General Relativity Examined

In 1915 Dr. Einstein published the General Theory of Relativity. It
accepted the Principle of Relativity (the laws and constants of the Science of
Physics were the same in all reference frames) as a postulate (upon which
Special Relativity was based) and added the Principle of Equivalence. The
Principle of Equivalence asserts that it is not possible to distinguish between
the effects of inertial acceleration and gravitational acceleration.

In a Force-Length-Time system of units, the Special Theory of Relativity
(STR) can be expressed in terms of the Lorentz Transformations for Force,
Length, and Time. (These Transformations plus the fact that information could
not, at least at that time, be transferred faster than the velocity of light
completely explained the effects of velocity in terms consistent with the idea
that an "absolute velocity reference" (i.e.- the Aether) was not required for
evaluating observations (usually ignored is the fact that the existence of the
Aether was not forbidden by STR).

The appropriate Lorentz Transformations for velocity both as provided by
the Lorentz Transformation-Aether Theory and by Special Relativity are provided
below:

Dimensional Entity--------------Value

Force (F)-----------------------1
Length (L)----------------------1/(1-[V/C]^2)^0.5
Time (T)------------------------(1-[V/C]^2)^0.5

(All other required transformations can be derived from the above by applying
19th the Century technique of Dimensional Analysis to known and well tested
physical laws.)

When one examines the above transformations, he finds that the Principle
of Relativity is satisfied because they have the property of "multiplicative
commutivity". This means that one can use the transformations to go from one
reference frame to another to another successively and obtain the same result
as if he went from the first reference frame directly to the last. This
property occurs in the Lorentz Transformations because the transformation for
energy (force-length product) and the transformation for time are reciprocal to
each other and because they contain a minus sign which allows the
transformation to have a zero value when V=C. The rotation of axes introduced
by the mathematical treatment of STR results from the fact that the Lorentz
Transformations are identical to the expressions of the Pythagorean theorem.
There is no conflict between the Lorentz Transformation Aether Theory and the
Special Theory of Relativity since the former is a special case solution of the
latter.

The writer's first had cause to question the validity of General
Relativity in the early 60's when, in studying the mathematics of GTR, he came
across GTR’s transformations equivalent to those of STR:

Dimensional Entity------------Value

Force (F)----------------------1
Length (L)--------------------1
Time (T)-----------------------1/(1+$)
Space (S)----------------------1/(1+$)

Where "$" is the gravitational potential between two elevations as defined with
the upper elevation units of measurement for energy. (The value of "$" is
identical with the equivalent term in the time dilation provided by GTR.) It
will be noted that, in order to solve the equations used in deriving GTR, Dr.
Einstein found it necessary that space be "curved" and thus the transformation
represented by that curvature is also provided.

The difficulty with the above transformations is that, without a
transformation for energy that was reciprocal to the transformation for time,
GTR cannot satisfy the Principle of Relativity and, since it doesn't, it must
predict that physical laws change as a function of elevation. Such an effect
should quickly become obvious. Since these laws do not appear to change, even
in strong fields, the writer began to search for a better way of deriving the
nature of the gravitational field and to determine where the mathematics of GTR
went wrong. (The subject is amply covered in "Gravity" [1987] at the Website.)

Examination of the above table also shows that, in addition to violating
the Principle of Relativity, it violates the Principle of Equivalence because
it does not provide transformations that are analogous to the Lorentz
Transformations. The dilation for time is not balanced by a reciprocal
transformation for energy and does not contain a minus sign that would allow
the dilation to have a zero or infinite value. With these transformations, one
would obtain the absurd conclusion that a different result would occur if an
elevator going from the first floor to the third floor happened to stop at the
second floor.

It would appear that GTR is flawed. Not only does it violate its basic
postulates, the Principles of Equivalence and of Relativity, it provides the
strange conclusions associated with GTR (e.g. - curved space, black holes,
singularities, wormholes, incompatibility with Quantum Theory, the existence of
a quantum foam at the scale of 10^-34 meters, Superstring Theory, and its
failure to account for the forces effecting interstellar matter [“dark
matter� and the increasing rate of the Universe’s expansion].) Most
significantly, it also leads to the conclusion that the alleged "Big Bang"
origin of the Universe resulted not from an observed expansion of the location
of matter but from an expansion of space itself that will continue
indefinitely. Unfortunately the latter conclusion has several weaknesses. It
requires that energy be continuously added to our Universe from some
unexplained source in gross violation of the First and Second Law of
Thermodynamics and it requires that space must have somewhere in which to
expand that is outside of space. Concluding that space itself is expanding and
that the energy implied by this expansion is continuously being supplied from
an external source is one of the most extreme acts of "Faith" in what can only
be described as a "Religion" built around GTR. The concept certainly does not
meet the requirements of a self consistent fact based Science.

Once the correct time dilation for gravity has been determined though a
simple thought experiments relying on basic, well known, and easily testable
physical laws, it is easily shown that the requirement of multiplicative
commutivity and the Principle of Equivalence is satisfied in terms of Euclidean
Space by the following gravity transformations:

Dimensional Entity-------------------Value

Force (F)------------------------------1
Length (L)----------------------------1/(1-$)
Time (T)-------------------------------(1-$)

It should be noted that the above could be derived by applying the Rules
of Dimensional Analysis to accepted and readily verifiable physical laws in
simple “thought experiments� and by a second independent method. Analyzing
Dr. Einstein's Elevator Model rigorously and taking into account the external
work being done on the elevator in order to accelerate it "upwards" (as model
theory requires but was not done) yields the identical transformations.
Including the transformation for length increases the gravitational mass of
photons and neutrinos to twice the gravitational mass of material particles of
the same energy content. The effect of the gravitational transformations is
that light is refracted by a gravitational field, in terms of three dimensional
space, by the amount revealed by astronomical observation. It is also easily
shown that the paths of moving material objects are also refracted by
gravitational fields to the same degree as are photons and neutrinos. The
observations that allege to show that the gravitational field causes space to
be "curved" actually result from this refraction is terms of "flat" space. (The
false conclusion that, while our overall Universe has been shown
observationally to be "flat", space is "curved" in the presence of local
gravitational fields results from that refraction in locally "flat" space. If
this were not true, a perpetual motion machine of the first kind would be
possible in principle, an obvious absurdity.)

When one apples these transformations to the gravitational field, it is
found that energy in the gravitational field is conserved in the "absolute
sense" because the Principle of Relativity and the reduction in size of the
units of measurement of energy causes a reduction of that "absolute" energy
contained in matter. This reduction in the "absolute" energy of the matter
appears as the energy of fall, and, since the units of measurement for length
are shrinking, space is not expanding but only appears to do so! The overall
universe, as observed from within, must be as has already been observed, "flat"
and it will appear to expand forever, probably at what appears to be an ever
increasing rate.

The observed expansion does not result from an unexplained repulsive force
acting on the matter contained within it but as a result of the gaseous
pressure exerted by the neutrinos and photons existing in space. The estimates
that the writer has seen of the amount of matter in the known Universe suggest
that the observed electromagnetic radiation of 3 Kelvin’s has an energy of at
least 10 times the energy represented by the matter in the Universe and, as
such would have a gravitational mass of at least 20 times the mass of the
matter contained in the Universe. In addition, since the nucleon is 1800 times
more massive than the electron, the energy represented by neutrinos COULD be as
large as 1800 times the energy represented by photons. Following this argument,
the combined gravitational mass of photons and neutrinos in the Universe COULD
be as large as 36,000 times as large as the trivial gravitational mass of the
matter it contains. Such a Universe would be reasonably described as a balloon
of gaseous photons and neutrinos containing a minute sprinkling of matter
"dust". (These results are shown in "Gravity" copyright 1987.) Also shown is
that the observations that allegedly validated GTR are a natural result of the
transformations in the above table without the need for the artificiality of
"curved space."

It has always puzzled the writer as to why photons and neutrinos are
considered to be "massless" particles. They clearly possess inertial mass as
evidenced by the radiation pressure exhibited by light, and they can be shown
to possess gravitational mass. The fact that they do not possess a "rest mass"
would hardly seem to justify considering them to be massless since they do not
exist unless they are traveling at the velocity of light. Maintaining correct
definitions is important if one's thinking is to be accurate.

The test of any physical theory is whether it agrees with the results of
mathematical analysis and with all of the relevant observations. The generation
of General Relativity contains a mathematical error that would not be tolerated
if made by a student of freshman calculus. As a result, the derivation could
not be completed without adding the extra degree of freedom that the
artificiality of non-Euclidean geometry provides. General Relativity agrees
with observation only with respect to 1st order effects, hence its apparent
agreement with observation in the extremely weak gravitational fields in the
Solar System. (The observation limit is at least 5 orders of magnitude too
coarse to reveal GTR’s 2nd order errors and allows the acceptance of the
current absurdities.) When the appropriate corrections are made, the alleged
"Big Bang" origin of the Universe is seen to be a natural process of
gravitational collapse as observed from the interior of the collapsing object
late in its history. Most importantly, General Relativity contains a zero order
error with respect to gravitational force and energy and as a result it cannot
explain the force that holds you to your chair and the energy that injures you
when you fall. (This should be the prime purpose of any gravitational theory.)
A treatment based upon the gravity transformations consistent with the
Principle of Equivalence as listed above seems to meet all of the requirements.


One might ask how General Relativity could be wrong. The answer is that
its derivation applied the mathematical process of integration and attempted to
use the results of that integration to derive the constants of the terms to be
integrated. If any student of elementary calculus repeatedly attempted to
perform such an operation, he would find himself repeating the course. In order
to overcome the effects of his mathematical mistake, Dr. Einstein resorted to
the fiction that space is "curved" and that gravity results from that
curvature. This, despite the fact that an intelligent man should immediately
recognize that such a curvature cannot produce the force which hold you to your
chair any more than the curve of the Earth's surface can impel you to move from
New York to Chicago. When examining the history of General Relativity, it is
hard to understand how such an error could have been made unless one or more of
the following were true:

1:- Dr. Einstein did not understand the physical significance of Relativity.

2:- He did not understand the rules of integral calculus.

As a result of failing to solve his difficulty in terms of Euclidean space
because of his error in the use of Tensor Calculus, it would seem possible that
he solved his dilemma by "faking it", either intentionally or in ignorance, by
resorting to the artificiality of non-Euclidean geometry. He certainly would
know that the gravitational fields available in the Solar System were too weak
to reveal the effects of any 2nd order error. (It has been reported that Dr.
Einstein was extremely uneasy at the extension of GTR to extremely strong
fields, and at a conference where GTR was debated, the conclusion reached was
"why shouldn't we consider space to be curved, no one can prove it isn't".
Actually they can and the proof is easy.)

There are at least two lessons here. One lesson is Dr. Einstein's warning
that "one should rely on observation and reasoning and not be swayed by the
unproven opinions of others no matter how numerous or renowned they may be".
(This also applies to Dr. Einstein’s conclusions). The second lesson is that,
while mathematics is a very useful tool, but it is only a tool and has its own
limitations. A major limitation is that the probability of error increases as
the number of steps involved become larger and quite often the existence of
such an error is not revealed by the results. Another limitation is that there
are processes that can be described mathematically but which cannot work in
reality unless an additional mechanization not considered in the mathematics is
present. (An example is the calculation of the output of a vacuum tube using
its property of transconductance. The mathematics shows that applying a
negative voltage to the control grid produces an increase in its positive plate
current. The mathematics does not show that this cannot occur unless there is a
bias plate current already flowing and that the apparent increase in plate
current results from a reduction in the flow of the bias current electrons.)

Mathematics should never be used without the an intelligent understanding
of the mechanisms involved, as was the practice prior to Dr. Einstein's work.
(In the case of GTR, one of the errors was the fact that the definition of a
straight line currently in use is inadequate even for Euclidean geometry. A
straight line is more properly defined as the shortest distance between two
points WHICH REMAINS WITHIN THE GEOMETRY IN QUESTION. This additional
requirement is automatically met in Euclidean Geometry, but, in the case of
non-Euclidean geometry, the shortest distance between two points does not meet
that definition. In the two dimensional non-Euclidean geometry represented by
the Earth's surface, the shortest distance between New York and Los Angeles is
not a great circle as we have been taught, it is through a tunnel which passes
about 200 miles below the Mississippi river.)

For decades, it has been recognized that GTR and the related concept of
"space-time" of STR conflicted with Quantum Theory. Experimental results
indicate that Quantum Theory is valid to an extreme degree of accuracy, but,
for some reason, no one seems to have questioned the validity of GTR. To
resolve the dilemma Superstring Theory has been developed which asserts that
space is actually 10 dimensional and that the excess dimensions were in the
form of loops having a conveniently unobservable diameter of 10^-34 meters. It
must be pointed out that any jackass can solve a problem by adding an otherwise
unnecessary degree(s) of freedom.

The source material for this posting may be found in "Gravity" (1987),
"The Einstein Hoax" (1997), and "Corrections to Residual Errors in Special
Relativity (1999) located at http://www.members.aol.com/einsteinhoax/site.htm .
EVERYTHING WHICH WE ACCEPT AS TRUE MUST BE CONSISTENT WITH EVERYTHING ELSE WE
HAVE ACCEPTED AS TRUE, IT MUST BE CONSISTENT WITH ALL OBSERVATIONS, AND IT MUST
BE MATHEMATICALLY VIABLE. PRESENT TEACHINGS DO NOT ALWAYS MEET THIS
REQUIREMENT. THE WORLD IS ENTITLED TO A HIGHER STANDARD OF WORKMANSHIP FROM
THOSE IT HAS GRANTED WORLD CLASS STATUS.

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