Posting #4:-"General Relativity Examined"
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"Great spirits have always encountered violent oppositions from mediocre minds." - A. Einstein
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:
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:
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:
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 "The Einstein Hoax" (1997) ; "Gravity" (1987) ; and "Corrections to Special Relativity" (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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