Chapter 2. On Relativity

2.1 Special Relativity

The result of the Michelson-Morley experiment has deeply affected the conceptual foundations of physics. Along with the many scientists eager to defend or revive the ether, there were those, more mathematically-minded, who accepted the absence of the ether. Like H. Poincare in 1901, and Lorentz in 1904, they were making suggestions of what to sacrifice or change in physics, in order to adjust its functioning without the ether. Then, in 1905, Albert Einstein (1879-1955) introduced his special theory of relativity, which seemed to have reached this goal.

Einstein's theory of special relativity is based on two postulates. The first postulate states that:

In all frames of reference for which the equations of mechanics hold good (i.e., to the first approximation) the laws of electrodynamics and optics are the same.

This means that all inertial frames of reference have the same status and that the laws of physics are identical in all of them.

Thus, all parts of the universe are ruled by the same laws. There is not an absolute frame of reference as, e.g., the ether could be considered to be. Also, it is impossible to detect the motion of an inertial frame of reference from measurements made entirely within that frame.

The second postulate of special relativity states 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.

Also,

Any ray of light moves in the 'stationary' system of coordinates with the determined velocity c, whether the ray be emitted by a stationary or moving body.

Thereafter, Einstein states with ease that

... the luminiferous ether turns superfluous.

The two postulates of relativity contradict the customary laws of velocity addition, which are a result of at least two centuries of scientific development. Einstein just dismisses them, together with the ether concept, without even trying to refer to a physical explanation. Such an explanation would have to disclose what in the nature of light makes it so special that its velocity does not obey customary laws. The disclosure would also have to explain the results of Michelson-Morley's experiment. Without it, one can only say that the results of Michelson-Morley's experiment agree with or obey the postulates of relativity or, vice versa, relativity postulates agree with or comply with the results of this experiment.

We should keep in mind the General Rule, that:

as long as a postulate remains unexplained, it cannot explain a thing; anything behaving in accordance with such postulate, or in accordance with a prediction based on such postulate just behaves so, but is not explained by the postulate.

Based on the two postulates, Einstein developed a very complex mathematical system, accessible to the 'chosen' only. Out of this system, along with the time-dilation and length-contraction, etc., he derived two very important laws, which were later proven experimentally: the dependence of the electron mass on its velocity, and the relation (named 'equivalence') between the electron mass and the electromagnetic radiation energy.

2.2 Dependence of mass on velocity

Einstein's derivation was made for electrons. Mathematically complicated, it led to different formulas for a longitudinal mass of the electron and for a transverse mass. Out of them, one obtains the dependence of the electron mass $m$ on its velocity $v$,

where $m_e$ is the mass of a resting electron. Einstein also derived the expression for the relativistic kinetic energy ${}_kE$ of the electron,

Both $m$ and ${}_kE$ become infinite when $v = c$. Einstein stated, therefore, that

Velocities greater than that of light... have no possibility of existence.

Unfortunately, Einstein generalized his results, derived for electrons only, onto any material point. i.e., also on atomic matter, by saying:

We remark that these results as to the mass are also valid for ponderable material points, because a ponderable material point can be made into an electron (in our sense of the word) by the addition of an electric charge, no matter how small.

Thereafter, the uncautious generalization expands to 'ponderable masses as well', i.e., to extended atomic bodies, just by stating that

This expression for the kinetic energy must also, by virtue of the argument stated above, apply to ponderable masses as well.

This automatic generalization is illegal, because it does not consider the structural differences between electrons and atomic matter. It makes believe that atomic bodies can be accelerated, just like electrons, to velocities close to the velocity of light. We shall prove later (Section 9.6) that in the epola space, atomic bodies would disintegrate at velocities a hundred times lower than the velocity of light.

2.3 Illegality of substituting any mass for the electron mass

There is a striking structural difference between electrons and 'ponderable' atomic bodies. Thanks to the 1911 works of E. Rutherford (1871-1937), the planetary structure of atoms became known. It also became known that only a $10^{-15}$ part of the volumes of atoms and atomic bodies is occupied by tiny particles of very dense or nuclear matter, i.e., by electrons and nuclei. Except for this occupied millionth of a billionth part of their volumes, bodies of atomic matter (including ourselves!) turned out to be 'empty' just as empty as the vacuum space itself.

The difference in structure beween the dense electrons and the almost vacuum-like-empty ponderable atomic bodies was not known by 1905. The atom was then considered as a droplet of a positively charged liquid, with electrons in it. However, even with this model, an automatic extension of results obtained for electrons onto atomic bodies should not have been considered lawful. This, provided that physical thinking was not overwhelmed by mathematical formulations and by the eagerness to extrapolate the obtained results upon everything, everywhere.

2.4 Aristotle's Four-Horse Rule

The eagerness to extrapolate any rule on everything everywhere adheres to a fundamental quality of human nature. Hence, the useful attributes of this eagerness (to the bearers, not necessarily to the species as a whole) must exceed the harm. Here, 'useful' does not mean 'right'. Very often, wrong extrapolations or deductions are the profitable ones. For example, the compiler of 'practical' mathematical exercises like "How many people would be awakened by $x$ roosters, if one rooster wakes $y$ people?" got his collection profitably published. Hundreds of wrong extrapolations and deductions made by prominent scientists can be found in the book "A Random Walk in Science", edited by E. Mendosa.

As an example of a wrong extrapolation or deduction made by a genius, we take the statement in the book "Mechanics" by Aristotle (384-322 B.C.E.):

Obviously, four horses move a carriage with a velocity four times larger than one horse.

We consider this statement as a memento, which anyone has to keep in mind and recall before extrapolating a good formula or making deductions from it. We shall recall this statement when facing a wrong extrapolation. (Unfortunately, this will happen quite a few times.) We shall then refer to it as to "Aristotle's four-horse rule". We shall do our best not to have this rule recalled in connection with our own deductions.

2.5 Mass-energy equivalence

Einstein derived his famous mass-energy relation, $E = mc^2$, for electron masses and electromagnetic radiation energy. Thereafter, as in the dependence of mass on velocity, he replaced the electron mass by any mass and stated:

If a body gives off the energy $E$ in the form of radiation, its mass diminishes by $E/{c^2}$.

Einstein also unjustly equated electromagnetic radiation energy, for which he made the derivation, to any other energy, by simply declaring that

The fact that the energy withdrawn from the body becomes energy of radiation evidently makes no difference...

Then, he extrapolated the validity of his formula onto any mass and any energy, by just stating that

The mass of a body is a measure of its energy content; if the energy changes by $E$, the mass changes in the same sense by $E/{c^2}$.

We have seen that the substitution of any mass for the mass of the electron is illegal. We are now to show that so is, too, the substitution of the electromagnetic radiation energy by any energy. Hence, in Einstein's $E = mc^2$ formula, the derivation relates to electrons and to the electromagnetic radiation enery caused by them. Any, other understandings should be carefully examined before use.

2.6 Illegality of substituting any energy for the electromagnetic radiation energy

The equivalence of various kinds of energy means that they can be expressed in the same units, and that when an amount of one kind of energy turns into an amount of another energy, then these amounts are equal to each other. However, there are strict limitations as to the amounts of energy allowed to convert under the physical conditions, which enable and regulate the turnover. The second law of thermodynamics, e.g., yields theoretical limits for the conversion of heat into mechanical energy. On top of those, there are the very severe limits put by the technologies and machinery used. In the turning of chemical energy into heat there are no theoretical limitations, and nothing looks simpler than burning. Though, not to the one who freezes and starves at a wet campfire, or to the one who is serving the economy and environment by trying to increase the efficiency of industrial fuel burning by a quarter of a percent.

The strictest limits are on the conversion of any kind of energy into the energy of electromagnetic radiation. The conversion apparata, which turn the most versatile energy, the energy of electrical currents, into electromagnetic radiation (e.g., radio and TV transmitters, fluorescent bulbs, X-ray sources) have efficiencies in the range of 1 percent to less than 10 percent. Hence, rephrasing George Orwell's saying, all energies are equal but some energies are more equal than the others, the energy of electromagnetic radiation being the most 'equal' or the most 'expensive'. Therefore, the substitution of radiation energy in a formula by just any energy, is theoretically wrong, physically unlawful and practically similar to the substitution of a Harlem Globetrotter by just any basketball player.

2.7 Uniqueness or correlation between electrons and electromagnetic radiation

By 1905, it was already experimentally established that electromagnetic radiation is produced by accelerated or vibrational motion of electrons. The reverse production of vibrational motions of electrons by electromagnetic radiation was also known (in antennas, e.g.). Also known was the photo-electric effect, in which there is a direct and intimate transfer of radiation energy to electrons. All these experimental facts pointed strongly to a unique correlation between the electromagnetic radiation and the electrons. This correlation is much stronger than the relation between any energy and any ponderable mass. Einstein must have been aware of this unique correlation while working on the law of the photo-electric effect. In this law, he did not extrapolate the energy of the radiation-quantum onto any energy, or the electron mass onto any mass.

It is possible that by keeping also the mass-velocity and the mass-energy relations as derived, i.e., for electromagnetic radiation and electrons only, Einstein might have been directed (or directing) toward a search of the physics behind the strong correlation between just the electromagnetic radiation and just the electron (and possibly other dense particles). Such physical approach, after the inclusion of positrons, leads to the epola model of space, in which electromagnetic radiation is the direct result and the direct cause of vibrations of the electrons and positrons of the lattice. Then, based on the epola model, the dependence of mass on velocity and the mass-energy relation fall to our hands as a ripe fruit, with a slight shake of the Tree of Derivation (Sections 6.8, 8.13).

2.8 Start of divergence between relativity and quantum physics

Einstein's mass-velocity and mass-energy relations are pillars of relativistic physics, while his law of the photoelectric effect is a pillar of quantum physics. These two branches of physics are so divergent, that after 80 years of trials to unify them, this 'grand unification' did not come. With some exaggeration, we might say that Einstein started the divergence by keeping the photoelectric law as derived, i.e., for electrons and radiation only, whilst illegally extrapolating the mass-velocity and mass-energy relations onto any mass and any energy. Hence, quantum theory got from Einstein a sound physical start, while his relativity was from the beginning aiming to embrace everything everywhere, with little care about physical limitations and soundness. Too little in absolute terms, but especially when compared with the freedom and unlimited opportunities which it provided for mathematical development and phantasies.

We may imply that by keeping the mass-velocity and the mass-energy relations for electrons and electromagnetic radiation, for which they were derived, Einstein might have been directed toward an a priori unified physical theory. In fact, such a theory can easily be built on the basis of the epola model of space.

2.9 General relativity and gravitation

In his general theory of relativity (1916), Einstein expanded the first postulate of special relativity to also include accelerated frames of reference. Hence, the postulate states that it is impossible to detect the motion of any frame of reference by measurements made entirely inside this frame. Related to it is the postulate of equivalence between acceleration and gravity, stating that it is impossible within a frame of reference to distinguish between the effect of gravitational attraction and the effect of a suitably chosen acceleration of the frame. Another expression of the principle of equivalence is the equality of the inertial and gravitational mass, first proven by Newton.

Based on the principles of general relativity, Einstein developed his theory of gravitation. His strategy was to replace the Newtonian physical theory, based on forces in a three-dimensional space, by a purely geometrical description, using the four-dimensional space-time and transferring the motion of the system into an imaginary Riemannian space. The mathematical development is so complicated that only the very chosen can enter it, let alone understand. Of interest to us are the achievements of Einstein's theory.

The first achievement of Einstein's theory of general relativity and gravitation is the improved calculation of the precessional motion of the perihelions of planets. For the perihelion motion of Mercury, the observed rotation is 572.7 seconds of arc per century (572".7). The perturbating field of other planets is known to contribute 529".2, so that the residue is 43".5. The Schwarzschild solution of the Einstein law of gravitation yielded the extra 43".11, which is an argument in favor of the theory. However, for the perihelion motion of Earth, the measured residue is 5".0, while Einstein's theory yields only 3".84.

Two other achievements of Einstein's theory are the predictions of a gravitational redshift in the spectra of stars and of the bending of light-rays passing near a star. These predictions were first published (1911) in a paperl "On the influence of gravitation on the propagation of light". Einstein assumed that radiational energy, therefore also any energy, gravitates and changes in a gravitational field, according to the fonnula $E = mc^2$. The energy has a gravitational mass $E/{c^2}$, which also is the inertial mass of the energy. In this paper, Einstein considered that the velocity of light $c$ is due to change in a gravitationally distorted space. Later (in 1916), he denied the possibility of such change, pronouncing the vacuum light velocity c as a universal constant, unsurpassable and unchangeable in the whole universe.

2.10 Gravitational redshift

The gravitational or Einstein redshift should be observed in the spectra of light emitted from massive stars. The shift of spectral lines toward the red end of the spectrum, considered due to the gravitation of energy, was later also regarded as a loss of energy by the photons in escaping from the gravitational attraction of the star.

The derived theoretical value for the increase $\Delta\lambda$ in the wavelength $\lambda$ is

Here, $M$ and $R$ are the mass and radius of the star, in solar units. For the Sun $(M = 1, \ R = 1)$, the redshift, $\Delta\lambda/\lambda = 2.12 \cdot 10^{-6}$ is equivalent to the first-order Doppler shift in the spectrum of a light-source recessing with a speed of $600 \ \mathrm{m/s}$.

Redshifts of the predicted order of magnitude have been measured in the solar spectrum. However, there are difficulties of interpretation arising from atomic collisions in the atmosphere of the Sun. In addition, the observed redshift varies with the part of the Sun's surface from which the light is received. Redshifts in the spectra of a number of stars, e.g., Sirius B, agree with Einstein's formula. However, for certain white dwarfs, for which large values of the Einstein redshift would be expected, the measurements yield only small values at best.

2.11 Bending of light

Einstein's formula for the bending of light-rays is too complicated to be presented here. For the bending of light-rays passing near the Sun and then approaching Earth, the deviation from a straight line, calculated from this formula, should be 1".745. The observation can be made only on starlight during a full eclipse of the Sun. The first (well-announced to the general public) measurement was made during the eclipse of 29 May 1919. The value obtained for the bending of starlight passing at the totally darkened disk of the Sun was 1".75, very close to the predicted value. This result was considered as an unbeatable argument in favor of the relativity theory and brought the theory to the attention of the general public.

Measurements of the bending of starlight carried out after 1919 yielded values larger and smaller than the predicted 1".745, sometimes by 25 percent and more. It turned out that the data require troublesome corrections, which make it difficult to arrive at definitive results. Measurements made in 1947 average 2".01, while those of 1952 yield an average of 1".70.

The perihelion motion of Mercury's orbit, the gravitational redshift and the bending of starlight were devised by Einstein as the three tests of his theory, suitable for experimental examination. As we could see, these tests have worked in favor of the theoretically predicted values, hence, in favor of the theory, only in certain cases. Other measurements and observations yielded results quite remote from the predicted values, so that the test of the theory cannot be considered sufficient. Thus, Max von Laue in his "History of Physics" had to say that general relativity is not completely proven.

2.12 Cosmological applications, Hubble redshift and Big Bang

Cosmological applications of the general theory of relativity were discussed by Einstein in his 1917 paper "Cosmological considerations on the general theory of relativity". He made attempts to apply the general theory of relativity to the study of the physical universe, to create hypotheses concerning the large-scale distribution of matter in the universe, the possible finiteness of the universe, its time of existence, its contractions and expansions.

Einstein's ideas received great impetus from the discovery by E. Hubble (1889-1953) and M.L. Humason (1891-1972), in 1929, of a redshift in the spectra of light received from distant nebulae. The value of this redshift was found to increase roughly linearly with the distance to the nebulae. Normally, physicists would consider such redshift as due to factors acting on the radiation along the distance. However, under the influence of relativistic ideas, the 'Hubble' redshift was interpreted as a Dopplerian redshift, resulting from a runaway motion of the extragalactic nebulae. The velocities $v$ of these runaway motions should then be proportional to the distance $l$ to the nebulae,

Here, the proportionality factor $H$ is the 'Hubble constant', $H = 100 \ \mathrm{\left(km/s \right)/Mpc}$, and $l$ is expressed in megaparsecs ($1 \ \mathrm{Mpc} = 3.3\cdot 10^6$ light years, or $2.1 \cdot 10^{11}$ astronomical units, or $3 \cdot 10^{19} \ \mathrm{km}$).

Measurements of the Hubble redshift gave rise to the acceptance of the relativistic postulates leading to the relativistic theory of an expanding universe. With the development of astrophysical instrumentation, more distant nebulae were discovered, showing the Hubble redshift in their spectra. At gigaparsec distances, the Dopplerian interpretation of the observed redshifts means that the velocities of such distant nebulae would be approaching the velocity of light. Amazingly, this did not frighten the expanders of the universe. They progressed from an expanding universe to an exploding one, allegedly created in a Big Bang explosion from a subpoint in space in a split-second of time, so and so billions of years ago (exact agreement not yet reached). This universe is still exploding in all directions, and will do so for such and such period of time (agreement not yet reached).

The development and acceptance of the theory for the Big Bang-created, ever-exploding universe is based on illegal extrapolations of two postulates of the theory of relativity. First, that the velocity of light, measured here in our backyard on a table length or on a 47-mile distance, must be the same in the whole gigaparsecs-wide observable part of the universe. Second, that the laws which are established satisfactorily in our backyard must be identical in the whole universe. Clearly, what is good on Earth and maybe within a distance of several light-years is not necessarily right at distances of 5 billion light-years away.

2.13 Number of world's dimensions

Our natural perception of space is three-dimensional. This corresponds to our experience that every object in space has length, width and height. Then comes our 'primitive' natural perception of time as a dimension, connected with the concepts of 'earlier' and 'later'. As opposed to the space coordinates, which can decrease and increase, the change in time always aims toward increase, to 'later' and later, never backwards, towards 'earlier'. This flow of time cannot be stopped; it is uniform and independent of anything we know or can think of. On the other hand, the three space-coordinates are time-dependent, and so are all processes and actions we know. Hence, the position of time as a dimension is a very special one, different from and 'superior' to the space coordinates.

In relativity, the world was pronounced to be four-dimensional, with time as just the fourth coordinate. Hence, the consideration of physical processes in real time and space could be replaced by the treatment of geometrical problems in the four-dimensional space. Then, in 1919, Kaluza introduced a fifth dimension, to make relativity more potent. (The paper was published only in 1921, because referee Einstein rejected it.) Kaluza was later joined by Klein, and their theory of adding dimensions to the troubled world developed into a superstring theory, in which everything in physics could be worked out, if the world be considered 10- or 11-dimensional. However, in July 1985, M. G. Duff had to announce (in his plenary lecture at the Bari International Conference on High Energy Physics) that this goal could be achieved if 496 dimensions are added to the 10 superstring dimensions, so that our world became 506-dimensional.

In mathematical problem-solving, it is customary to consider a space having as many dimensions as there are parameters or variables in the particular problem. For example, the mathematical treatment of a system of $N$ particles can be replaced by a much simpler treatment of a single body in a $3N$- or $4N$-dimensional space. The trouble to physical understanding starts when the success of such treatment is presented as proof that the multi-dimensional space is not merely a mathematical device, but reality itself. This undermines the natural belief in the independent existence of the real world, the processes in which can be understood on the basis of appropriate physical models. Instead, a belief is forced upon people, that all there is are the mathematical procedures and results. In the epola model, space remains three-dimensional and time-dependent, as in our natural perception, while allowing the experimentally-proven achievements of relativity and relativistic field and particle theories to be derived and understood.

2.14 Relativity and the understanding of physics

The understanding of physical phenomena did not gain from the development of the relativity theory and from the advancement of physics caused by this theory. On the contrary, by introducing its principles in a postulatory way without explanation, and by presenting the physics-related results without physical explanations, the relativity theory has promoted the extinction of the natural belief that physical phenomena can be understood, and not only manipulated, calculated or predicted.

Einstein's goal of reducing physical problems to problems of geometry was achieved by degrading time from its position as an independent coordinate, on which other coordinates and all processes depend, into the rank of a mere fourth coordinate. However, the geometrical or geodesic problems in the imaginary four-dimensional space sometimes required a complicated mathematical treatment, which Einstein himself could not handle. For example, the solution to his equation for the gravitational field was given by K. Schwarzschild (1916). Thereafter, the mathematics of relativity expanded very rapidly, serving overwhelmingly itself. Hence, the contribution of relativity to physics diminished, especially as compared with the development of mathematics, which it caused. This includes also theories inspired by relativity, as the theory of the Big Bang exploding universe (Section 2.12), and Kaluza-Klein theories with their expanding number of world's dimensions (Section 2.13).