Challenging Einstein
Einstein the Hoaxer

A Review and Comments on Pari Spolter's Mathematical and Scientific Forensic Investigation into the Suspicious Claims of Einstein's Theories of Relativity, both General and Special 

by John Lear

Einstein was a brilliant mathematical hoaxer. While other hoaxers use simple tricks and tools with a common objective, usually money, Einstein used advanced mathematics to perpetrate his hoax and it is unknown what his true objective was.

His hoax was so complex that the only people who suspected it was a hoax were ignored as terms like "special relativity", "curved space", "simultaneity", time dilation and length contraction exploded in popularity.

The ingenious key to the hoax was two-fold: its complexity and audacity.

That it was deliberate and continuing cannot be denied. Numerous contemporaries and others including, Bruno Betotti, Robert H. Dicke, Edmund Whittaker, Harald Nordenson, G.H.Keswani, Herbert Dingle, Alfred O'Rahilly, Leon Broullouin, Louis Essen, Hendrik Lorentz, G. Burniston Brown, F. Gonzalez-Gascon, Artemio Gonzalez-Lopez, S. Marino, A.A.Logunov, P. Lenard, Tullio Levi-Civita, M.A. Mestvirishvili, P.W. Bridgeman, H.K.Wimmel, N.T.Bishop, Richard Tolman, David Bohm, Mendel Sachs, D.F.Lawden, Dewey Larson, George Gamow and Ian Stewart all questioned the mathematical basis, physical theories and lack of experiments on which Einstein based both his General and Special Theory of Relativity.

Pari Spolter, in her book "Gravitational Force of the Sun" takes a mathematically forensic look at General Relativity and its illegitimate son, Special Relativity and exposes as fraudulent what many have claimed to be one of the greatest mathematical achievements of all time.

She begins by reminding us how students at the undergraduate or graduate level are introduced to what O'Rahilly describes as 'the monstrosity of space-time."

She shows an example of a problem advanced students of applied mathematics and physics are asked to work out as an exercise to help understand the subject.

The problem involves:

  • (a) a tachyon transmitter emitting tachyons at speeds greater than the speed of light, 
  • (b) observers, and
  • (c) a second tachyon transmitter.
The solution involves proving that a reply is received before it is transmitted. Pari presents this problem to show the absurdity with which students are confronted and forced to accept in the study of higher mathematics.
She also points out that Lorentz, on whose equations the entire scheme was based, never accepted the concept of a merged spacetime and that Michaelson had expressed regret that his work had been turned into this 'monster'. As Robert Shankland relates, Einstein told him, "He (Michelson) told me more than once that he did not like the theories that had followed from his work."

Pari shows us how from three dimensional Euclidean geometry we get the velocity vector by differentiating with respect for time. From that velocity vector we obtain the acceleration 

a = ax + ay + az

Acknowledging that force is proportional to acceleration we take the equation for the four dimensional spacetime and differentiate it with respect to time, and, assuming that c is a constant according to Einstein's Second Postulate of special relativity we get



and taking the time derivative of this velocity equation we get

a = axi + ayj + azk - c2

Pari has shown that the fourth dimension has disappeared in calculations of accelerations. She points out the acceleration vector is identical to the acceleration vector of three dimensional space except that the same value starts at – c2.

Pari concludes "that an imaginary four dimensional spacetime continuum is unfit as a foundation for physics, a science which mainly deals with measurements of velocities, accelerations and the changes of these vectors."

She also states that Einsteins field equations, actually a set of 10 second-order partial differential equations using the "Einstein tensor", the Riemann tensor of curvature, the scalar of curvature formed by repeated contraction, the tensor of mass or energy density and a proportionality constant. The left-hand member of these equations represents the geometry of spacetime, and the right-hand member is an expression for the distribution of matter and energy. The solution of these field equations was only possible in a limited number of simplified physical situations and was nothing more than elegant mathematics; complex equations for naught.

Neither was Einstein's field equations based on an independent analysis of observation or an interpretation of experimental data. When his mathematical symbols take on physical expression, he assumes approximation to Newton's theory and borrows the classical figures. His proportionality factor is based on the Cavendish gravitational constant.

As Pari says, "Newton's concepts of absolute time, absolute space, and a centripetal force, and Einstein's notions of a merged spacetime, and of relativity of simultaneity, are mutually exclusive and contradictory ideas. We cannot accept both of these opposing views at the same time."

Brillouin puts it more bluntly, "General Relativity is a splendid piece of mathematics built on quicksand and leading to more and more mathematics about cosmology (a typical science-fiction process)."

General Relativity was a mathematical scam introduced and 'proven' by 'sleight of mathematics'. 

Pari Spolter begins her forensic investigation which questions Einsteins Theory by disproving the four experimental tests cited in the literature in support of General Relativity: 

  • (1) The Principle of Equivalence
  • (2) The Gravitation Red Shift
  • (3) The Gravitational Bending of Light, and
  • (4) Perihelion Rotation
On the Perihelion Rotation front Pari addresses
  • (a) Optical Photography
  • (b) Radio Interferometry and
  • (c) High Powered Radar
Addressing the Principle of Equivalence, Pari notes that Einstein stated it was the complete physical equivalence of a gravitational field and a corresponding uniformly accelerated reference system.
Pari points out that the experiments cited in the literature actually fail to show the one and the same bulk of inert matter is endowed with two separate attributes: 
  • (1) inertial mass, and
  • (2) gravitational mass and that inertial mass is equal to the gravitational mass.
She further points out that the experiments have shown and to a very high degree that gravitational force is independent of the nature (and of the quantity) of the attracted body.
Addressing the Gravitational Red Shift Pari points out that Einstein interpreted the change in wavelength of the spectral lines of the Doppler Principle (for which no relativistic concepts are involved) in the derivation of the Doppler Principle for the velocity of a photon in an accelerated field as evidence of time dilation. She points out that:
  • (1) There is no credible basis for this claim, and
  • (2) Orwood J.Johnson lists 12 arguments for rejecting the idea that light frequency is a measure of time or time dilation.
In fact the whole issue of time dilation and Einstein's use of the Lorentz time dilation equation to support his theory of Gravitational Red Shift started with U.S. physicist Albert Abraham Michelson and Edward William Morley's attempt to measure the velocity of the Earth in laboratory experiments using an interferometer.
They measured the displacement of the fringes upon rotating their apparatus by 90 degrees. The magnitude of the shift observed was less than what they expected, based on the assumption made by their calculation. To explain this Michelson-Morley data, the Dutch theoretical physicist, Hendrik Anton Lorentz, suggested a (purely) hypothetical change in length produced by motion.

The French mathematician Henri Poincare made some revisions to the Lorentz (hypothetical) equation and proposed that the modified formula be called the Lorentz Transformations which are now referred to as the Lorentz Transformation equations with no reference to its hypothetical derivation.

As Pari correctly points out, Einstein in his celebrated paper of 1905 extrapolated the behavior of undulatory photons to rigid bodies of all sizes travelling in a straight line; and for the first time in history he created a science based on the manipulation of dates and the manipulation of measurements of length.

In fact,'length contraction' is based on Lorentz's arbitrary contraction factor and Poincare's subsequent 'revision'; and 'time dilation' which is a convolution of the same.

A concept with even less fact but double in fantasy was Einstein's 'relativity of simultaneity',("There is no such thing as simultaneity of distant events") which Einstein claimed was an "insight(s) of definite nature which physics owes to the special theory of relativity." His other 'insight' was "eliminating mass as an independent concept".

Addressing the Gravitational Bending of Light Pari notes that Bavarian astronomer Johann Gorg Soldner in 1804, derived an equation for the gravitational bending of light to be 0".84, as the angle of deflection of a ray of light from a fixed star to the surface of the Sun.

In the last section of his 1911 paper, Pari says Einstein calculated that a ray of light from a distant star, grazing the limb of the sun on its way to earth, would be deflected by 0.83 seconds of arc. He also stated that the fixed stars near the sun were visible during total eclipses of the sun and suggested that astronomers should look for this effect.

Four years later Einstein allegedly used the field equations of his newly proposed Theory of Gravitation and doubled the deflection angle to 1.7 arcsecond.

Two British astronomical expeditions in 1919 provided an 'approximate confirmation' of Einstein's prediction which he claims, "half of the deflection is produced by Newtonian field of attraction of the Sun and the other half by geometrical modification ('curvature') of space caused by the sun. Although later scrutiny of the specific photographs taken on the Arthur Stanley Eddington expedition showed the experimental uncertainty to be about the same magnitude as the effect Eddington claimed to have demonstrated, the media had already launched Einstein into meteoric popularity.

Pari, calculating the acceleration due to solar gravity, establishes by Fs = a. A the gravitational force of the Sun, (the correct interpretation of Kepler's Third Law) arrives at 1".75 using no relativistic concepts.

She discusses the problems of measuring light deflection by solar gravity using:

  • (a) Optical Photography
  • (b) Radio Interferometry, and
  • (c) High Powered Radar
In addressing Optical Photography observations Pari notes that "in analysis of the data it assumed that Einstein is correct and the least square fit is calculated. Pari also notes that "Often analysis of the same observations by different authors has produced different figures" and that "In all these observations a considerable percentage of the actual measured data have been discarded as 'accidental errors'. Data from the original 1919 and the 5 subsequent total solar eclipses observations are plotted on page 50 of the book. The data are all over the graph. They do not prove anything."
In addressing Radio Interferometry Pari notes that in these experiments radiation emitted in cm wavelength from a quasar was monitored by an interferometer as the radio source is occulted by the Sun. A number of assumptions were made in the calculation of the gravitational bending including, as in both optical and high power radar measurements, that Einsteins General Relativity was correct.

Pari notes that in addition to bending, the solar corona also causes scattering of the radio waves. As the solar limb approaches the line of sight, the apparent size of the quasar steadily increases because of the scattering in the corona. Thus the effective signal to noise decreases. For this reason, she notes that her prediction of a decrease in the deflection angle as the inverse square of the impact parameter for less than 4R cannot be obtained by radio interferometric observations and therefore a critical test of Einsteins light bending equation (based on Newton's Theory of Gravitation) is not possible with this method.

Addressing High Powered Radar detection of light deflection by solar energy using time delays in transmitting and receiving signals from planets, artificial satellites or spacecraft anchored to a planet Pari notes that in all of these radar time-delay experiments the data was processed by computer programs assuming that (as in all other experiments) General Relativity was correct and the least squares fit was calculated, and that further, the collected data at distances close to the sun were downweighted or ignored.

She also notes that R.D.Reasenberg, et al, (The Viking Relativity Experiment: Verification of Signal Retardation by Solar Gravity) claim to have verified the prediction of General Relativity to an estimated accuracy of 0.1% although they admit that they had deleted 10% of the data because of their very large, up to 20 microsecond residuals; and that most of the deleted data were obtained near conjunction. They further stated that "No definite explanation has been obtained for these anomalies."

Also noted is that radar cannot be directed towards the solar limb because of interference with the corona.

Pari concludes "In the time-delay radar experiments as in the radiointerferometric methods no data for her prediction of a decrease in the deflection angle as the inverse square of the impact parameter for less than 4R are available; and thus a conclusive verification on Einsteins light bending equation (based on Newton's Theory of Gravitation) is not possible using high powered radar.

The fourth front of Pari's forensic dissection of the General Relativity fraud is Perihelion Rotation.

The issue of Perihelion Rotation is this: In 1859 French mathematician and astronomer Urbain Jean Joseph Le Verrier reported that the advance in the perihelion of Mercury (arriving at its closest point to the sun) was greater than could be accounted for by adding the gravitational effects of the known planets. In 1895 Simon Newcomb, a U.S. Navy Admiral, leading astronomer and superintendent of the American Nautical Almanac published "The elements of the four inner planets and the fundamental constants of astronomy" and confirmed the discordance discovered by Le Verrier. In 1915 Einstein derived an equation in which he purported to account for the variation for the longitude of perihelion of a planets orbit using the field equation of General Relativity and claimed that his new theory of gravitation explained the anomalous motion of the perihelion of Mercury.

Pari takes issue with Einstein's claim noting that "Here again Einstein has combined two contradictory concepts:

  • (a) the classic absolute time, absolute space, and Newton's idea of a centripetal force, with
  • (b) general relativity's hypothesis of a curved four dimensional spacetime continuum; and has come upon an equation that gave the expected advance in the perihelion of Mercury; but that accounted for only 1/6 of the advance in the perihelion of Mars, and could not explain the anomalous motion of the nodes of Venus.
Pari notes these comments by Einstein's friends and contemporaries regarding the perihelion equation:
Max von Laue (close friend of Einstein):
"The agreement between two individual numbers (the perihelion prediction of Einstein and Newcomb anomaly) achieved under conditions which cannot be arbitrarily altered, so that it seems uncertain whether the suppositions (specifically the assumption of two mass points) are fulfilled with sufficient accuracy, does not seem to be sufficient reason, even though it is note-worthy, to change the whole physical conception of the world to the full extent as Einstein did with this theory."
Jean Francois Chazy (noted French mathematician);
(Translation) "In all fairness, at the present status of science, the value of the advance of Mercury's perihelion as an argument for the theory of Relativity does not, could not have the definitive character that some people believe it to have."
Pari skewers Einstein's claim to have solved the anomalous motion of the perihelion of Mercury with an equation based on his Theory of General Relativity with nine other different arguments.
Pari further remarks that Einstein's general theory of relativity does not explain:
  • (1) the rotation of the celestial bodies
  • (2) the orientation of the axis of rotation of the planets
  • (3) the orbital planes of all the planets approximately on the solar equatorial plane (±12?)
  • (4) the inclination of the plane of the orbit of each planet
  • (5) the direction of movement of the planets (counterclockwise) as viewed from north)
  • (6) the distance law (Titius-Bode)
  • (7) the eccentricities
  • (8) the regression of the nodes
  • (9) the precision of the equinoxes
  • (10) the perturbations
Other noted scientists and mathematicians comment on general relativity:


Dicke writes, in the preface of his book, 'The Theoretical significance of Experimental Relativity';

"In my view the grand opportunity for the experimentalist lies not in the applications of General Relativity but rather in its foundations. It would be a shame for dozens of very able theorists to devote a second half century to developing the results of General Relativity only to discover that the theory is defective, and that some basic assumption is incorrect."
Later, in the 'Introduction' of the same book, Dicke writes;
"Here is an elegant, well defined theory but almost no experiments…Far from experimental science being a crutch on which the theory leans, in the case of general relativity, theory has far outstripped experiment, and the big problem is one of finding significant experiments to perform. This situation raises serious problems for theory and our understanding of gravitation. For where there are no experiments the theory easily degenerates into purely formal mathematics".
Louis Essen points out that the Lorentz length contraction factor is an arbitrary assumption. He remarks that physicists seem to abandon their critical faculties when considering relativity. Essen concludes;
"The so-called theory of special relativity is thus not a theory at all but simply a number of assumptions and the assumptions made implicitly in the course of thought experiments contradict those made initially."
G. Burniston Brown indicates that many physicists feel that the theory of relativity is not a genuine physical theory.
Pari summarizes;
"There is no direct experimental proof of the assumptions made by Einstein to postulate the relativity theory, the special or the general. Plausible alternative explanations can be offered for all laboratory and astronomical observations cited in support of the theory."
Einstein's equations of relativistic dynamics are mathematically incompatible with the experimentally verified Plank's formula of quantum mechanics. These problems, as well as the concept of "negative mass" in relativity and Einstein's postulates of "longitudinal mass" and "transverse mass" are all hypothetical concepts with no experimentally provable or other basis in science.
Pari then points out that many physicists who believe that Einstein's theory of relativity to be flawed have not been able to get their papers accepted for publication in most scientific journals. Eminent scientists are intimidated and warned that they may 'spoil their career prospects,' if they openly opposed Einstein's relativity. 

Louis Essen cautions;

"The continued acceptance and teaching of relativity hinders the development of a rational extension of electromagnetic theory"
He is concerned that;
"students are told that the theory must be accepted although they cannot expect to understand it. They are encouraged right at the beginning of their careers to forsake science in favor of dogma."
Pari also points out that "In deriving the field equations of general relativity, Einstein has used partial differential equations, which assume continuity of a uniform field or of the spacetime continuum. A mathematical law expressing a regularity in the successive distances of the orbiting bodies around a central primary would be inconsistent with the assumptions of general relativity. And this regularity exists in the form of the Titius-Bode law from which Pari also concludes that the distance law is an integral part of gravitation; i.e. gravitation is quantized.
In a series of articles, A.A.Logunov and co-workers have made several important remarks. They point out that in general relativity the energy of a system and, therefore, its inertial mass does not have any physical meaning, since it depends on the arbitrary choice of the coordinate systems. Therefore, the assertion of equality of the "inertial" and "gravitational" masses in Einstein's theory is devoid of all physical meaning. 

Moreover, the arbitrariness of the coordinate transformations in general relativity makes it incapable of giving unique predictions for gravitational effects (bending of light, perihelion rotation, red shift and time-delay experiments.) They conclude that the absence in the general theory of relativity of conservation laws for energy, momentum, and angular momentum of the matter and gravitational field taken together, and also its inability to give unique predictions for gravitational phenomena, make it necessary to abandon the theory of relativity as a physical theory.

Pari states that general relativity is a very long and complicated theory. The derivation of Einstein's field equations required many pages of abstract mathematical operations. Perhaps the most obvious criticism is that by P.Lenard that Einstein's theory is 'far less simple than all great theory's of physics'.

In addressing Einsteins theory of relativity Pari reminds us that his special theory is based on Lorentz transformation equations:

with a contraction factor of the square root of 1–v2/c2 in the denominator for measurements of length and time. When v reaches the velocity of light c, length and time become undefined. For v > c, these measurements become imaginary. In Einstein's words;

  • (1)"In the theory of relativity the velocity c plays the part of a limiting velocity, which can neither be reached nor exceeded by any real body" and
  • (2)"The velocity c plays the part of an unattainable limiting velocity", also
  • (3)"For velocities greater than the speed of light our deliberations become meaningless" and,
  • (4)"Velocities greater than the speed of light have…no possibility of existence."
Pari says "That photons exist and travel at the speed c, is sufficient to invalidate the equations of special relativity; the reality of velocities greater than c, is an additional argument to refute the theory."
She then discusses the illogical theory of 'tachyons', proposed to rationalize the existence of superluminal velocities within the theory of relativity. Richard Tolman's equations that would have an 'effect precede the cause' and Bilaniuk's (et al) 'reinterpretation principle' which attempts to confirm Tolman's equation by having a tachyon travelling with negative energy and backwards in time, interpreted as one traveling with positive energy forward in time.

Pari concludes;

"The logical consistency of this reinterpretation principle has been challenged by a number of authors who have convincingly demonstrated that cause and effect cannot be interchanged arbitrarily".
David Bohm discusses the causality problem of tachyons and concludes;
"Either we have to assume that no physical action faster than light is possible, or else we have to give up Einstein's form of principle of relativity."
Mendahl Sachs states that the existence of tachyons would be a refutation of the theory of relativity.
Pari then presents three examples of particles having velocities greater than c:
(1) Cerenkov radiation
(2) antimesons, and
(3) superluminals
Pari concludes that the designation of c as the maximum velocity by Einstein was an arbitrary choice and in view of the subsequent observations summarized here, it is no longer tenable.
In addressing Einstein's unified field theories Pari quotes a number of scientists, beginning with a statement by Einstein himself and Rosen made in 1935;
"In spite of its great success in various fields, the present theoretical physics is still far from being able to provide a unified foundation on which the theoretical treatment of all phenomena could be based. We have a general relativistic theory of macroscopic phenomena, which however has hitherto been unable to account for atomic structure of matter and for quantum effects, and we have a quantum theory, which is able to account satisfactorily for a large number of atomic and quantum phenomena but which by its very nature is unsuited to the principle of relativity."
Lincoln Barnett in his book, "The Universe and Dr.Einstein, quotes Einstein;
"The idea that there are two structures of space independent of each other, the metric-gravitational and the electromagnetic, is intolerable to the theoretical spirit."
Dewey Larson comments;
"Most scientists accept the General Theory of Relativity but no one uses it except as a mental and mathematical exercise; indeed it is doubtful if anyone knows how to use it in anything other than an artificially simplified situation."
George Gamow likens the Einstein field equations of the general theory of relativity to the Taj Mahal; 
"a structure standing out there in majestic isolation, without any connection to the rest of Physics".
Mendahl Sachs discusses the "Fundamental Conflicts Between the Quantum and Relativity Theories". Sachs points out that these two theories (the quantum and the relativity,) cannot be treated separately from each other in a logically consistent way.
Pari states that the goal of a Unified Field Theory was to unite the laws of gravitation and the laws of electromagnetism within a single basic structure of a universal law and that further, a great number of other capable mathematicians besides Einstein, also worked on this subject. In some of these theories, a fifth dimension was introduced. These attempts, by Einstein and numerous other authors, of unifying physics have all failed.

The recent versions of the unified theories, the "Superstrings" and the "Theories of Everything," says Pari, are pure speculations involving 10 or even 26 dimensions. The extra dimensions are supposedly curled up into invisible wormholes.

Ian Stewart in his book "The Problems of Mathematics" comments on these new developments in the Unified Field Theories;

"From such grotesque mathematical equations may the twenty-first century's System of the World be fashioned."
Harald Nordenson, in his book "Relativity, Time and Reality: A critical investigation of the Einstein Theory of Relativity from a logical point of view";
"I have often met persons, especially outside Sweden, who have expressed their astonishment that Einstein was not awarded the Nobel Prize for his Theory of Relativity, which many people consider as one of the outstanding achievements of this century. As a member of the Swedish Academy of Science which distributes the Nobel Prizes of physics I am on the other hand very glad that this was not done, since the Theory of Relativity is not physics but philosophy and in my opinion poor philosophy."
O'Rahilly describes the theory of relativity as "highly metaphysical"
Pari concludes;
  • "We consider the theory of relativity as science fiction or pseudoscience," and
  • "Mathematics, which is the most advanced science, should be used to analyze observations and experimental data. It should not be used to create a new physical science base on hypothetical equations."
My opinion is that General Relativity, 'the spacetime continuum' was a deliberate scientific and mathematical hoax perpetrated on the scientific community for reasons that are unknown at this time. This scientific and mathematical hoax is still firmly in place with current scientific experiments continually being weighted in favor of, and data contrary to, being discarded in favor of the theory.
John Lear
September 21, 2008
Las Vegas, Nevada
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