Einstein assumed that all physical laws of nature must be symmetrical and transformed into the same algebraic form for every inertial observer; that all measurements must be physically made with coordinates by hand and eye approximations; and that stationary ether was superfluous to his theory, therefore all motions and times are relative. He postulated that a radical mathematical principle of relativity applies so as to make all laws of nature “co-variant.” For Einstein, “co-variance” meant that each law of nature must be constituted so that its space-time coordinate variables of magnitude will be transformed by Lorentz transformations into a law of exactly the same algebraic form for every inertial observer. As a result, 1) the magnitudes of all non-EM physical phenomena must mathematically vary depending upon their relative velocities, and similarly 2) Einstein postulated that mathematically light en vacuo must propagate relative to all linearly moving inertial bodies at the absolutely constant velocity of c. But it turns out that most of Einstein’s mathematical assumptions, and both of his fundamental mathematical postulates, were not correct: logically, physically or empirically.
Remember from Chapter 16 that Poincaré assumed in 1904 that all physical laws of nature (including light) must be the same for all inertial observers, regardless of their different uniform velocities (Logunov, p. 25). This assumption (which Poincaré called the principle of relativity) seemed to be reasonable: 1) because the algebraic laws of mechanics were empirically the same (mechanically covariant) for all inertial observers regardless of their different uniform velocities (Galileo’s Relativity); 2) because Maxwell’s law for the constant transmission velocity of light at c relative to the medium of stationary ether was theoretically the same for every inertial observer (Rohrlich, p. 52); and 3) above all because such assumption would theoretically explain why terrestrial light experiments could not detect the motion of the Earth through the stationary ether.
Remember also from Chapter 16, that in his April, 1904 treatise, Lorentz transformed the space and time coordinates in the M & M experiment with his own radical Lorentz transformation equations. Lorentz did this for three main reasons: 1) in order to mathematically do away with the troublesome factors (c – v and c + v) which the Galilean transformation equations had previously produced;[1] 2) to achieve the necessary theoretical contraction of the longitudinal arm on Michelson’s apparatus in order to explain away Michelson’s “missing” time interval and thus to mathematically justify the paradoxical M & M null result with respect to stationary ether; and 3) so that his results would be consistent with Poincaré’s principle of relativity (expanded to include electrodynamics and light as well as mechanics) which Poincaré had been talking about.[2]
It is asserted by the author that when Einstein read Lorentz’s above described April 1904 treatise and Poincaré’s writings about his expanded principle of relativity in the latter part of 1904 or the early part of 1905, Einstein soon realized that Lorentz’s and Poincaré’s new concepts could mathematically resolve the “difficulties” between the relativity of mechanics and Maxwell’s velocity of light, if they could be reinterpreted in a radically different way. Most importantly, Einstein realized that Maxwell’s electromagnetic law for light waves at velocity c (when transformed by the Lorentz transformations) would remain mathematically invariant and constant in both of Lange’s inertial reference frames. In other words, Maxwell’s law could retain the same invariant algebraic form (c) for every inertial observer anywhere in the Cosmos, regardless of such inertial observer’s different linear velocity v relative to the light ray. This result could also mathematically explain why no light experiment (including the M & M experiments) had been able to detect whether an inertial frame (i.e. Earth) was moving or not.[3]
The ad hoc 1904 theories of Lorentz and Poincaré then became a template for Einstein’s 1905 Special Theory, his two fundamental postulates, his Lorentz transformations, his relativistic kinematics and dynamics, and all of the other bizarre mathematical consequences of his Special Theory. One major problem with this happy scenario was that the “difficulties” which Einstein imagined to exist with respect to the velocity of light were never a real problem that needed any solution, mathematical or otherwise. Such “difficulties” (including the baffling M & M null results) were merely very explainable paradoxes. All that was needed was the correct analysis and explanation of the situations, so that all of such perceived “difficulties” and paradoxes would completely disappear. These correct analyses and explanations are primarily set forth in Chapters 6 – 7, 10 – 12 and 19 – 24 of this treatise.
Before Einstein began to write his Special Theory in 1905, he obviously had developed various goals for his treatise (Memo 20.1), and numerous fundamental assumptions concerning its content. In this chapter, we shall identify, discuss and begin to analyze these basic assumptions, his two fundamental mathematical postulates, and the major goals that Einstein assumed would resolve all of the “difficulties” and paradoxes described in our Chapter 19 and elsewhere in this treatise.
A. Einstein assumed that all physical laws of nature (including the velocity of light) must be constituted so that they are described to be algebraically symmetrical for every inertial observer.
The word “symmetry” is generally defined as a “similarity of form or arrangement on either side of a median or dividing line that results in an aesthetically pleasing whole or beauty.” It implies a graceful proportion, a pleasing harmony and aesthetic balance of the parts. “Symmetry” can also be interpreted to have other meanings. For example, in mathematics, it can mean creating an equation or relationship whose terms or parts can be interchanged without affecting its validity[4] (Webster’s Dictionary). When a mathematician (such as Einstein) describes a formula or a mathematical law as beautiful or elegant, he usually means that it has most or all of the above qualities.
It is apparent from the very first paragraph of Einstein’s 1905 Special Relativity treatise that he was convinced that all physical laws of nature (including electrodynamics) must be described so that they are symmetrical for every inertial observer, but that they were not being described by the scientific community in a symmetrical manner.[5] For example, Einstein asserted that the “customary view” of Faraday’s reciprocal electrodynamic action of a magnet and a conductor (which induces an electric current in a wire) involves two very asymmetric descriptions: one body or the other is at rest and the other body is moving[6] (Hoffmann, 1972, p. 69). Instead, Einstein concluded: “the observable phenomenon here only depends upon the relative motion of the conductor and the magnet”[7] (Einstein, 1905d [Dover, 1952, p. 37]).
It is true that many different types of symmetry do exist in physical laws. A sphere, a crystal and a snowflake are all symmetrical in “shape.”[8] A flower, a vegetable, and a human being show some degree of symmetrical shape. There are also symmetries of “identity” in physics. For example, all electrons and all hydrogen atoms are theoretically identical, so in this sense they are symmetrical.
There are other interpretations of symmetry. The horizontal displacement of two identical moving apparatuses in space or in time on the surface of the Earth should have no effect upon their physical operations. Their motions should be exactly the same (symmetrical) regardless of their locations (positions) or times of operation (Feynman, 1963, pp. 52-1, 52-2). Similarly, there is a symmetry or equivalence of accelerated motions that occurs on any terrestrial platform with a uniform velocity in a straight line (a motion of translation). Such accelerated motions will occur so that the laws of mechanics (and the algebraic form of such laws, F = ma) will appear to be the same (mechanically covariant) on all inertial bodies (Galileo’s Relativity) (Ibid). The Galilean transformation equations mathematically inferred this type of symmetry for two inertial reference frames in a relative translational motion, and accelerated motions occurring thereon (Chapter 14). This mathematical version of Galileo’s Relativity, the implied covariant symmetry of mechanical accelerations produced on inertial reference frames in relative translational motion, is also what Einstein was alluding to in his “induction of a current” analogy.[9] However, Einstein’s “induction” analogy went far beyond Galileo’s Relativity and further inferred that relative inertial motion applies to the realm of electrodynamics, as well as to mechanics.[10]
Based partly on his very limited knowledge of astronomy and partly on his assumptions of symmetry, Einstein later conjectured in his Special Theory that space is isotropic (it has the same properties in all directions), and that space and time are both homogeneous (all points in space and time are equivalent) (Einstein, 1905d [Dover, 1952, pp. 43 – 44]). As we shall see in Chapters 25 and 27, these theoretical extensions of symmetry to space and time would be necessary for Einstein to assert the constancy of light propagation in opposite directions, and to “derive” his Lorentz transformation equations[11] (Resnick, 1968, pp. 56 – 57).
On the other hand, it is also true that there are as many exceptions and limitations to such symmetries as there are valid applications of them. For example, all snowflakes are symmetrical in “shape,” but no two are symmetrically “identical.” Identical apparatuses will not necessarily operate the same way if they are located in very different climates, at very different altitudes (because of gravitation), or if they are rapidly revolving (because of centrifugal forces). An apparatus or structure that operates well at one scale may not operate the same way (symmetrically) at a much larger or smaller scale. Most living things have many asymmetries, such as a head and a tail, roots and flowers, one heart on one side of the body, etc. Many revolving spheres (such as the Earth) bulge asymmetrically at their equators; their orbital motions are not symmetric circles, but rather are ellipses. Similarly, time is not necessarily symmetrical. For example, an egg once cracked and cooked cannot be symmetrically reversed in time[12] (Feynman, 1963, pp. 52-2, 52-3). Thus, not all physical laws or phenomena are or can be symmetrical in every way (Ibid, pp. 52-11, 52-12). As Smolin concludes, “Nature becomes less rather than more symmetric the closer we look” (Smolin, p. 219).
Why was Einstein so demanding of symmetry in his Special Theory? One major reason is because he needed the concept of symmetry in order to rationalize his way to his ultimate ad hoc conclusion: that all laws of nature (including the velocity of light at c) must retain the same (symmetric) algebraic form for every inertial observer (Chapter 20E). This false conclusion grew out of the fact that the algebraic form of Newton’s laws of mechanics (i.e. F = ma) always remains the same (mechanically covariant) for every inertial observer. Another major reason is that, with the aid of symmetry, Einstein was able to rationalize his way to a new ad hoc mathematical concept: that Maxwell’s natural law for the constant velocity of a light ray en vacuo must always retain exactly the same (symmetrical, invariant and covariant) algebraic form of c (300,000 km/s) with respect to every inertially moving observer on every inertial frame or body, regardless of such observer’s different linear velocity relative to the light ray (Chapter 20F and 21D). There were also many other applications of symmetry in Einstein’s Special Theory (Memo 20.2).
Concerning the velocity of light, and contrary to Einstein’s new relativistic covariant concept, we will discover in Chapters 21 and 22 that the constant transmission velocity of a light ray at c should theoretically be described to have the same invariant magnitude of 300,000 km/s relative to the medium of empty space through which it propagates.[13] However, with respect to each material observer moving linearly at a different speed relative to such light ray, the velocity of the propagating light ray is logically and empirically measured to have a different magnitude (either more or less than 300,000 km/s) relative to such linearly moving observer. Such relative velocity of the light ray propagating over varying distances and time intervals depends upon the speed of the inertial observer and his direction of motion either toward or away from such light ray (Figures 20.3 and 21.1). Einstein’s impossible attempt to mathematically require that every light ray propagating over different varying distance/time intervals must always have exactly the same (symmetrical) absolute velocity (of 300,000 km/s) relative to every different material observer moving at a different linear velocity relative to the light ray (Chapter 21E), is what Special Relativity is all about.
“The symmetries most deeply embedded in contemporary theory are those that come from Einstein’s special and general theories of relativity. The most basic of these is the relativity of inertial frames” (Smolin, p. 219). Because of the almost universal acceptance of Einstein’s relativistic theories, “observed symmetry” has now been elevated to a necessity in theoretical physics (Ibid, p. 218).
“Modern physics is based on a collection of symmetries, which are believed to enshrine the most basic principles. No less than the ancients, many modern theorists believe instinctively that the fundamental theory must be the most symmetric possible law”[14] (Ibid).
Throughout the remainder of this treatise we will demonstrate that this absolute necessity of symmetry in physics is not correct.
B. Einstein assumed that all measurements must be physically made with Cartesian coordinates, by hand and eye approximations between inertial reference frames.
As will become obvious during the remainder of this treatise, Einstein assumed the validity, applicability and necessity of his artificial system of measurement for the description of physical laws, which system of measurement he designed for the express purpose of achieving his relativistic goals. Briefly, Einstein’s system of measurement was as follows. An observer (a measurer) situated in one inertial frame of reference (which he also defined as a system of coordinates[15]) would visually measure and physically plot on Cartesian coordinates the time and space coordinate magnitudes of an event occurring in another inertial frame of reference (system of coordinates) which was moving linearly with respect to the first frame at the uniform relative velocity of v, and vice-versa.[16] Einstein generalized his system of measurement, as follows:
“Of course we must refer the process of the propagation of light (and indeed every other process) to a rigid reference-body (co-ordinate system)” (Einstein, Relativity, p. 22).
In Chapter 22 we will explain why this reference of light propagation to a material co-ordinate system is, in general, an impossible concept. All of the spurious axioms, assumptions, rationalizations, and conventions that Einstein invented for his system of measurement are further described and analyzed in Chapters 21 and 24 – 29.
It is an obvious fact that hand and eye coordinate measurements made between two distant inertial frames (bodies) with different velocities will always produce imprecise, distorted and at best approximate coordinate results. One reason is that during the time interval delay for the light signal to propagate from one frame to the other, the relative velocity of the frames will constantly change the relative coordinate positions of objects being measured on the two frames. It is also obvious that this archaic method of distant measurement is inherently an unreliable and imprecise method of measurement.[17] Yet, without this dubious type of coordinate measurement, Einstein would never have been able to contrive his concept of Relativistic Kinematics (Chapter 28) nor his Special Theory as a whole.
In the 21st century, radar and laser beams, light and electronic sensors, software programs, digital computers and television cameras describe and measure physical laws and magnitudes on one inertially moving distant planet (i.e. Mars) and transmit such data at the speed of light to another distant inertially moving planet (vis. Earth) without any coordinate measurements or transformation equations. However, even if such modern technology had been available in 1905, Einstein could not have used such modern methods of measurement for his Special Theory. Why? Because he would not have been able to manipulate such high-tech measurements and misinterpret their results in order to construct his relativistic mathematical theories.
Einstein’s arbitrary system of measurement resulted in numerous spurious relativistic concepts and in numerous mathematical formulae, most importantly his Relativity of Simultaneity and Distance (Chapter 26), his Lorentz transformation equations (Chapter 27), his Relativistic Kinematics (Chapter 28), and his relativistic formula for the Composition of Velocities (Chapter 29). Once Einstein arrived at a mathematical formula for such measurements he no longer had to physically make eye and hand coordinate measurements. At this point, all Einstein had to know were the relative velocities involved, and the distorted “measurements” that he needed would follow with mathematical precision.
Einstein used his artificial system of measurements and his mathematical formulae to demonstrate his concept for the absolute propagation velocity of light at c and the rest of his Special Theory. He also attempted to extend his Special Theory to other phenomena (i.e. mass and energy, and space and time) and to confirm his Special Theory with data selectively chosen from somewhat related experiments. The only problem was that his system of measurements and his relativistic mathematical formulae, data and concepts derived therefrom were all completely ad hoc, artificial, arbitrary, contrived, invalid and meaningless.
C. Einstein assumed that ether was superfluous to his Special Theory, and that all motions are relative.
Directly after Einstein’s example of asymmetries in the description of Faraday’s process for the induction of an electric current, Einstein asserted as follows:
“Examples of this sort, together with the unsuccessful attempts to discover any motion of the earth relatively to the ‘light medium,’ suggest that the phenomena of electrodynamics as well as of mechanics possess no properties corresponding to the idea of absolute rest” (Einstein, 1905d [Dover, 1952, p. 37]).
One assumes that these statements were made to bolster Einstein’s aforementioned assumption that all motions are relative, and to imply that the fictitious “light medium” of stationary ether might not exist.[18]
If there is no such thing as “absolute rest,” it follows that there can be no absolute space and no stationary ether reference frame from which to absolutely measure: motion, direction of motion, velocity, distance traveled, or anything else. It also follows that if there is no absolute motion then all motion must be relative. For this reason, all measurements of motion must be made from a relatively stationary point or event, or from one co-moving reference body to another co-moving reference body, and vice-versa. It also follows that rest, velocity, distance traveled, and direction of motion are also relative concepts. These are all reasonable and correct assumptions.
However, we must then ask the question: Were Einstein’s above assertions and suggestions concerning the non-existence of absolute rest only intended to bolster his assumption that all motions are relative, and to imply that stationary ether might not exist? One would think not, for the following reasons:
First, the assumption that all motions are relative had already been implied or asserted by numerous other scientists, including Galileo, Newton, Maxwell, Lange, and Poincaré, so by 1905 it was not a new idea. Other prominent physicists (including Maxwell, Lange and Poincaré) had also questioned the existence of stationary ether and/or absolute rest; Michelson had even categorically denied the existence of ether in his 1881 paper (Chapter 9). Therefore, by 1905, Einstein’s aforementioned suggestions were only echoing the conclusions of others concerning relative motions and the non-existence of ether and absolute rest.
Second, Einstein’s example of “the unsuccessful attempts to discover any motion of the earth relatively to the ‘light medium’… [which] has already been shown to the first order of small quantities” (Ibid, p. 37), undoubtedly refers to the failure of all light experiments conducted on the Earth which were intended to detect and measure the solar orbital velocity of the Earth (30 km/s) relative to stationary ether. In the very next sentence of his 1905 paper, Einstein conjectured that the failures of such light experiments suggest that the concepts of Galileo’s Relativity and the Galilean transformation equations of mechanics should be extended and generalized so as to apply to electrodynamics and optics as well as mechanics. Einstein’s exact words were:
“[Such failures] suggest that…the same laws of electrodynamics and optics will be valid for all frames of reference for which the equations of mechanics hold good. We will raise this conjecture (the…‘Principle of Relativity’) to the status of a postulate…”[19] (Einstein, 1905d [Dover, 1952, pp. 37 – 38]).
Thus, it appears that Einstein’s major reason for all of such aforementioned assertions and such examples was really to bolster his conjecture that Galileo’s Relativity and the Galilean transformation equations of mechanics should be generalized to include electrodynamics and optics. In any case, Einstein’s above conjecture was a non sequitur, because it turns out that Galileo’s Relativity had nothing to do with such light experiments or their failures, nor with electrodynamics or optics (Chapters 23 & 24).
Third, Michelson’s 1881 and 1887 interference of light experiments would also come within the category of such failed light experiments, albeit to a higher order of approximation. We now know the reasons why Michelson’s experiments did not detect any motion of the Earth (Chapters 10, 11 and 12), and these reasons had nothing to do with Galileo’s Relativity, nor with the Galilean transformation equations of mechanics. So why should we believe that any of such failed light experiments are compelling evidence that the concepts of Galileo’s Relativity and the Galilean transformation equations for mechanics should be extended to apply to electrodynamics and optics? There is no logical or empirical reason.[20]
Einstein’s real reason for all of the above suggestions was his attempt to generalize Galileo’s empirical and sensory concepts of relativity and the Galilean transformation equations to include electrodynamics and optics (in other words, to include the velocity of light), because the generalization of such concepts was absolutely essential to his Special Theory. Einstein needed an empirical foundation for his mathematical Special Theory. Without the empirical foundation which Galileo’s Relativity might provide, his Special Theory would have no empirical basis, and like Lorentz before him it would be viewed by the scientific community as only an ad hoc mathematical exercise of the imagination. Therefore, Einstein needed to attempt to connect and characterize Galileo’s sensory and empirical concept of relativity as his empirical foundation. He also needed the Galilean transformation equations to blame for the “difficulties” with the velocity of light that he imagined, and in order to modify them into his Lorentz transformation equations. Much more about this later.
Specifically with reference to relative motion, Einstein stated, “every motion must be considered only as a relative motion” (Einstein, Relativity, p. 67). He also asserted that relative linear motion exemplified the symmetry of reciprocity. For example:
“we can express the fact of [relative linear motion]…in the following two forms, both of which are equally justifiable:
(a) The carriage is in motion relative to the embankment.
(b) The embankment is in motion relative to the carriage” (Ibid).
With respect to these examples, Einstein would state that the relative linear velocity v in example (a) is reciprocal to the relative velocity –v in example (b), and vice-versa (Einstein, 1905d [Dover, 1952, p. 47]).
Let us now analyze these concepts of relative linear velocity with other specific examples. The Stanford Linear Accelerator is a huge building that is approximately 2 miles long. Inside the accelerator building, atomic particles of matter are theoretically accelerated down its length at about 99% of the velocity of light relative to the accelerator building (Figure 20.3A). Special Relativity claims that at this relative velocity such particles contract in length to only about 15% of their former rest length, that the mass of such particles increases about 7 times, and that the duration of time (eternity) on such particles slows down about 7 times (Chart 15.4 & Figure 15.3, and Figure 16.2 & Chart 16.3). It would, of course, be difficult or impossible to empirically prove or disprove any of these claims, so Einstein implied that we should just take his word that such claims are valid.[21]
But, what about the linear accelerator and the people in it? If such atomic particles were relatively moving in one linear direction at 99% of c, then Einstein would say (based on symmetry) that the accelerator building and the people in it are reciprocally moving at 99% of c relative to the atomic particles in the opposite linear direction (Einstein, Relativity, p. 67). According to Special Relativity, this means that the accelerator building (and such people) should contract in length to only about 15% of their former rest length, that the mass of such building (and such people) should have increased about 7 times, and that the duration of time (eternity) in such building should slow down about 7 times.
However, we, situated in the accelerator building, do not notice any of these relativistic effects. Neither do any of the other people on the Earth, many of whom are also theoretically moving reciprocally at 99% of c relative to such atomic particles. Therefore, it is rather difficult for us to believe Einstein’s relativistic predictions. The empirical results of these simple thought experiments should give us pause and make us wonder: Do not such null results constitute a serious contradiction to Special Relativity? Such null results should also (at this early juncture) be a convincing demonstration that Einstein’s Special Theory is possibly internally inconsistent and even meaningless.
Einstein also stated that he could not attach any meaning to “motion in itself,” but only to “motion with respect to the body of reference chosen in the particular case in point” (Einstein, Relativity, pp. 59 – 60). In other words, Einstein could not find any meaning with respect to motion or velocity in the abstract, but only with respect to relative motion. For example, Einstein claimed that the abstract motion of the Earth through cosmic space does not produce a contraction of things on Earth, whereas the same motion of the Earth through cosmic space relative to the Sun does (Ibid, p. 60).
Einstein’s definition and description of relative motion depends upon the body of reference that the measurer chooses in order to mathematically describe such motion (Ibid, pp. 59 – 60). Since there are an uncountable number of linearly moving bodies in the universe, the relative motion that the measurer describes depends upon which reference body such measurer chooses. Thus, such measurer could describe one or an infinite number of relative motions. If, after making a choice, the measurer changes his mind and chooses a different body of reference, then theoretically his relative motion will also suddenly change. But, again, no physical effect is noticed.[22]
Strangely enough, Special Relativity does not claim that length, time, mass and many other physical phenomena are velocity dependent. Instead, it only claims that these phenomena are dependent upon a relative velocity. Think about this claim for a few moments. Why is an abstract velocity through empty space physically different than a velocity relative to a body? What is so special about a relative velocity that theoretically it can relativistically and physically change the magnitudes of such physical phenomena, and at a distance (Figure 20.3B). How does this magical process occur?[23]
When a body translates from one point to another at a uniform velocity, the laws of nature on such body are the same at any point along the way. Galileo demonstrated this fact with respect to mechanics with his uniformly moving ship analogy. At the end of the nineteenth century this fact was also described mathematically with the Galilean transformation equations, which compared the coordinate measurements of a body at two different points along its uniform translation.
But when Einstein and others tried to do the same thing with the constant velocity of light at c (300,000 km/s), the coordinate measurements of c at point A mathematically changed to c – v when compared to the coordinate measurements of c on body B moving away from A at uniform velocity v. Einstein interpreted this result to be a violation of translational symmetry; in other words, Maxwell’s law of the constant velocity of light at c had a different velocity at two different locations…point A and point B (Einstein, Relativity, pp. 22 – 23).
Einstein’s entire Theory of Special Relativity was invented in order to mathematically require that the measurement of a relative velocity (i.e. c – v) would always remain absolutely velocity c with respect to any linearly moving body B when measured from point A. In other words, mathematically symmetrical.
D. Einstein assumed that all times are relative.
It follows from the finite velocity of the light signal and the abolition of absolute rest, stationary ether, and absolute space that there can be no absolute measurement of an instant in time or of an interval of time that would be valid for all observers in the Cosmos. Thus, there can be no such thing as an absolute “true time” for all observers measured from absolute rest, from absolute space or from stationary ether. Nor can there be a “local time” based on “true time.”[24] All instants and time intervals must also be relative to an observer. Therefore, all measurements of an instant or of a time interval must be made from one relatively stationary point or event to another, or from one co-moving reference body to another co-moving reference body, and vice-versa.
Based upon Römer’s observations of eclipses of the Jovian moon Io, the resulting finite distance/time interval delay of the light signal, and Bradley’s empirical confirmation thereof (Chapters 6 and 7), it follows that the instant of occurrence of a distant light event cannot be simultaneous with the local observation of such event. A local observer’s judgment of the local time for the occurrence of a distant light event must factor in the distance/time interval delay of the light signal at c from the position and instant of such distant event, to the position and instant of its observation by such local observer. Therefore, the Galilean transformation equations for an instant in time (t = t′) with respect to the occurrence of spatially separated events cannot be simultaneous; in other words, t cannot equal t′. Einstein assumed and asserted that the Galilean transformations for the local instant in “time” (t) of a distant event must be revised.[25] These assumptions by Einstein were correct,but they were not a revelation.[26] We shall discuss them in much greater detail in Chapter 25.
Based on his above assumptions, Einstein further assumed that a local inertial observer could not simultaneously physically measure the coordinates for the instant in time at the front end and at the rear end of a distant linearly moving object on another frame of reference. Without this simultaneous measurement of time, Einstein also assumed that a local observer could not accurately physically measure with coordinates the length of a distant linearly moving object on another frame of reference. Therefore, Einstein concluded that relative motion between reference frames affects an observer’s hand and eye coordinate measurements of length and time (Chapter 28). For this reason, Einstein also assumed that length and time coordinate measurements between inertial reference frames could only be defined in terms of a distorted “relative simultaneity” and therefore such kinematic concepts and measurements were dependent upon such relative velocity (Chapter 26).
It turns out that all of the above dubious measurements and rationalizations were only made to further Einstein’s relativistic agenda: to make his concepts of Relativistic Kinematics, Length Contraction and Time Dilation mathematically consistent with his impossible second postulate concerning the absolute velocity of a light ray at c (Chapters 20F and 20G). We shall discuss the fallacies of these absurd measurements, rationalizations and their related assumptions in detail in Chapters 25, 26 and 28.
E. Einstein’s first postulate: His radically changed and expanded principle of Galileo’s Relativity.
Right after Einstein abolished “the idea of absolute rest” in his 1905 Special Theory, he conjectured a definition for his ad hoc, radically changed and expanded Principle of Galileo’s Relativity:
“…the same laws of electrodynamics and optics will be valid for all frames of reference for which the equations of mechanics hold good”[27] (Einstein, 1905d [Dover, 1952, pp. 37 – 38]).
He then arbitrarily “raised this conjecture to the status of a postulate,” which he stated would “hereafter be called the ‘Principle of Relativity’”[28] (Ibid, p. 38). It also became known as the “first fundamental postulate” of Einstein’s Special Theory.
What does the above conjecture by Einstein really mean? Is it simply an ad hoc generalization of Galileo’s Relativity to include EM (light) and optics? Is it just a generalization of Lange’s relatively moving inertial reference frames and the Galilean transformation equations that described them? Is it merely a restatement of Poincaré’s 1904 Principle of Relativity (Chapter 16)? The answer to all of these questions is: No.
Simply stated, Einstein’s first postulate (his so-called “relativity principle”) really asserts: that the laws of electrodynamics, optics (including the velocity of light), and mechanics will be valid within his Special Theory only with respect to the abstract mathematical concepts of inertial reference frames, artificial coordinate measurements, and the Lorentz transformation equations. In effect, his first postulate is really just a short summation of his Special Theory. These conclusions only become evident later in Einstein’s Special Theory when he asserts that: 1) the only mathematical reference frames that he is talking about are those in “uniform translatory motion”[29] (Einstein, 1905d [Dover, 1952, p. 41]), and 2) that the laws of mechanics only “hold good” in inertial reference frames when such laws are measured by his artificial coordinate measurements and are transformed by the Lorentz transformation equations (Ibid, pp. 41, 43 – 48; Einstein, Relativity, pp. 34 – 39, 47 – 48). Also, “the equations of mechanics” which Einstein was referring to in his first postulate had to be the Lorentz transformation equations (rather than the Galilean transformation equations), because otherwise his first postulate would not be valid within the meaning of his Special Theory.[30]
In Chapter 14 of his book Relativity, Einstein specifically stated what he meant mathematically by his Principle of Relativity:
“Once in possession of the Lorentz transformation…we can combine this with the principle of relativity, and sum up the theory thus: Every general law of nature must be so constituted that it is transformed into a law of exactly the same [algebraic] form when, instead of the space-time variables x, y, z, t of the original co-ordinate system K, we introduce new space-time variables x′, y′, z′, t′ of a co-ordinate system K′. In this connection the relation between the ordinary and the accented magnitudes is given by the Lorentz transformation. Or in brief: General laws of nature are co-variant with respect to Lorentz transformations”[31] (Einstein, Relativity, pp. 47 – 48). “This is a definite mathematical condition that the theory of relativity demands of a natural law” (Ibid, p. 48).
In other words, for Einstein, “co-variance” meant that each law of nature (including the velocity of light) must be constituted so that its space-time coordinate variables of magnitude will be transformed by Lorentz transformations into a law of exactly the same algebraic form for every inertial observer. This is how the velocity of light mathematically became c for all inertial observers in Einstein’s Special Theory.[32]
It must be emphasized at this early point that Einstein’s “principle of relativity” was not at all the same as the principle of Galileo’s Relativity. Einstein’s principle of relativity is strictly mathematical, not empirical. It is a greatly expanded ad hoc concept that incorrectly includes all of optics, electromagnetics, and other physical phenomena as well as mechanics, and it requires the ad hoc Lorentz transformation equations (instead of the so-called Galilean transformation equations) in order to make it mathematically appear to work. For all of the above reasons, and many more described in Chapters 23 and 24, Einstein’s first postulate, his principle of relativity, is invalid and meaningless.
What was the empirical basis (if any) for Einstein’s conjecture concerning his radically expanded Principle of Relativity? How did Einstein rationalize his way to the above radically expanded mathematical conclusions? Does Einstein’s Principle of Relativity have any physical validity? We will discuss and answer these and related questions in Chapters 23 and 24.
F. Einstein’s second postulate: The impossible absolutely constant propagation velocity of a light ray at c relative to any inertial observer …anywhere…at any time.
Immediately after postulating his expanded “Principle of Relativity,” Einstein introduced a “second fundamental postulate” for his Special Theory, which he claimed was “only apparently irreconcilable with the former…,” to-wit:
“…that light is always propagated in empty space with a definite velocity c…”
“which is independent of the state of motion of the emitting body”[33] (Einstein, 1905d [Dover, 1952, p. 38]).
Although Einstein hardly mentions James Clerk Maxwell by name in his 1905 Special Theory, it is quite obvious from his 1905 paper (Ibid),[34] from his book Relativity,[35] and from his other writings, that by “velocity c” Einstein was intending to refer: 1) to Maxwell’s equations which described the constant velocity of light as c (300,000 km/s) with respect to the stationary ether[36] (Chapter 6A), and also 2) to velocity c relative to inertial bodies (such as a railway carriage) that are moving linearly relative to a propagating light ray (Chapter 21).
The first part of Einstein’s second postulate has uniformly been interpreted to mean that: “all uniformly moving…observers obtain the same measured velocity of light, independently of their own speeds” (Bohm, pp. 54, 60). In other words: “Light waves must travel with the same invariant speed of 186,000 miles [per second] through any Galilean [inertial] frame when this speed is measured by the observer located in the frame”[37] (D’Abro, 1950, p. 146).
What exactly do these assertions concerning the velocity of light really mean? Simply stated: they mean that the velocity of a light ray propagating over changing distance/time intervals toward or away from any inertially moving body in the Cosmos is theoretically measured by an observer on such inertial body to be the same velocity of c (186,000 miles/s or 300,000 km/s), regardless of the magnitude of the linear velocity of such inertial body and such inertial observer either toward or away from the light ray (Resnick, 1992, p. 469; Goldberg, p. 105). However, this so-called measurement of light at c would be an impossibility, because the inertial observer would be moving linearly at v relative to the tip of the light ray. Therefore, any so-called measurement of such light velocity would be a relative velocity of c + v or c – v (more or less than c) depending upon the relative direction of motion of the observer and the light ray (Chapter 21, Feynman, 1963, p. 15-2, and Sobel, p. 200).
Thus, according to Einstein, every light ray has an absolute velocity of c relative to every inertial observer and every inertial body in the universe, regardless of their linear motions relative to the light ray.[38] For example, as Resnick stated, where Observer A is situated at the emitting light source, Observer B is moving away from A, and Observer C is moving toward A, “Einstein’s second postulate…asserts that all three observers measure the same speed c for the light pulse”[39] (Figure 20.4; Resnick, 1992, p. 469; Goldberg, p. 105)!
In effect, Einstein made no distinction between the instantaneous emission velocity of a light ray at c and its constant velocity of transmission at c relative to the medium of empty space (a “vacuum,” as Einstein called it) through which it passes, on the one hand, and the light ray’s varying velocities of propagation over varying distances and time intervals relative to different linearly moving bodies, on the other hand. This “requires us to express…the velocity of light with respect to two relatively moving bodies [so]…that the value c results for both” (Dingle, 1961, p. 20). In other words, “Einstein’s special theory of relativity…compels us to consider the velocity of light as an absolute”[40] (D’Abro, 1950, p. 154). Einstein acquiesced to all these interpretations, because during the 50 years from 1905 until his death in 1955 he never claimed that they were wrong nor proposed a different interpretation.
What could have prompted Einstein to postulate such a ridiculous concept (Chapter 21E). In Chapters 21 and 22, we will further analyze and explain the invalidity and fallacies of Einstein’s second fundamental postulate, which constituted a major false premise for his entire Special Theory.[41] In such chapters we shall also explain how and why light really transmits and propagates.
G. Einstein’s (implied) third postulate: The magnitudes of all non-light physical phenomena must vary depending upon their relative velocities.
In the previous Sections E and F of this chapter, we have discovered the following. Einstein’s second postulate was really just an application and a mathematical consequence of his first postulate: his radically expanded “principle of relativity,” which conceptually implies and includes the Lorentz transformations. In order to make his second postulate (the absolute velocity of light at c) work mathematically relative to all inertial frames of reference, Einstein had to apply the Lorentz transformations to the velocity of light propagating in such moving frames of reference. The symmetrical and “co-variant” transformation result was that the velocity of light is always measured by any inertial observer (using coordinates and synchronized clocks) to have the same algebraic form c in any inertial frame. Therefore, Maxwell’s velocity of a light ray propagating relative to a linearly moving inertial observer, which is logically and empirically dependent upon the velocity v and direction of motion of such inertial observer, artificially becomes mathematically independent of the different velocities of all linearly moving inertial bodies in Einstein’s relativistic Special Theory.
However, Einstein could not just apply the Lorentz transformations to just one phenomenon of nature in his Special Theory, the velocity of light, because this would appear to be too ad hoc. To remain mathematically consistent, he would also have to apply the Lorentz transformations to all of the other physical phenomena of physics, such as length, mass, time, force, electricity, energy, etc. But this created another serious conceptual problem for Einstein, because all of these phenomena of physics had always been considered to be completely independent of their velocity and thus invariant in all inertial frames. If Einstein applied the Lorentz transformations to these velocity independent phenomena, then the laws of physics would be different in every inertial frame.
The only way out of this theoretical conundrum was for Einstein to conceptually change the laws of mechanics and all the other physical laws and phenomena of physics so that they would be considered to be dependent upon relative velocity.[42] Then, when the Lorentz transformations were applied to them, such changed velocity dependent laws would be the identical (algebraically co-variant) in every inertial frame. This would, of course, mean completely changing all of mechanics and physics so that its phenomena could be considered to be velocity dependent, algebraically co-variant, and consistent with Einstein’s impossible second postulate for the absolute velocity of light at c (D’Abro, 1950, p. 162). In other words, the impossible tail would be wagging the logical and empirical dog. But so be it.
Most of the rest of Einstein’s Special Theory after he stated his second postulate was devoted to arbitrarily and conceptually changing all of the velocity independent phenomena of physics, one by one, by dubious rationalizations, analogies, and the Lorentz transformations, so that theoretically and mathematically they could be considered to be velocity dependent. This is why we must consider the theoretical velocity dependence of all of the non-light phenomena of physics to be tantamount to Einstein’s third fundamental postulate. Einstein’s relativistic concepts of “Simultaneity,” “Common time” and synchronous clocks (Chapter 25), his concepts of the “Relativity of Simultaneity” and the “Relativity of Distance” (Chapter 26), his “Relativistic Kinematics, Length Contraction and Time Dilation”[43](Chapter 28), his “Relativistic Composition of Velocities” (Chapter 29), his “Relativistic Dynamics and Relativistic Mass”[44] (Chapters 31 and 32), and of course his Lorentz transformation equations (Chapter 27) were all primarily devoted to achieving this spurious mathematical goal.[45]
By way of example, Einstein asserted in his concept of the “Relativity of Distance” that the length of a rigid meter rod contracts (shrinks) in the direction of its velocity relative to another inertial body of reference, which “Length Contraction” was then mathematically confirmed when the Lorentz transformations were applied to such rod in two different inertial frames. Einstein’s “new law” of the velocity dependent length of a rod was then algebraically the same (“co-variant”) in each inertial frame. Likewise, all of the above-described relativistic concepts were little more than Einstein’s radical conceptual manipulations of classical physics.
As we shall discover in Chapters 25 through 29 and in Chapters 31 to 33, when Einstein (the “mathematical magician”) was in charge of the thought experiments, the ad hoc equations, the arbitrary definitions, the artificial coordinate measurements, the illogical interpretations, the bizarre analogies and rationalizations, and the topological approximations, there was no limit to the phenomena and theories that he could invent. Mathematically, he could turn a long rigid rod into a short one, a small mass into a large one, and a normal time into a slow time. Mathematically, he could even make a long rod disappear, make a tiny mass become infinitely large, make time stand still, and make any two velocities that were less than c, add up to c.[46]
H. Einstein assumed that his two fundamental postulates taken together would resolve the mathematical “difficulties” that he perceived.
After describing his second fundamental postulate, Einstein assumed and concluded that his two postulates taken together would solve all of the “difficulties” that he perceived, and which we described in Chapter 19. In Einstein’s words:
“These two postulates suffice for the attainment of a simple and consistent theory of the electrodynamics of moving bodies based on Maxwell’s theory for stationary bodies.”[47]
“The theory to be developed is based—like all electrodynamics—on the kinematics of the rigid body, since the assertions of any such theory have to do with relationships between rigid bodies (systems of co-ordinates), clocks, and electromagnetic processes.[48] Insufficient consideration of this circumstance lies at the root of the difficulties which the electrodynamics of moving bodies at present encounters”[49] (Einstein, 1905d [Dover, 1952, p. 38]).
The kinematics of a rigid body and the above-described material relationships were evidently what Einstein meant by the phrase: “the electrodynamics of moving bodies.” However, by 1905, the term “electrodynamics of moving bodies” and such relationships were normally reserved for electric charges in motion (electric currents), EM forces, and the relationships between them…not the relationship between propagating electromagnetic waves (light) and linearly moving bodies. Maxwell never used the term “electrodynamics” in his theories or equations (Chapter 6B), and he never applied the phenomena of light to frames of reference, stationary (ponderable) bodies, nor linearly moving bodies.
We will begin to demonstrate in the next four chapters that actually it was Einstein’s insufficient consideration of the velocity of light, and of the mathematical results (c – v and c + v) which occurred when the Galilean transformations were misapplied to the constant velocity of light at c in two inertial frames of reference, that lies at the root of Einstein’s mathematical “difficulties.” When these circumstances are properly analyzed, it turns out that (strange as it may seem) there were no real “difficulties” that needed any solutions (Chapters 21 through 24). Thus, Einstein’s entire ad hoc and artificial Special Theory for the “electrodynamics of moving bodies” was totally unnecessary. It merely distorted Maxwell’s natural law concerning the constant velocity of light at c en vacuo relative to its medium of empty space, and in the process it distorted all of the rest of physics as well.