Journal of Theoretics  Vol.3-6

Restricted Relativity

A Detailed Account of the Main Objections

Author:  Ali A. Faraj  <a_a_faraj@hotmail.com>

Abstract: In this paper the cogency and relative strength of Einstein's Special Relativity Theory (SRT) are evaluated. Additionally, the conceptual framework of SRT is reviewed in some detail. This exposition may also serve as a brief review of the criticism that has been directed against SRT during the second half of the last century.

Keywords: electromagnetic, theory, aether. 

Introduction

     Maxwell's electromagnetic theory requires an "aether" [preferred spelling so as not to confuse with the anesthetic gas]. Without a carrying medium such as the aether, the wave concept of light becomes incomprehensible. The dynamic properties of the aether are well-known and considered by many to be ad hoc and superfluous.1 Within the context of this discussion, only the kinematical aspects of the aether are relevant. These are certainly more transparent and internally consistent. A few points need to be emphasized about the kinematical characteristics of this medium:

  1. There is nothing in Maxwell's theory that prohibits the motion of the observable part of the universe along with its aether, with a constant speed in some direction.  Motions relative to the Maxwellian aether therefore, are not equivalent in any strict sense, to motions relative to Newtonian space.
  2. In Maxwell's theory, every motion of a physical object must be relative to the aether. That is because a symmetrical assignment of motions in this case, renders long-range measurements of motions by optical means useless. Also the motion of the aether leads to mirage motions of stationary bodies easily noticeable in short-range measurements. Since no such mirage motion is ever observed, the above generalization is admissible.
  3. The notion of a stationary aether with respect to moving bodies, does not exclude however, the possibility of independently contracting or expanding aether at a cosmic scale. In fact, phenomena explainable by the conventional model of 'expanding universe' are equally explainable by the idea of 'expanding aether'.

     Since the velocity of light relative to the aether is always equal to c , the ethereal velocity of an isolated system in which the observer is at rest, can be measured in terms of displacement. Now, the velocity of the earth around the sun is well-established from dynamic perspective. Experimental attempts to determine this velocity on the basis of Maxwell's theory have failed. Positive experimental results do exist, although they do not unambiguously accord with the prediction of the theory.2 

     Many theoretical projects have been undertaken to resolve this quandary, ranging from directly adjusting the physical parameters of the aether to adopting the corpuscular theory of Newton. The general consensus however, is that the kinematical asymmetries predicted by Maxwell's theory are basically correct, albeit concealed by some effect. This concealment, according to the Lorentz theory, is due to the contraction in the physical dimensions of moving objects in the direction of their motion. Dilation in local time is dismissed as a mere algebraic curiosity. By contrast, according to SRT, the concealment of asymmetries is due to changes in space and time caused by relative motions. In this theory the loss in depth inflected on the modified electrodynamics is offset by extending its scope to areas that were previously considered to be in the domain of mechanics.

The proposed modification of universal logic constructs, like space and time, is bound to stir up considerable objections. The main objective of this paper is to investigate those objections and to evaluate their weight and relevance in context.

Postulate of Relativity

     This postulate is a collection of relatively independent assumptions:

A. The laws of nature are the same with respect to reference frames in uniform motion.

This assumption is a special case that lies at the foundations of Natural Philosophy (The study of the laws of nature in the universe).

     Obviously, such an assumption cannot be falsified because whatever exceptions are encountered, they are automatically utilized in developing more general laws of the natural world. Consequently, violations to this axiomatic rule, if found, will not necessarily be fatal to SRT or any other theory for that matter.

B. No experiment inside a physical system can reveal its space motion.

     This assumption is in fact a statistical conclusion based on fairly large, but by no means encompassing, samples of physical situations. It emerged during the Galilean campaign against the Ptolemaic System. It has been used ever since by various competing schools against the aether hypothesis. As a principle, however, it has little or no logical force of its own.3 That is because the number of potential phenomena inside a physical system, which may reveal its motion, is unlimited and it cannot possibly be exhausted. It should also be pointed out that not only are the supporters of SRT, who have used this assumption, but also the proponents of the corpuscular model have used it as well against the wave theory. This is despite the fact that all corpuscular theories predict the feasibility of measuring absolute velocities, not just relative to the aether, but also relative to immobile space in the Newtonian sense.

     On a corpuscular theory, by carefully measuring variations in the apparent diameters of rotating spheres (inside a moving system) as a function of perspective, one can in principle find  the velocity relative to Newtonian space. In any case, exceptions to the above assumption, if found, will probably destroy the conventional form of SRT, and weaken the case against bringing back the aether.

C. Two observers in uniform motion must measure exactly the same value of relative velocity between their co-ordinate systems.

     This is by far the most important assumption in the cluster of the relativity postulate. Any violation of this axiom, simply renders the Lorentz equations useless.

D. Temporal and spatial distortions as computed via the Lorentz transformation, must be reciprocal between two coordinate systems in uniform relative motion.

     The failure of this assumption will destroy the metrical interpretation of Einstein's theory. At present, it is widely acknowledged that measurement distortions are real in a moving system, and illusory in its stationary counterpart. That is the reciprocity in the theory, is part ontological and part metrical. This consensus has been developed almost unconsciously in the wake of the Dingle campaign against SRT during the 1960s.

E. Each member of a group of observers in relative motion, can equally assert he is the one who is at rest and that it is the others that are moving. 

     This assumption, of course, flies against a whole set of known procedures that are routinely used to identify states of rest and movement in the physical world. For instance, from dynamical considerations alone, one knows for sure that the Earth is moving relative to the sun and not the other way around. Nevertheless, this assumption is not entirely worthless. It points to a background difficulty associated with measurements in absolute space. For the practical-minded, absolute space presents a notorious problem, because if it exists, it is rigid and immobile, yet one can not go out and grab it. Every point is exactly the same to every observer whether they be in motion or at rest.  It is the homogeneous continuum at its worst.

Postulate of Constancy

In all inertial systems, the velocity of light is the same.

     This postulate is composed of three independent assumptions:

1. The velocity of light is always c, regardless of the light transmitter's velocity at the time of emission. 

As long as light is assumed to be a wave phenomenon, this assumption is misplaced and redundant. The independence of velocity of light relative to the velocity of its source, is simply a result direct deduction from the wave concept. Nonetheless, the validity of this assumption is very crucial for SRT. Maxwell's theory for example, if this assumption is invalid, can be easily saved by a helper hypothesis such as the hypothesis of 'Tubes of Force' used by J. J. Thomson in his theorizing about the ballistic theory.5 None of that is available to Einstein's theory.  If the assumption is proved experimentally to be incorrect, the theory just collapses.

2. The velocity of light is independent from the velocity of the observer.

     The dependency of every velocity, measured by an observer, on the rate of change in the displacement of that observer with time, is one of the most self-evident truths encountered anywhere in physics. A direct denial of such a truth, therefore, is out of the question. What Einstein has done in this case, is to assume that the simple truth is concealed by length contraction and time dilation. Theoretically, it works. If someone insists that all airplanes bound for Rome have the same speed, he will undoubtedly account for the ensuing discrepancies when given the luxury of elastic space and time.

3. The velocity of light is absolute. No material body can be accelerated to a velocity that is equal to or exceeds the velocity of light.

     The assumption of a limiting velocity that cannot be exceeded, is of course a borrowed analogy from thermodynamics in reference to the absolute-zero temperature.  It appears unjustifiable and paradoxical.6 However, within the framework of the current theory, there is no other alternative. Velocities greater than c, lead to time compression and gross violations of the law of causality.

Lorentz's Equations

     To assume that a composite quantity (e.g. velocity of light) is constant and its basic units variable, is quantitatively the equivalent to taking it for granted in reverse. The various sets of equations that can be deduced from the above symmetry are limited only by imposing a purpose. Since the objective here is to hide Maxwellian asymmetries, some additional information is needed. One must know how the velocity of light along longitudinal and transversal paths, is calculated for a moving system based on Maxwell's theory. One also must be informed somehow that all of the attempts to detect the ethereal velocity of Earth, have been unsuccessful. A convenient way to compute ethereal inequalities of a moving system, is to apply them in terms of travel-time differences between round trips along closed paths.

     If L is the path length in the direction of a system that is moving with a velocity v, then according to Maxwell's theory, the total time of a round trip along the longitudinal path, t1 is:

t1 = 2Lc / (c2 - v2)                 (1)

and along an equal path in transversal direction, t2 is:

t2 = 2L / (c2 - v2)1 /2              (2)

Now, if all attempts to detect ethereal asymmetries have failed, then the failure can mean only one thing: that t1 = t2 . If one is still assuming that Maxwell's theory is valid, then t1 = t2 either because the longitudinal path is contracting, or because the transversal path is expanding. Quantitatively, length expansion is more complicated than length contraction as it requires taking care of length expansion not only along one dimension, but also through an angle of 360 degrees around the velocity vector of a moving system. Furthermore, transversal expansion cannot be used to account for other optical phenomena such as the Doppler Effect and the Fresnel convection. Longitudinal contraction, therefore, is the right choice.

     Total longitudinal and transversal paths of a light beam in a moving system are readily available via the multiplication of t1 and t2 by the velocity of light in vacuum, respectively. By assuming that they are equal, one can obtain the so-called Lorentz factor, f :

 f = t2 / t1 = [1 - (v2 / c2)]                 (3)

This factor is then used to create a Lorentzian analogue to the Galilean equations for the two Einsteinian co-ordinate systems, x-y-z-t and x'-y'-z'-t', in uniform relative motion:

       x' = (x - vt) / [1 - (v2 / c2)]               (4),

       y' = y                                                   (5),

      z' = z                                                      (6),

      t' = [t - (vx / c2)] / [1 - (v2 / c2)]          (7) .7

     If an object is moving with a constant velocity u relative to one of the two co-ordinate systems, then its relative velocity u' as observed from the other system is

u' = (v + u) / [1 + (vu / c2)]                        (8) .8

     Now, we must note two major difficulties for the theory under discussion:

  1. According to the above equations, all things, as viewed from the other system, run slow. All motions, physical and physiological processes, clocks, cause and effect nexus, etc., go sluggish, on the basis of these equations . Why do all velocities within the system, slow down, but not the velocity of the system as whole? It has been, of course, exempted by the third assumption in the relativity postulate. Einstein's theory, therefore, appears to be self-contradictory. It presupposes absolute space and time in order to move forward.9 That is not unexpected. The whole concept of relative motion is a Galilean creation. The current theory does not redefine the concept nor does it contain any new procedure for measuring relative velocities between moving systems.
  2. Length contraction by the Lorentz factor, does not entirely eliminate Maxwellian asymmetries. The transversal path in the Michelson-Morley experiment, for instance, is an isosceles triangle with a base that lies along the longitudinal direction. It must therefore be contracting by the same factor as well. The total transversal path in this experiment, Ptrans, is

Ptrans = 2 [L2 + (vt2 / 2)2]1/2              (9)

     The displacement ( vt2 ) is in the longitudinal direction, and it must be contracting by the Lorentz factor. Since time flow is the same for the whole system, the factor of its slowdown cancels out, upon computing the ratio of the two paths. Thus, if it is assumed that only the arms of the apparatus are contracting, then after contraction, the ratio between the longitudinal path Plong  and the transversal path Ptrans , is

Plong / Ptrans = [(c2 - v2 f2 ) / (c2 - v2 )] = [1 + (v4 / c4 )/f2]       (10a) ,

where f is the Lorentz factor. On the other hand, if it is assumed that the whole horizontal path is contracting, then the ratio between the longitudinal path Plong and the transversal path Ptrans , after contraction is

Plong / Ptrans = cf / (c2 - v2 f2 ) = {f2 / [f2 + (v4 / c4 )]}               (10b) .

In both cases, a moving observer is therefore able, in principle, to notice that the velocity of light is not the same in all directions, contrary to the second assumption in the constancy postulate.

     In his 1905 paper, Einstein started out with the notion of total contraction but then switched to the Lorentzian notion of partial contraction, without stating clearly his motivation.9 It should be noted however, that it is not enough to assert that c is invariant. Length contraction and time slowdown are the basic requirements for the postulated invariability of velocity of light in every coordinate system. The problem is that no coherent set of equations can be constructed to achieve that goal in a self-consistent manner under all circumstances.

Universal Simultaneity

     Maxwellian asymmetries can be grouped into two categories: plane asymmetries and linear asymmetries. Plane asymmetries, although they are not completely concealed as demonstrated above, are practically made unaccessible to experimental testing by the Lorentz equations. Those equations however, cannot be used in any way to hide linear asymmetries. Within the framework of the present theory, the exclusion of universal simultaneity is the only way to conceal linear asymmetries. The procedure is illustrated by Einstein's imaginary train. Consider a point O midway between two distant points A and B, along a railway station. Then imagine a very long train traveling with a constant velocity v. When the A' (front end of the train) coincides with A (its rear end), B' with B, and its midpoint O' coincides with O, then two flashes of light are sent.10 There are three theories applicable to this situation, namely the Maxwell theory, the Emission theory, and the Einstein theory. Two cases have to be considered here:

     I. The two sources of light are located at A and B respectively.

In the reference frame of the railway station, the three theories agree that the two flashes arrive simultaneously at O, after a time t has elapsed since emission, i.e.

t = AB / 2c                     (11) .

In the reference frame of the moving train, Maxwell's theory and the Emission theory maintain that flash A arrives at O' after a period t1:

 t1 = A'B' / 2(c + v)            (12) .

Flash B arrives at O' after a period t2:

t2 = A'B' / 2(c - v)             (13) .

By contrast, Einstein's theory asserts that the two flashes arrive at O' after a period t',

t' = A'B' / 2c                     (14) .

They did not arrive simultaneously at O', not because their velocities relative to the moving train were different but because, according to this theory with respect to the moving frame of reference, flash A was emitted earlier and flash B later than the time of emission as measured in the stationary reference frame of the railway station. 

     Earlier and later, it's just like that! The problem, of course, is that there is no quantitative method for determining by how much they are earlier or by how much they are later, on the basis of this theory. As a result, Einstein's operational procedure, which works just fine within a single coordinate system, breaks down completely when it comes to synchronizing clocks in relative motion.

     II. The sources of light are mounted at A' and B' respectively:

1. According to Maxwell's theory, the two flashes arrive simultaneously at O, after a period t:

t = AB / 2c                     (15)

Relative to the moving train, flash A' arrives at O' after a period t'1 as shown by:

t'1 = A'B' / 2(c + v)         (16)

Flash B' arrives at O', after a period t'2 as shown here:

 t'2 = A'B' / 2(c - v)          (17)

Therefore for this theory, it makes no difference whether the source of light is stationary or moving. 

2. According to the Emission theory, flash A' arrives at O, after a time tA' :

tA' = AB / 2 (c - v)            (18)

Flash B' arrives at O, after tB' :

tB' = AB / 2(c + v)               (19)

In the reference frame of the moving train, flash A' arrives at O', after a period t'A' :

t'A' = (A'B' / 2) - v t'A' ) / (c - v) = A'B' / 2c    (20)

Flash B' arrives at O', after a period t'B' ,

t'B' = (A'B' / 2) + v t'B' ) / (c + v) = A'B' / 2c     (21)

Therefore, according to this theory, the two flashes arrive simultaneously at O'.

3. According to Einstein's theory, the flashes arrive simultaneously at O', after a period t':

t' = A'B' / 2c                    (22)

With respect to the railway station, the actual travel time for the two flashes t, is the same, i.e.

t = AB / 2c                       (23) 

The two flashes arrive one after the other at O, only because they were emitted this way, as observed from the stationary frame of reference of the railway station.

     Thus Einstein's theory has removed the problem of Maxwellian asymmetries from the domain of physics and dropped it into the realm of formal logic. After imposing an elasticity of time by the Lorentz transformation, thereby denies the validity of universal simultaneity, and it does not seem too audacious in the context of this theory. The consequences of this action may not be harmful in the short run but in the long run, they could be very damaging to any theory. Through the ages, no hypothesis has ever held its ground for long against the enormous pressure exerted by the universal principles of Reason.11

     It should be clear from the above comparison of the three theories, that relative simultaneity and the severe limitations placed on the synchronization of time-measuring instruments, are peculiar aspects of the Einstein theory.12 Synchronizing clocks, in order to establish temporal relations between events, poses no problem whatsoever within the framework of the other two theories. It should be noted, however, that temporal relations, when based on actual measurements not on assumed initial conditions, are never exact. Universal simultaneity, therefore, always implies a certain level of accuracy. Accordingly, the probability of two events remaining simultaneous beyond this implied level, approaches zero as the degree of precision in measuring time approaches infinity.

Modification of Mechanics

     According to Maxwell's theory, the velocity of all ethereal disturbances is constant. Constancy of ethereal velocity has an immediate consequence. Curvature of tracks is employed in the measurement of charge-to-mass ratios for charged particles in motion perpendicular to the electric and magnetic fields. The observed variability of those ratios, therefore, must be on the basis of this theory caused by variable mass, i.e.

m' = m / [1 - (v2 / c2)]                (24)  

where m is the rest mass of the particle, and v is its velocity as deduced from the path curvature. Clearly, the deduced velocity is hypothetical, and a by-product of adjusting the theoretical parameters to fit the observations.13 Einstein's theory has generalized this case and extended its scope to include mechanics.

     Thus for an object of mass m and velocity v , the linear momentum p and the kinetic energy E are

p = mv / [1 - (v2 / c2)]                              (25)  

and                                      

E = m c2 / [1 - (v2 / c2)]                          (26) .14

Obviously, this modification is necessary. Without it, the third assumption of the constancy postulate would be disposed with, by experiment at once. In other words, if velocity of light is an upper limit for all velocities, then variability of mass is the only available alternative to account for unlimited linear momentums and kinetic energies of moving materials. Finally, the equivalence of mass and energy is deduced from the previous formulae. The procedure seems arbitrary,9 but there is little doubt that the existence of many hypothetical entities in particle physics depends entirely on those modifications.

     It should be pointed out that the redefinition of the concept of mass has been proposed earlier by E. Mach who considered the given definition in Principia unsatisfactory and circular.  He proposed a redefinition in terms of interaction with distant matter. This, however, is even more circular and unsatisfactory. The circularity of Principia is benign and harmless, while the Machian circularity is vicious and malignant in that a body cannot have a mass without interaction with distant matter and it cannot interact with distant matter without first having mass.

     Increasing spheres of influence may soften this circularity, nevertheless, Mach himself has little patience for such fundamental locality. In fact, he does not challenge Newton's law of gravity.15  His gravitational field, therefore, is a virtual solid body extending to infinity. It behaves as single unit and when it moves, the universe is instantly informed of that movement.

Dingle's Paradox

According to Einstein's theory, two similar clocks, A and B, in uniform relative motion, work at different rates. Since this situation is symmetrical, it follows that if A is faster than B, then B must be faster than A. This is impossible. The theory, therefore, must be false.3

     H. Dingle has worked out the details, and transformed this paradox from vaguely conceived idea, to a bullying device of the first order to silence his opponents. Like Galileo before him, Dingle is a great believer in the power of Reason, and was clearly frustrated by the inertia of his contemporaries. In any case, he has succeeded in restoring respect to Newtonian absolutes and linking his own name with the clock paradox forever.

     Dingle's paradox destroys the reciprocity of real effects, and forces the defenders of the theory to make one of two difficult choices, both of which would reduce absolute time and absolute space to mere 'shadows':

A. Temporal and spacial distortions are optical illusions.

     From the standpoint of logic, this option is very appealing. It restores the harmony between the two Einstein postulates, leaving the concealment of the Maxwell asymmetries intact and weeding out all claims against absolute space, absolute time, and absolute velocity. Currently, this choice is the least popular, but there can be no doubt about its importance as the last line of defense for the current theory.

B. The dilation of time and contraction of length are real in the moving system and illusory in its stationary counterpart.

     This popular option destroys the second and the fifth assumptions in the relativity postulate, and restores the Maxwellian asymmetries at a different level. As mentioned earlier, Einstein's theory takes for granted the Galilean concept of relative motion between coordinate systems. As far as the banishment of Newtonian absolutes from physics is concerned, this concept is a Trojan horse. The concept is neither simple nor axiomatic. Relative velocity is a combined velocity. The following points can be made about this velocity:

  1. For every value of the relative velocity v, there is an infinite number of actual velocities that can be combined in infinite number of ways, to produce the observed resultant velocity. The relative velocity of two systems velocity could be, for example, the resultant of (v + 0), (0 + v), (0.5v +0.5v), (2v - v), (-v + 2v), or (100v - 99v).
  2. Relative velocity as measured by any observer, is a mixture of two types of velocities, namely, actual velocity and apparent velocity. The actual velocity is the velocity of the external system. The apparent velocity is the reflection of the observer's own velocity on the external system.
  3. Absolute velocity is a generalization by induction from actual velocities. To deny the validity of absolute velocities in kinematics, therefore, is as pointless as denying the validity of limits in calculus.

     According to the above choice, real Einsteinian effects are produced by actual velocities, and the illusory ones are caused by apparent velocities. It is well-known that the reunion of two Einsteinian observers, ends always in a disaster for the relativity postulate.9  It re-introduces the notorious asymmetries of Maxwell. Even without a reunion, the theory still faces difficulty. The reciprocity of the results, real or illusory, obtained by employing the Lorentz transformation, is tacitly based on the assumption of equal units of length and equal intervals of time in the two systems. What each observer observes in the other system, is simply those units and intervals multiplied by the Lorentz factor and the reciprocal of the Lorentz factor, respectively. If, for example, the intrinsic duration of a particular process is t, then its duration as viewed from the other system is slowed down by the reciprocal of the Lorentz factor. The observer compares the duration of this process with the duration of a similar process in his own system, and concludes that it is longer by the reciprocal of the Lorentz factor. Now, if the time in a system moving with the actual velocity is intrinsically slower, and the time in a counterpart moving with the apparent velocity is intrinsically faster, then how can the apparent reciprocity be preserved? The only way to preserve reciprocity, in this case, is to postulate that the apparently-moving observer sees real slowdown of duration, and the actually-moving observer observes the intrinsically faster durations multiplied, not by the reciprocal of the Lorentz factor, but by the square of the reciprocal of the Lorentz factor. Obviously, this procedure is ad hoc, and its main purpose is to keep the appearances of symmetry between Einsteinian coordinate systems.

     Acceleration provides no way out of the above difficulty. Accelerations and decelerations, in this case, have non-varying effects on clocks.  Therefore, they cannot be used to account for accumulative differences in the time flow of the Lorentz equations, in any consistent way.

     A very popular variation on the Dingle paradox, is the so-called 'twin paradox'. The clock, in this case, is biological. Two identical twins, one stays on Earth, and the other is ejected with c[1 - 10-99] towards the galaxy of Andromeda. This form of the Dingle paradox certainly has some psychological elements attached to it. As deduced from the Lorentz equations, the traveling twin shall live for eons as observed by the twin remaining on Earth. Interestingly, the space twin will experience a normal lifespan even though the Earth bound twin sees his brother living for eons. So it is more a time travel into the future rather than an extension of mortality. 

     The special case above is very convenient for highlighting the central difficulty posed by the Dingle Paradox. As it is known, many of the so-called resolutions have been geared primarily towards justifying the reappearance of the old asymmetries in this paradox. But that is a secondary and minor problem. In a nutshell, the primary and the most daunting problem is the following: Those asymmetries, in their new disguise, provide the experimenter with exactly the same opportunity to carry out exactly the same unsuccessful attempts as the old Maxwellian asymmetries. In particular, these new asymmetries can be easily plugged into the Lorentz Equations to compute no less than the absolute velocity of the Earth without any reference to any thing else in the universe. It is clearly a violation of the Relativity Postulate. Let's assume, for a moment, that Earth is moving with a constant speed of 0.555c relative to Mach's Distant Matter. Using only spaceships, multiple identical twins, and Einstein's Theory of Relativity, can we determine that velocity? The answer is yes. Spaceships are well-behaved projectiles. They acquire the velocity of their launching pad in the Einsteinian sense, that is. Another important note is that no time reverse is allowed by Einstein's theory albeit postulated by many modern SRT theorists such as Kip Thorne, that time for an object traveling away from the observer will slow down, while time for an object traveling towards the observer will speed up, leaving the two twins the same age when they are reunited on Earth.17 

     For all practical purposes, the idea of motion being relative to the universe, is nothing but a grandiose metaphor for the notion of motions relative to Newtonian space. It is true that one cannot determine, by practical means, whether the Earth is moving relative to the universe or that if the universe is moving relative to the Earth.18 Also one cannot determine by the same means, whether or not the Earth is rotating relative to Absolute Space, or whether Absolute Space is rotating with respect to Earth. Of course, the idea of rotating or moving space is a sheer nonsense. But the motion of the entire universe (its space included) is no less nonsensical. In any case, the idea of velocities relative to the universe, is the re-installment and triumphant return of the notion of the absolute velocities of kinematics.

General Remarks

     The representation of Einstein's theory in the form of postulates and deductions, has some resemblance to the method employed in Euclid's geometry. This similarity, however, is superficial. The Euclidean method is strictly top-down and deductive. Take for granted Euclid's axioms and the consequences followed by logical necessity. This is not the case with the Einsteinian postulates. Unlike the axioms, these postulates are not at the top of the conceptual hierarchy.  Also, they are not simple, abstract, or even self-evident. Furthermore, Einstein's postulates require modifications of space and time. Because these concepts are higher and more general than the postulates of relativity and constancy, the required reformulation can only be done by induction. Thus, by Euclidean standards, the representation above is upside down. This upside-down method is the main cause for making arbitrary decisions by Einstein at every turn in his theory.9

     Induction and deduction are, of course, complementary. That is, to extract the abstract from the concrete, induction must be used, and to reach the concrete through the abstract, deduction must be employed. Induction is basically, guessing. There are no well-established procedures, no formal rules, and certainly no logical necessity. Induction, however, is not a game of free associations. For the inductive method to work properly, the following conditions have to be fulfilled:

  1. Inferences must be based on specified sets of concrete cases.
  2. These sets of actual situations must be deducible from the inferences. If they are non sequitur, then the inductive process has failed.
  3. Inferences must not have consequences that conflict with experience and observation.
  4. Inferences must not contradict other inferences higher on the conceptual scale. Because these are based on larger samples of concrete situations, it is highly unlikely that offending inferences of this sort are correct.
  5. The inductive aspects of the scientific method, are also subject to further restrictions imposed by Baconian procedures.

     Although induction and deduction are complementary, induction is by far the most fundamental. The roots of every idea in every field, can be always traced back to induction. Even if it is proved that all or some of the general principles of reasoning are hard-wired into the human brain, these principles are still independently reproducible by induction.

     Clearly, the number of potential inferences that can be drawn from a given set of physical phenomena, is infinite. The state of absolute conceptual perfection, therefore, is only a potentiality. It is true that in physics,  the claim of nearing the end has been made from time to time. Examined closely, however, this claim is often just an other way of saying: 'The current theories and research programs have been exhausted. They offer no opportunity for discovery. Change them'.

     Moving upward, along the conceptual pyramid, one notices a trend of convergence and drastic drop in the number of potential inferences to finally find an upper limit for the abstraction process. In other words, the levels of generalization are steep and limited. At the top of the hierarchy, there are only very few independent concepts that cannot be abstracted any further. These include the three logical laws (Is, Or, Excluded Middle), the three essences (Space, Time, Matter), and the Law of Causality. They are simple, axiomatic, self-evident, and their denial presupposes their validity.

     Throughout history, there have been countless attempts to break away from those perceived shackles. They all have one thing in common. After an initial flurry of activities, those attempts, without exception, always end up in stagnation, superstition, and self-imposed blindness and deafness towards very essential aspects of reality.

     Since the days of Thales and Anaximander of Miletus, it has been a rule of thumb in Natural Philosophy, that phenomena of matter must be explained by the dynamics of matter. No advance, in this field, can be achieved by mixing up the essences, or by importing extraneous hypotheses. Einstein's theory, clearly, violates this rule. Mixing up the essences, in this case, is done in two separate steps. It is done in the theory under discussion as well as by assuming the motion of matter effects space and time. In his general theory, Einstein also assumes that space and time are produced by gravity of matter . In both cases, beyond the initial assumptions, there is not the slightest possibility of discovering mechanisms or even developing a theoretical rationale, for this postulated process. 

     The gap between space, time, and matter, is simply unbridgeable. Furthermore, the proposed tests to verify these assumptions are anything but relevant. For instance, the clocks may run faster or slower, for countless number of dynamical reasons. Why should anyone ignore the dynamics of matter altogether and make an unjustified jump to a completely different essence in order to explain the phenomenon? In addition, time by definition is a homogeneous continuum. In other words, the flow of time already has all the capabilities to accommodate all paces and rates for all processes at once. It is up to the processes of matter themselves to choose the paces that suit them from this universal continuum.

     With regard to geometry, in the current theory, Einstein works within the framework of Euclid's geometry. For his theory of gravitation, however, he chooses as a basis Riemannian geometry. Riemann's geometry, of course, is based on removing the impossibility of intersection imposed by the Euclidean axiom of parallelism. Denying this impossibility, as well as extending its scope further, both leads to two self-consistent geometries that differ from each other, and from that of Euclid in many respects. However, there is a catch. A denial of the parallelism axiom implies inescapable demotion in the abstract standards of the definitions. That is, the points, the lines, etc., are no longer absolutely abstract as in the Euclidean geometry, but rather relatively abstract and closer to the physical dimensions from which they have been abstracted in the first place. This lowering in the standards, could be useful in dealing with some particular problems such as the trajectories of moving bodies, for example. Geometries of this kind, however, are not rivals or substitutes for Euclid's geometry in dealing with the spatial continuum. They don't even come close to the level of universality and simplicity of Euclidean geometry.

Conclusion

     Theories and hypotheses in physics are always exposed to endless challenges by observation and experiment. Einstein's theory is no exception. Most of the assumptions of its two postulates are under continuous threat of being experimentally invalidated. It is not inconceivable that a clock synchronized and thrown at 0.999c will come back synchronized. In addition to this burden, Einstein's theory as shown in this paper, faces serious difficulties at two fronts. From inside, the theory is plagued by internal inconsistencies,19 fuzzy logic,20 and perpetual tension between its two postulates. From outside, the current theory is subjected to a tremendous pressure by the universal concepts that have been left behind. The theory has placed itself firmly against some of the absolutes of Natural Philosophy. At the same time, it has done its best to save the laws of logic and causality. The problem is that the general principles of Natural Philosophy form a highly integrated package. Take it all or leave it all. There is no possibility of choosing only the items that one likes from this package and to do so would be to invite irresolvable contradictions.

     Einstein's theory has been criticized by the importing of many metaphysical issues into the heartland of physics. It is not easy to evaluate the possible effects of this import on the development of physics in the long term. On one hand, one may say: "Let main-streamers wrestle with the eternal conundrums of metaphysics and build up philosophical muscles." On the other hand, it is well-documented that the ancient Greeks, during the Hellenistic Era, had engaged in just the same  playing around with essences and principles, and the Dark Ages weren't far behind. The current state of physics should be a source of concern, but not overwhelming so, as the present status quo is likely to persist for the next hundred years.

 

References

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Acknowledgments

My thanks to JW, Rosen, and Leon, for many interesting and stimulating discussions on Special Relativity and related matters.

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