gonna sow hoe and reep Eebles,

Sluggo is thinking mightily. Sluggo can see Eebles slaving away trying

to figure if the conjugations conjugate. Sluggo can hear, over and

over, in the ear in his mind, his special effect voice that sounds like

a long strong earthquake, as Eebles hits the critical mass and sails out

in the twilight zone when Sluggo's programming takes over, easily ending

the claims of Eebles' 'intelligence willability'.

Right now, the result of daydreaming in duality, during this

interlude, is Sluggo's screen rapidly filling to the hilt with gibberish.

Because, Sluggo has in the past ten minutes overlooked one important

ingredient. A failsafe factor in the realm. To wit: Human made

machines are only as good as the humans who use them.

Momentarily caught up in the style; the razzle dazzle of ego

rather than the use of intelligence; Sluggo in his dual minded state had

focused in on staring rigidly at the keyboard itself, attempting to type

faster than the eye could follow. In a testing of personal skill, in

this, Sluggo had also deliberately left the Copywriter strip on the

keyboard off.

That isn't what was overlooked. What was overlooked was that

such was the effect of Sluggo's 'flourishes', that the keyboard had been

thoroughly thumped out, damaged right from the start by the fist blows

plus the strikes from Sluggo's bone hard forefingers.

The jolt for certain must have jarred a few people sitting around

in stupors on the planet. The jolt happened when Sluggo tunes back into

the here and now.

Sluggo alas finally tunes in to the fate that his dazzling display

of personal brillience has been lost to gibberish.

You should have seen the nonsense cunningly disquised as content

in his Farstar screen; phrases collapsednospaces, psuedowords

undeciferable through szelling errors, etc.

What makes it worse is there are strange alien symbols coughed up

from the codals, including little happy faces, instead of periods and

paragraph breaks. There are puzzling gaps within words as if pistons are

missing, and lengthy all aabrrrrticc conglomerates that have no reason

whatever. For instance it was supposed to be 'all phrases', not

'allpthhhrraakkk '.

In other words, nothing. Not a single salvagable thought to speak

of remains. A brillient flourish has been ignoblized. So has half an

hour.

Yes, Sluggo feels that old sinking feeling, when finally he

learns, glancing up from the keyboard to admire his accomplishment.

Holy shit!

Ah yes, the worst of the bad news is confirmed, the broken

keyboard wouldn't even scroll backwards.

"Fuck-It!" I beg your pardon?; says Nancy.

Disliking such pressure intensly, Sluggo is forced into a last

minute let's pretend attempt at producing SOMETHING. He rapidly switches

over to voice and thought mode, and is soon quickly revved up in the

skill of entering advanced algebras in flat screen mode effortlessly.

And now is when the idea of officially fanning the secrets of the

electrons in the motor of a casablanca fan in space free of gravity,

finally occurs to him.

I think I can demonstrate a way of getting around, without having

to know the second watch's real universal rest states; says Nancy, after

a long concern at typewriting.

Wow, what a leap in dejavu; thinks Sluggo, fanning a quick glance

sideways to Nancy to see if she is still there functioning in the third

dimension.

Sluggo's screen is rapidly filling to the borders with differential

equations. It looks IMPRESSIVE to those who are impressed by totally obscure

looking mathematics. Vocalizing algebra is HARD, and Sluggo is rapidly

becoming IMPRESSED by his success with it.

Nancy isn't impressed at all.

More time passes.

What are you up too? inquires Nancy eventually. Sluggo has been

slowly folding over, his jaw only inches above the keyboard.

Sluggo bongs straight up and manages to pretend his way out of the

fact that he'd nodded off; I'm trying to explore the flow of gravitationally

effected electrons through the relativistically effected atomic lattices of

a motor. See how this fan is fluctuating in subtle surges of power? (Sluggo

quickly points in the room to the overhead casablanca fans made of helicopter

blades). If a fundamental force powering the behavior of my FIRST fan is

given equally to this SECOND fan when it is out in space, the power, or its

effect, or the mechanics it effects, have somehow been ALTERED, because if

the beat of the blades is used to mark TIME, my second fan will be running

FASTER out in space.

Nancy responds not, except to say; getting anywhere?

At this, warm giggles are heard, incoming from a few remote

sources through the two cadets' Farstar units in the space academy.

Sluggo points overhead to the two fans; I'm trying to imagine what

is intrinsically involved, as the speed of the fan in outer space revs

up and slows down in power fluctuations similar to the fan here on

Earth; Sluggo continues, as if completing another conversation.

After looking hard at Sluggo for a moment, Nancy finally comments;

are you sure you want to ask what kind of force would be powering the

behavior of your admirerers?

Everyone laughs including Sluggo. Several laughter sources come

echoing in loud and honest into the room straight through the two Farstar

units. By co-incidence this happens to be the end of the theoretical part

of the experiment, because clango the bell rings to end the round.

Let's go, the main equipment is ready; the supervisor says.

What main equipment?; asks Nancy.

On the other hand Sluggo is busy keeping a hype up, because it seems

like he, or both of them, might have just passed something critical. Didn't

have enough time to get to the heart of the problem, er, ah, er, says Sluggo,

faking it a bit, knowing that his last minute spate of impressive looking

equations hadn't even begun to define the problem, let alone come to grips

with the question of Space and Mass in gravitational relativity.

Actually, all Sluggo had been attempting to do, at the end, was

to define a few key terms, between brief periods falling asleep sitting

upright.

Whereas Nancy had been busy all along, having had just enough time

to finish recording a numbered list of several hundred points. The points

are arguments which re-inforce rather than deny that Space can contract,

and Mass can expand, in relativistic effects induced by gravity. Whereas,

in every alternate case she had tried, any other variations such as space

expanded and mass reduced, all sailed headfirst into fishy situations,

the gists vigorously conflicting, at least for those alternate cases

she had actually tried.

At the very last, Nancy had begun to erect a six sided figure in

free space around the Earth to see what this might avail, but this is

when the test ended.

Nancy had run short of time to finish the project, hence it is

short of several conclusions. But while leaving the room, Nancy can

quickly think of several features worth noting, amongst which are the

following:

Eidetic memory, (i.e. the photographic kind), is not dominant in my

presentation; Nancy is thinking. She continues, thinking; the presentation

is developed along the lines of nmemmonic memory (ie. memory by association

and intuition, using images rather than pages memorized from a text book

to identify certain answers).

But now, because its the bell, Nancy hits a key which returns one

of the previous images which had been put together just before the end of

the test, in the form of a quick summary. She leaves the summary behind

on the screen of her Farstar, as both cadets leave the room.

In the meantime, away the cadets go for a lunchbreak, to next return

to the same room for the next part of the experimental tests. This next part

will be to see how readily, or easily, each of the cadets can use nmennonic

images to successfully store and recall data and to operate on the spur of

the moment in ways that simply cannot be approached by people who rely on

eidedic memory for all of their accumulated understanding. Apparently

someone else in the academy, someone who can force command decisions,

is also not an admirer of Preebe Eebles' preposterous scientific conceit.

- FINISHED -

-- Continue with STORY.7 --

Item G if using the SHORT STORY menu.

STORY SEVEN

(Story.6 cont.)

THE 2-D MECHANICAL MODEL

Unbeknownst to the observers, Nancy has actually stored a solution

to the MASS and SPACE problem in gravitational relativity, in her Farstar

unit. It will happen that the insights for the solution will be uncovered

later in her notes and brought foward for interpretation at another time.

Meanwhile, in the screen of Nancy's Farstar is the following.

A DEPICTION WITH IMAGES REGARDS A MECHANICAL DEMONSTRATION OF GRAVITY

RELATIVITY INFLUENCE ON SPACE AND MASS, USING THREE POCKET WATCHES

CALLED CLOCKS, IS AS FOLLOWS:

IMAGE 1

This position is where CLOCK 3 ... would be if its chain Ha

/ is not contracted to ba

H ù---------------------------ù i by gravity relativity.

| Length Ha = Hi.

| / CLOCK 4 (a dummy) CLOCK 2

b ùÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ< c -- CLOCK 2 at c is cloned

³ by swinging CLOCK 1

³ from LAB 1 into free

³ space to point c.

³ Chain ba expands

a ³ CLOCK 1 in LAB 1 to length bc when

ÚÄÄÄ^ÄÄÄ¿ SPACE in its length

³ ³ is free of gravity's

³ earth ³ relativity contraction.

ÀÄÄÄÄÄÄÄÙ

IMAGE 2 b ùÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ< c -- CLOCK 2 in free space.

³ | Free space is removed

³ | far enough from Earth

³ | that Earth's relativity

³ | due to gravity has no

a ³ CLOCK 1 in LAB 1 | effect.

ÚÄÄÄ^ÄÄÄ¿ |

³ ³ |

³ earth ³ |

ÀÄÄÄ^ÄÄÄÙ |

LAB 2 |

g ^ -- CLOCK 2 is -X- d Points d and b are

³ swung from | equidistant from

³ point e to | point c, and lengths

³ point g, and | bc, cd, de, ef, and

³ hangs in space | fg are all equal to

³ above LAB 2. | free space length bc.

³ | 'Before Contraction'

³ |

³ | CLOCK 2 is swung from

³ | point c to point e at

f ùÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ> e pivot point -X- .

NOTICE CLOCK 2 actually arrives in space hanging above LAB 2

at point g by a distance equal to 2 units of length Hb of

IMAGE 1. This is shown as point g in IMAGE 2, but actually

this is not its true position, as shown properly in IMAGE 3.

Scaling problems distorting the precise lengths in the images are due

to quick sketches not done in 3-D stereo in the computer screen. If

drawn on paper then scaling is less of a problem.

Of course the Earth's gravity mass is so small that relativistic

effects are extemely minor. However, if the Earth mass is increased

by a factor of (say) 1,000 then relativity effects due to gravity

would be more noticable. Let us assume, then, that the Earth is very

heavy, for the moment.

In gist, CLOCK 1 cloned as CLOCK 2 is marched around the Earth by 180

degrees, by swinging CLOCK 2 on its chain three times, the chain being

at full length in free space free of influences of the Earth's gravity.

(Length ab of IMAGE 1 is the length of the chain if contracted by

a relativity influence of Earth's gravity.

IMAGE 3 CLOCK 1 in LAB 1 |

ÚÄÄÄ^ÄÄÄ¿ |

³ ³ |

³ earth ³ |

g ^ a ÀÄÄÄ^ÄÄÄÙ ÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ¿ |

³ (g) k | CLOCK 2 in LAB 2 ³ |

³ | ³ |

³ j ^ ÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ¿ ³ |

³ | ³ ³ |

³ | Actual position of CLOCK 2 for IMAGE 2, per more precise

m ù b g ^ -------------------------- -X- d scaling in these

| ³ ³ ³ | images.

| ³ ³ ³ |

L ù H ³ ³ ³ |

³ ³ ³ |

m ³ÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ³ÄÄÙ |

³ ³ |

L ³ÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÙ |

³ |

f ùÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ> e

HERE IS THE NEWS

Suppose CLOCK 2 arriving at position g has just barely dipped into the

Earth's range of influence, close enough to Earth that the Earth's

gravitational relativity can have an effect on the MASS of CLOCK 2, so

as to begin to increase the MASS of CLOCK 2. The relativity increase

is just enough to tip the balance, so that Earth gravity can now cause

CLOCK 2 to start moving closer to Earth.

Mass increasing continues until original rest mass and maximum gain in

MASS caused by the Earth, pulls CLOCK 2 into LAB 2 at the Earth. At

this moment, both CLOCKS 1 and 2 should have identical MASSES,

consisting of their original rest masses, plus their extra masses

gained by the relativistic effect of Earth's gravity.

At the same time, as CLOCK 2 begins to move closer to the Earth, the

LENGTH of it's CHAIN begins to contract due to the Earth gravity's

relativity effect on SPACE. In effect, g moves to k, and length gm of

IMAGE 3 will end up the same as length ab of IMAGE 2, as shown in the

line to the left in IMAGE 3.

THIS IS THE JIST

Suppose the two watches (CLOCK 1 at LAB 1, and CLOCK 2 at position g

in IMAGE 3) were connected by a single line, and that all points (b,

c, d, e, and f,) were pulleys locked in position in free space by

thrusters, so that effectly pulling on CLOCK 2 at position g would

result in inertia free movement of the string, such that CLOCK 1 would

be pulled out of LAB 1, if CLOCK 2 is pulled into LAB 2.

THEN THE FOLLOWING LITTLE STORY COULD HAPPEN ....

.... A lab technician reaches up and pulls CLOCK 2 in IMAGE 3 from

position g where it hangs in space, down into LAB 2 at position k.

Technically the lab technician is adding extra MASS to CLOCK 2 to pull

it home in place in the lab. This extra is (FORCE E), which also has

to be exerted constantly by the technician to keep CLOCK 2 in place in

the lab.

The technician notices that this amount of force (FORCE E) can thus

be equal to that which would constantly result, if CLOCK 2 became

heavier on its own, due to Earth's gravity relativity. However, in

order for CLOCK 2 to be pulled into LAB 2, the attraction of all

gravity at CLOCK 1 would have to be shut off, so that CLOCK 1 could be

pulled into space free from LAB 1. A break in symmetry. On the other

hand, (FORCE E) is extra tug needed to pull CLOCK 2 from where it

hangs in space into LAB 2, when all gravities for the Earth stay as is.

And so the technician reaches up and pulls CLOCK 2 into LAB 2.

Since CLOCK 2 is attached to CLOCK 1 by pulleys, CLOCK 1 leaves LAB 1,

and its chain expands, as simultaneously its total MASS decreases.

What interesting news, exclaims the technician, that (FORCE E) is the

net consequence of two effects of a single ratio, which the technician

now calls (RATIO E).

The technician already knows what (RATIO E) is. The technician knows

it by the simple fact that if the relativity effect of Earth's gravity

is (EFFECT G), then the time (TIME 1) of CLOCK 1 in LAB 1 of IMAGE 1

has slowed by the factor (TIME 1) x (EFFECT G), such that (RATIO E) is

the ratio of times between (CLOCK 1) ö (CLOCK 3), since CLOCK 1 runs

slower than CLOCK 3, due to relativity in Earth's gravity.

And so: (RATIO E) = (EFFECT G).

In the mechanical model the technician is playing with, the technician

can see right away that the effects of gravity relativity on SPACE and

MASS are supportive, rather than singular. That is, that the amount

of force expended in pulling CLOCK 2 from position g to position k

is accumulatively a two step deal, in which (RATIO E) expands the MASS

of CLOCK 2 by: MASS ö (RATIO E), and actually contracts the universe

which contains the CHAIN of CLOCK 2 by: SPACE x (RATIO E).

It is clear that the two steps accumulate together to bring CLOCK 2

into LAB 2 in IMAGE 3. Whereas in IMAGE 1 just by itself, an expansion

of MASS at LAB 1 is merely assumed. And the contraction of space in

the watch's chain is assumed in the difference between lengths ba

and Ha. And both events are singular in keeping with a third singular

event which Is the dilation of time for CLOCK 1 when in LAB 1 on Earth.

Hmmmm. Well, actually, it seems in IMAGE 3 that a dilation of time has

no direct link with the expansion of MASS and contraction of SPACE

involving CLOCK 2. The technician is aware enough to write:

HOW DOES IT ALL ADD UP ?

Rest TIME x (RATIO E) = gravity effect on TIME at LAB 1.

Rest MASS ö (RATIO E) = gravity increased MASS = (INFLUENCE 1).

Rest SPACE x (RATIO E) = gravity contracted SPACE = (INFLUENCE 2).

And so: (INFLUENCE 1) with (INFLUENCE 2) = (FORCE E).

Wherein: (INFLUENCE 1) is equal to the effort needed to pull

the mass of CLOCK 1 free of LAB 1.

And: (INFLUENCE 2) is equal to the effort needed to pull

the SPACE of the universe inward toward

LAB 2, so that the length of the chain

gm of CLOCK 2 in IMAGE 3 is the same as

the length of the chain ba of CLOCK 1

when CLOCK 1 was in LAB 1 on Earth.

HERE IS A SUMMARY

At the onset, CLOCK 2 hangs in space by two units

of a measure in space above LAB 2 on Earth.

In order for CLOCK 2 to arrive in LAB 2 of IMAGE 3, two events in

gravitational relativity HAVE TO OCCUR simultaneously: The MASS of CLOCK

2 has to increase relativistically, and the length of CLOCK 2's chain

has to contract in SPACE relativistically. Contracting the SPACE of

CLOCK 2's chain, by effect of (RATIO E), is enough to move CLOCK 2 from

position g of IMAGE 3, to position j of IMAGE 3. And increasing the MASS

of CLOCK 2, by effect of (RATIO E), is enough to cause CLOCK2 to dip the

final distance into home plate at k in LAB 2.

No other operations can work in the model. For instance, a MASS

decrease and SPACE increase will not work, nor will simultaneous MASS

increase and SPACE increase. Etc. However an increase in the length of

the chain of CLOCK 1 when pulled out of LAB 1 could be said to provide

the extra unit of length needed to get CLOCK 2 into LAB 2 on the other

side of the Earth. Oh well.

Worth noting is that polarity of the CLOCKS has not changed, as

indicated by the up ^ arrows at point 'a' of IMAGE 1 and point 'k' of IMAGE

3. Whereas the direction of the pull of the Earth's gravity has reversed.

Ergo an obvious anomaly in symmetry.

CHAPTER 4

Nancy has left more of the above information recorded in her Farstar

unit in the form of a typewritten travalogue which can stand entirely on its

own as a workshop description, plus the visual 2-D non-stereo diagrams left

in the screen. Nancy's travelogue otherwise describes a sequential flow of

images and reasons for each image, the content of the storage comprising

that which was typed, that which is image, and that which happened to get

registered from Nancy's private thoughts, in that the stored information

also serves as a demonstration of leaks in thought of the kind which can

intuitionally stimulates and motivates other people privately.

So she sustained the recorded thought leaks, didn't earase them.

In other words, there is every reason to believe in the serendipity

factor, wherein, in some other minor or major corner of the planet, in

consciousness, someone else, or some others, are thinking along similar

lines to Nancy's. The thinking would be prompted upon illuminations that

originate in much deeper levels of reality.

(Also, of course, others could be getting merely the thought impulses,

and putting onto them false ideas. Witness Sluggo's attempt to use the model

of a pully to try to tautologize effects on Space and Mass by gravitational

relativity; the very reverse of Nancy's approach to the problem proposed by

the test; Sluggo being temporarily motivated by thoughts of reward amongst

Earth's famous peers, rather than urges for truth in reality).

Whereas, externalized in communications of outer thoughts, through

adapted languages via human made equipment on earth, (for instance via the

Farstar unit Nancy is thinking), the described gravity relativistic effects

pertaining to Mass and Space (in contrast to radiation and time) are revealed

through mechanical principles found in lineal 2-D space models, as opposed

to curved 3-D space (and accelaration) concepts.

The two most interesting models so far constructed, thinks Nancy,

are assemblies made of mechanical apparatuses, one a staight arrow system,

and the other a pulley system.

In the pulley model, an end of the apparatus is attached to a point

on one side of the earth and connected by a continuous string skirting in

a rectangular journey through free space to the other side of the earth.

The pulley model is not unlike magnetic lines looping from one pole

to the other. For instance there is a string connected to opposite points

on the Earth's surface, but no curves in the string, all parts are straight

line lineal, (although a giant curve around Earth could also work in the

pulley model, but describing THAT would be enough to drive a nut crazy).

The action in the pulley model originates with one of the pocket

watches at an original point on Earth, called LAB 1.

On the far side of the Earth is an identical lab with an identical

receptical to recieve the homecoming second pocket watch. As far as Nancy

can fathom, the homecoming watch falls short of falling snugly into place

into the receptical. The distance of the falling short is proportional

to the gravitational relativistic contraction in the link (the chain)

between the original watch in the lab on the starting side of the earth

(CLOCK 1) and the fixed watch in space (CLOCK 3).

As far as Nancy can deduce, if a small amount of mass weight is

added to the homecoming watch it will fall into the second receptical

waiting for it in LAB 2. As far as Nancy can deduce, the amount of added

mass (over the watch's original rest mass) is exactly proportional to the

amount of proportionate contraction in the string linking the fixed watch to

the original watch in the original lab, compared to the distance to a corner

point position labeled c, gained when the original watch in the lab is

cloned then arced out to position c to become the second watch. The

rate of proportion in the changed Space and Mass effect are idential to

the proportionate change in the rate of time between CLOCK 1 and CLOCK 3

due to the relativistic effect of Earth's gravity.

In this model which includes pulleys, (Nancy for the moment has

come to call it the 'freespace pulley model'), the point on the back side

of the earth is connected to a mass which is sustained out in free space.

The result is that a rotation around the Earth leads to a local break in

symmetry. And an increase in mass weight in gravity is revealed.

Connections in all of the models are made of a constant measure

repeated. But the lengths of the measure vary, depending on whether the

measure ends in space, or one end ends in gravity.

Another string-like assembly, which Nancy has called the 'straight

arrow' model, has a center point fixed in space, and the two ends ending

in gravity between two identical planets with identical labs on their

surfaces facing each other, and this is without a symmetry breaking

rotation. Identical pocket watches are located in the identical labs

at each end of the string.

And what is different about the 'straight arrow' model? Well,

(Nancy has recorded), the 'freespace pulley' model is a stationary one.

The images stand still as constant in space until I do something to change

the image, such as add a little mass to the second pocket watch, causing

it to drop homecoming into the second lab, changing the image at the

original end by means no more esoteric than pulling on a string.

Wherein the 'straight arrow' model demonstrates, why, haven't

you guessed? In its parameters the observable dimensions of space in

a straight line between the two bodies in the 'straight arrow' model

begins to inexorably CONTRACT (alter in outer appearance) due to

relativity, leading to motive power.

An accelaration in gravity has been laid bare.

In her simulations, Nancy has presummed the understanding that

effects in local fields of gravity of Earth size are so slight as to

be hardly discernable, nevertheless, inexorably, there. Not to mention

those ultra feeble tugs imparted by the masses of the two pocket watches.

Whereas, in fields of powerful gravity the actual effects would

be obvious. The contracting of space leads to motive power witnessed

as mutual gravitational attraction. Oh but wait. Not quite correct.

The contraction would stop unless something else besides space alone

also relativistically changed.

Ahah, (Nancy is deducing). The apparent weight (rest mass) grows

proportionately greater as the two objects gather closer together through

the contraction of space, the greater rest masses having the effect of

increasing the degree of collapse.

Since the effect of collapse in space is identically proportional

to the increase in rest mass per given distance separating the bodies,

the actual rate of closure between them accelarates as a squared factor,

rather than merely continuing at a fixed rate determined by the 'quote'

gravity of their combined original masses over an original distance

apart.

In any case, irrespective of the magnetude of the gravity field,

the understanding of existent mechancial properties that demonstrate

gravitational relativistic effects involving Space and Mass, are easily

intuited via the models. The models logically connect when gravity

relativisically contracts space surrounding a gravitational source in

a halo of diminishing effect further from the source, and relativistically

increases the rest mass proportionally, of the gravitational source itself.

In this case, greater rest mass field density in the two planet masses means

greater overall relativistic effect, an overall effect greater than just the

factor of the two rest masses by themselves.

Its no wonder that gravity pulls gravity. Its not the two gravities

at all. Its one thing only, it being the relativistic effects of the changing

contraction of space and changing gains in rest masses mutually doing their

thing in real time. The universal gravitational constant is simply the

measure of the resulting observable effect.

Eerie.

Elegant.

Think of it (Nancy revieries toward the departed Sluggo), the

constant crunching of relativistic space per unit distance apart, coupled

with the contant relativistic gain in rest mass per unit distance apart,

combines to create accelaration in the net effect continuing to grow more

powerful as the physical distance between the gravitation sources is

inexorably deleted, seen most ideally when the two bodies are moving

straight toward each other. Not to mention a slowing of time which

means the actual effect is a cube factor in the gravity between the

bodies.

This is not to say that such effects can be more truthfully

understood by means other than such models.

Whoa wait a minute. The relativity actions could contribute to,

but not be the source of, the force of gravity. Hmm and hmmmm.

Anyway, Nancy is now busy washing the static off in the shower.

Then next is to figure out what to make for lunch in the lunchroom. Its

a tossup between sardines and fresh picked sweet corn, or heading straight

to the fridge to her stash and making tuna fish sandwiches with a head of

lettuce, one that's been in the fridge long enough to turn brown in the

creases. GAD! the price of lettuce.

Hmmm, decisions, decisions.

- IN DIVINE ORDER -

RHAE S. LIVINGSTONE

JULY, 1990

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