"Is General Relativity Compatible With Special Relativity?"

When the writer first started to investigate General Relativity about
four decades ago, he was quite startled to learn that the results were
incompatible with the Principle of Equivalence and where therefore
incompatible with each other!. Until that point, the writer uncritically
accepted that both theories were completely valid, but this difference
signaled that something was wrong. To clarify, a brief digression would seem
to be in order.

In the late 19th century, the study of Dimensional Analysis was
developed. It was found that all physical relationships (equations) could be
defined in terms of three dimensional entities. Any three entities were
suitable and no more than three were required. The commonly chosen entities
were Mass(M), Length(L), and Time(T). There were attempts to reduce the
required number to two by substituting accepted physical constants, such as
the speed of light, for one of the dimensional entities. Careful examination
reveals however, that such a change merely substitutes that constant for the
eliminated entity and no simplification has occurred. (The writer has
received a few responses from individuals who strongly assert that
Dimensional Analysis is of no benefit in the study of Relativity. It is
obvious that they have not done their homework and their understanding of
the subject is marginal.)

For simplicity, the writer selected a system of dimensional entities
based upon Force(F), Length(L), and Time(T). (This choice is just as valid
as the conventional MLT system.) The dimensional entity content of all other
physical quantities, including mass, can be expressed in terms of force,
length, and time by using the appropriate expressions from the Science of
Physics. (A listing of the dimensional entity content of many common
physical quantities in the FLT system is provided in Table 8.2 of
http://einsteinhoax.com/hoax.htm.) The dimensional entity content of energy,
for example, equal to the product of force and length (F*L) and for velocity
is equal to length divided by time (L/T).

When one examines the Lorentz Transformations of Special Relativity he
finds that the transformations (parallel to velocity) for various physical
quantities may be determined by inserting the Lorentz Transformations for
force, length, and time for the dimensional entity content of the quantity
involved. Since, in terms of force, length, and time, the Lorentz
Transformations are, defining for velocity effects, $=(1-V^2/C^2)^0.5:

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

For example, the Lorentz Transformations for energy and for velocity thus
become:

Energy(E)= 1/(1-V^2/C^2)^0.5
Velocity(v)= 1/(1-V^2/C^2)

(It should be noted that the Lorentz Transformation for Velocity tells us
that, if the velocity of light measured locally is to be invariant (as
Special Relativity requires), then it must differ between velocity reference
frame in ABSOLUTE terms. This conclusion was clearly understood by the
intellectual giants of the time (Fitzgerald, Larmor, et al) but apparently
not by most of the individuals who followed (probably including Dr.
Einstein).

General Relativity provides a transformation for time which is
analogous to the Lorentz Transformation for Time (the time dilation) but,
unlike Special Relativity, does not provide an analogous transformation for
length. It asserts that the Gravitational Transformation for length is
unity! If we examine the equivalent functions provided by General Relativity
for gravity effects, defining # as the gravitational potential between
elevations, we find that
General Relativity provides:

Force(F) = 1
Length(L) = 1
Time(T) = G*M1*M2/(R*C)^2

And for the examples used above:

Energy = 1
Velocity = 1/G*M1*M2/(R*C)^2

To make up for the lack of a length transformation, General Relativity
assumes that space is distorted in proportion to the time dilation and also
provides a space dilation of (1-#). This incorporates the idea that space is
"curved" into a fourth spatial direction in the presence of a gravitational
field. Unfortunately, such a solution is only a partial fix for the conflict
between Special and General Relativity and cannot explain all of the
characteristics of the gravitational field nor rigorously define that field.

General Relativity is based upon the premise that the properties of the
gravitational field are identical to the properties of an accelerated
reference frame as defined by Special Relativity. Comparing the two lists of
transformations, one finds that this cannot be the case. As one changes
reference frames (elevation or Velocity), the results of observations would
differ depending whether one considered the observed force resulted from
spatial acceleration or from gravitational acceleration. For example, energy
as measured in the gravitational field would be unchanged while energy as
measured between moving reference frames would obey the Lorentz
Transformation for Energy! Obviously gravitational and inertial acceleration
cannot be considered to be the same under General Relativity and, since
Special Relativity seems to be beyond question, a mistake must have been
made in the derivation of General Relativity.

When one accepts the heretical possibility that a mathematical mistake
was made in the derivation of General Relativity it is not hard to find.
Embedded in the mathematics is an equation containing the second derivatives
of length and of time which must be integrated to achieve a solution. The
second derivative for time has a coefficient which allows the effects of
time dilation to be included. The second derivative for length has no such
coefficient! This omission arbitrarily forces a solution where any
gravitational transformation for length which results must be equal to unity
regardless of its proper value. Those familiar with undergraduate level
integral calculus will recognize immediately that the integration of the
length derivative without the allowance for a coefficient is a forbidden
operation and will normally yield erroneous results. The existence of this
error forced Dr. Einstein to spend almost 18 months seeking a means of
solving the equations of General Relativity. Unfortunately, instead of
fixing this basic mathematical error, he took the easy way out by asserting
that space was curved without any evidence of such curvature. In other word,
he FAKED IT! The justification given by a conference that accepted General
Relativity was 'why shouldn't we consider space to be curved, no one can
prove it isn't". Some science!

When one derives that nature of the gravitational field correctly one
sees that space is not curved and obtains, for the gravitational
transformations:

Force(F) = 1
Length(L) = 1/G*M1*M2/(R*C)^2
Time(T) = G*M1*M2/(R*C)^2

It will be noted that these transformations are analogous to the ones
for Special Relativity and the Principle of Equivalence really does work
since, for both theories, the product of the length and time transformations
is unity as is the force transformation. These transformations provide some
surprisingly rich results, including the source of gravitational energy, the
creation of our universe and provides insight as to what is external to it!
(Try it, you'll like it.) Dr. Einstein's blunder in the derivation of
General Relativity and the failure of the academic community to correct that
blunder has produced a great deal of mischief. This mischief has led to the
idea that Quantum Theory and General Relativity are in conflict (they
aren't). String Theory is not required.

The source material for this posting may be found in
http://einsteinhoax.com/hoax.htm (1997); http://einsteinhoax.com/gravity.htm
(1987); and http://einsteinhoax.com/relcor.htm (1997). 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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Weiv wrote:
"Is General Relativity Compatible With Special Relativity?"

Yes.

When the writer first started to investigate General Relativity about
four decades ago,

I'd say if that's the result of a 40-years long research then you
should give up the subject and pick a different hobby.

Spamming the newsgroup with a name handle that's changing every few
days to avoid killfiles doesn't help your reputation, BTW.

--
Jan Bielawski