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???????????? INTRODUCTION TO MASS INCREASES BY ????????????
???????????? GRAVITATIONAL RELATIVITY ????????????
???????????? ????????????
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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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? ????????????? GRAVITATIONAL RELATIVITY THEORY ???????????? ?
? CONNECTS CERTAIN SOLAR PLANET MASSES. ?
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? ????????????????????????????????????????????????????????????????????? ?
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? ALSO, GRAVITATIONAL AND SPECIAL RELATIVITY THEORIES ?
? ARE INTRINSICALLY RELATED ?
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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.
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? ????????????????????????????????????????????????????????????????????? ?
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? ABSTRACT ?
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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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? part 1 ???????????????? GRAVITATIONAL RELATIVITY ???????????????? ?
?????????????????????????????????????????????????????????????????????????
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.
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? part 2 ???????????????????? SPECIAL RELATIVITY ?????????????????? ?
?????????????????????????????????????????????????????????????????????????
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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? part 3 ??????????????? THE GOLDEN HARMONIC RATIO ???????????????? ?
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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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?????????????????????????????????????????????????????????????????????????
? ????????????? GRAVITATIONAL RELATIVITY THEORY ????????????? ?
? ????????????????????????????????????????????????????????????????????? ?
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? ?????? GENERAL INTRODUCTION for part 1 The Solar System ??????? ?
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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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??? GRAVITATIONAL RELATIVISTIC EFFECT ?
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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.
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??? GENERAL MASS QUANTA EFFECT ?
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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.
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? GRAVITATIONAL RELATIVISTIC EFFECTS ?
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The standard equation for gravitational relativistic effect
is described as follows:
EQUATION A
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? 2G (Mass)
E = ? 1 ? ???????
\? C? 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.
?? ??
? ?? ?? ? Where Re is the
? ? 1 ? ? amount of space
? R x ? ??? ? ? - R = Re by which the Sun's
? ? E ? ? radius is contracted
? ?? ?? ? by the relativity
?? ?? in the Sun's mass
?? ?? Ro is the original
?? Ro ?? 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.
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??? ESTIMATED ACCURACY OF SOLAR MASSES ?
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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 ? .004 x 10 to 27 grms)
is multiplied by the Sun to Earth mass ratio (332,995.9 ? .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.
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??? BASIC CONVENTIONS ?
?????????????????????????????
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.
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? MASS CONVENTIONS ?
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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 ? 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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? ????????????????????????????????????????????????????????????????????? ?
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? INFERRING A GRAVITIONAL RELATIVISTIC ?
? AUGMENTED MASS VALUE FOR THE SUN ?
??????????????????????????????????????????
TABLE 1 INFERRED VALUES
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? ?
? MM = Existing Sun mass, presumed to include ?
? original mass plus mass augmentation K ?
? ?
? = 1.9909930 x 10 to 33 grms ?
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? ?
? K = Gain in original mass of the Sun, the ?
? amount of relativistic augmentation ?
? due to the Sun's gravity ?
? ?
? = 4.226490 x 10 to 27 grms ?
????????????????????????????????????????????????????????????
? ?
? Mbh = Mass of a black hole having an event ?
? horizon equal to the Sun's radius R ?
? ?
? = 4.689536679 x 10 to 38 grms ?
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TABLE 1-A ESTABLISHED VALUES
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? ?
? R = Existing Sun radius ?
? = 6.96265 x 10 to 10 cms ?
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? ?
? C = Speed of light ?
? = 2.99792458 x 10 to 10 cms/sec ?
????????????????????????????????????????????????????????????
? ?
? G = Universal gravitational constant ?
? = 6.6720 x 10 to -8 cms3/grms sec? ?
????????????????????????????????????????????????????????????
? ?
? CR = A physical constant for Mass/Radius ?
? ratio of a black hole ?
? = 6.735275620 x 10 to 27 grs/cm ?
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? ?
? GH = Golden Harmonic Ratio ?
? = 1.61803398875 ?
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TABLE 2
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? ?
? Planetary masses - Data is from tables found at the ?
? back of the following reference: ?
? ?
? UNIVERSE by Don Dixon, Houghton Mifflin Co., ?
? Boston, 1981 ?
? ?
? Moon = .0735 x 10 to 27 grms ?
? ?
? Venus = 4.8683 x 10 to 27 grms ?
? Earth = 5.976 x 10 to 27 grms ?
? Mars = 6.4181 x 10 to 26 grms ?
? Jupiter = 1.901 x 10 to 30 grms ?
? ?
? Sun = 1.9888 x 10 to 33 grms ?
? ?
????????????????????????????????????????????????????????????
TABLE 3
Certain terms are used to generalize certain types of masses:
????????????????????????????????????????????????????????????
? ?
? Low mass - Masses in the range of those found ?
? in this solar system ?
? ?
? Enhanced mass - Solar mass aggregates other ?
? than the Sun, added or subtracted ?
? to the Sun mass ?
? ?
? - Specifically the mass of the ?
? Sun plus 1/2 Jupiter, and mass of ?
? the Sun minus 1/2 Jupiter, also mass ?
? of the Sun minus mass of Venus ?
? ?
? Higher mass - Mass of a black hole, and in mass ?
? range of a black hole ?
? ?
? - Specifically the mass for a ?
? black hole whose event horizon ?
? is the radius of the Sun ?
? ?
? ?
? Originating mass - Original mass accumulation without ?
? any relativistic augmentation ?
? ?
? Augmented mass - Existing mass assumed to include ?
? a change from the originating ?
? mass due to relativistic effect ?
? of gravity ?
? ?
? Existing mass - As physically measured, with ?
? any assumed augmentation present ?
? in the measurement ?
? ?
? Real mass - A real weight, in terms of a ?
? physical weight, for instance ?
? measured in grms as if weighed ?
? on a scale ?
? ?
????????????????????????????????????????????????????????????
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:
????????????????????????
? 2G (MM) Where MM is the mass
Em = ? 1 ? ??????? of the Sun, and R is
\? C? 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:
???????????????????????????
? 2G (MM+X)
Ex = ? 1 ? ???????????
\? C? 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:
???????????????????????????
? 2G (MM+1/2j)
E+1/2j = ? 1 ? ???????????
\? C? 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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? ????????????????????????????????????????????????????????????????????? ?
?????????????????????????????????????????????????????????????????????????
? VERIFYING A MASS OF MM FOR THE SUN ?
???????????????????????????????????????????????????
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
?????????????????????? (1.989 x 10 to 33 grms)
? 2G (b+X)
E = ? 1 ? ???????? And so (b+X) - ((b+X) x E) = K,
\? C? 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
?????????????????????? mass, so MM - ((MM) x Em) = K
? 2G MM where K = (Venus - Mars),
Em = ? 1 ? ????? and Em is the relativistic
\? C? 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.
?????????????????????????????????????????????????????????????????????????
? ????????????????????????????????????????????????????????????????????? ?
?????????????????????????????????????????????????????????????????????????
? SPECIFIC MASS QUANTA EFFECT ?
???????????????????????????????
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
????????????????????????? (MM+1/2j) is the
? 2G (MM+1/2j) aggregate of the Sun
E+1/2j = ? 1 ? ??????????? mass plus 1/2 the mass of
\? C? 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).
??????????????????????????????????????????????
??? VERIFYING THE COHERENT 1/2j STATES ?
??????????????????????????????????????????????
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
??????????????????????
? 2G Mtx
Etx = ? 1 ? ??????
\? C? 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
? 1/2 Jupiter as displayed in Equations E-1 to E-4 came to be
an issue.
???????????????????????????????????????
??? OTHER MASS AGGREGATE STATES ?
???????????????????????????????????????
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.
??????????????????????????????????????????
??? OTHER MASS EFFECT COHERENCIES ?
??????????????????????????????????????????
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 ? 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 ? 1/2 the mass of Jupiter
The case of X being equal to ? 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
????????????????????????
? 2G (MM-Me) Where (MM-Me) is mass MM
Ee = ? 1 ? ????????? minus the mass of the Earth Me.
\? C? 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
??????????????????????
? 2G (M-X) Where (M-X) is mass M minus
Ex = ? 1 ? ??????? any other mass X, and radius
\? C? 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 --
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