# "General Relativity Examined"

*From*: "Wol" <wol@xxxxxxx>*Date*: Wed, 18 Mar 2009 09:34:14 -0400

"General Relativity Examined"

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

Space (S) = G*M1*M2/(R*C)^2

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

http://einsteinhoax.com/gravity.htm [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 length and does not contain the 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/G*M1*M2/(R*C)^2

Time (T) = G*M1*M2/(R*C)^2

It should be noted that the above are 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

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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