Relativity: Right or Wrong?
Michael Ray Laurence © 1999
According to his own account, the young Albert Einstein could not accept the notion that an observer could travel with sufficient velocity to permit an accompanying light beam to appear “frozen” in space. This intuition led him to an equation which would asymptotically limit the velocity of material objects to that of light itself, thus preserving the value of light velocity at c for all observers, when the length, mass, and time-keeping properties thereof were transformed according to the implications of this equation for the addition of velocities, Einstein’s Special Theory of Relativity was completed when he extended this intuited equivalence principle for inertially-moving systems beyond the mere constant measurement of light velocity to include measurement of all physical phenomena given identical initial conditions. This “free invention of the mind” represented a sweeping apprehension of a fundamental symmetry, or invariance, in nature and, beyond that, a condensational transformation of physics into mathematics when his colleague, Minkowski, systematized relativity in terms of “space-time” geometry. However, by thus dispensing with rationalizations in terms of optics and electrodynamics (which do, admittedly, conspire to prevent detection of “absolute” motion), relativity theory has left itself open to questions about apparent paradoxes, which, we will maintain, can only be resolved by resort to “physical” explanations, as opposed to mere space-time, diagrammatic, “geometrical” representations.
An example of “physical” explanation is given by Fitzgerald’s response to the null result of the Michelson-Morley attempt to interferometrically detect the earth’s motion through the “luminiferous ether.” Fitzgerald reasoned that if the instrument contracted along its axis of motion, whatever its orientation, the movement of light beams between and through the mirrors of the mechanism would be consistent with the conventional reference- framework/ether concept and with the failure to detect a phase incoherence which would betray motion. In other words, Fitzgerald explained this experiment in terms of optics, the physical principles of light beams, lenses, and mirrors, and in terms of electrodynamics, an “actual” (if locally undetectable) , physical foreshortening of the instrument as it moved through the light- conducting medium. Further experimentation and reflection led Lorentz to adduce the time dilation and mass accretion effects (hence the “Lorentz Transformations”), while yet maintaining the necessity for an ether concept by implication of the non-ballistic, non-additive character of the velocity of light. Though it was realised that length, mass, and time distortions “conspire” completely to prevent detection of a reference framework, the superfluity of that concept for purposes of measurement was not thought to justify its abandonment until an apparent ethno-cultural predisposition of Einstein and his adherents went beyond the motive of conceptual economy to demand the discarding of an imputatively “reactionary” and absolutistic notion.
We maintain that there is philosophical “baggage” in the Einsteinian/Minkowskian approach to relativistic epistemology because its partisans seem to be at pains either to avoid explicit rationalisations of relativistic effects (a la Einstein’s light beam chasing the train down the track as if velocities were simply being subtracted) or to maintain that, since the conspiracy against ether detection is complete, the constituent physical effects can have no “reality.” Advocates of this epistemology positively reloice in the universality of relativistic principles, to the point of implicitly endorsing their extrapolation to all perspectives on human circumstance. This unwarranted extrapolation (condemned, if nothing else, by the self-consciously surreptitious manner in which it is suggested) has led, of course, to the fatuous popular formula that “everything’s relative,” culturally speaking, and to enduring confusion and suspicion of paradox in a theory that need only return to its roots in the Michelson-Fitzgerald-Lorentz-Poincare approach in order to resolve the problems in its exposition.
A classic example of this expositional problem is given by the notorious “twin paradox” which, among other induced difficulties, has caused physicists to be insultinglv critical of one another’s perspectives on this particular conundrum. In one instance, a physicist’s tone suggested that his professorial interlocutor was an imbecile for not seeing that the returning twin’s inertial system was “different” from that of his outbound voyage and thus accounted for the retarded aging of this “traveling” twin (despite the basic inertial equivalence of the two siblings). In fact, this rationalization is merely a variation on the argument that the accelerational asymmetry in their space-time trajectories accounts for the asymmetry in the aging of the twins, which argument,however, can only assert a significant rather than a functional relationship between the asymmetries, since excursions of infinitely variable length may have identical accelerational patterns. Our point is that geometrical, space-time diagrams thus lack “explanatory” value and that resort must be had to physical principles in order to avoid the type of misunderstanding mentioned above.
How then do we give a functional explanation of the actually non-antinomian character of the “paradox” just discussed? We do so by placing the pair in a spatial plenum which, among other effects, dilates time with motion referred thereto. Then, when one twin accelerates/coasts/decelerates/accelerates/coasts/decelerates in a pedantic but simple excursion away from and back to his stationary twin, this “moving” twin will find himself relatively youthful upon his return if his motion through space has an “actual,” physical, electrodynamic effect on his person that accordingly is retained after temporary, but no less real, contractional and mass-accretional effects are terminated by the rejoining of the pair. In this plenum, the time dilation (exclusive of accelerational effects) is proportional to the length of inertial travel, thus providing the sought-for functional relationship between motion and dilation plus a non-arbitrary distinction between otherwise equivalent twins during that inertial period. In the worst-case scenario, where both twins are initially traveling together in the medium, the excursion of the accelerating twin “downstream,” so to speak, (thus advancing rather than retarding his aging) is overcompensated by his “upstream” return, thereby illustrating the second-order character of the applicable Lorentz transformation (square root of the difference between unity and the ratio of velocity squared and c squared) and thereby maintaining the explanatory utility of our reference framework. (Note: The mutual-clock-watching variation of this example must take Doppler effects into account.)
To summarize the argument thus far: the orthodox, Einsteinian presentation of relativity is sweepingly elegant in its simplicity and universality and anticipates the emphasis of modern physics on the search for symmetry and invariance in comprehensive physical theory. It beautifully exemplifies the intensive exploitation of symbolic manipulation that is the hallmark of modern work. However, this attendant reduction of relativistic physics to Minkowskian geometry has permitted, not only a conceptual economy in relativity, but a dogmatic, ethno-culturally based, cabalistically-conditioned rejection of the concept of a universal reference framework. A connotation of reaction and absolutism is placed upon the notion of a “luminiferous ether” to such a degree that professors of the subject can be characterized as “etherophobic” when called upon to explain or reconcile relativistic effects. Furthermore, this epistemologically biased “relativism” is readily extrapolated into a Weltanschauung of its own, which subsumes the time-worn, internationalist, egalitarianist, utopian socialist cosmopolitanism that we all know and love. One final illustration of the pedagogical problem that this attitude induces should prepare the reader for a concluding discussion of an area where “relativism” may be burdening theoretical work at the forefront of physical research.
That illustration begins with preparation of the “thought experiment” with which this student once confronted an internationally-renowned professor of physics whose acclaim was specifically for contributions in relativity. Two identical squares are drawn, one above the other, representing a plane view from above of two cubes facing one another in a “plenum” such as described earlier. For purposes of reference, the corners of the squares/cubes as viewed in this manner will be labeled as they correspond to the intermediate compass points (i.e., northwest, northeast, southeast, southwest), and the cubes themselves will be regarded as elementary observational devices (e.g. , eyes, cameras, telescopes) comprised of a lens apiece in the single mutually-facing sides of the cubes, with an image-sensitive plate on the internal face of each cube opposite the lens.
With this construction on paper or in mind, let us imagine the upper cube moving rightward through this “ether” at a relativistically significant velocity, as we adopt the stationary lower cube’s viewpoint as depicted by the physicist, James Terrell. The upper cube appears contracted along its axis of motion, in accordance with the Lorentz transformation formula, thus the lens-bearing face of the cube is now rectangular (as seen through the lens of the lower cube), and the lens itself is elliptically shaped with its major axis vertically aligned. However, this orthodox effect is not the only consequence of such motion, as Terrell has pointed out, since the trailing face of the upper cube (corresponding to the line, northwest-southwest) is permitted by its velocity to emit photons laterally toward the lower cube and so give the appearance of the exposure of the trailing face in perspective, that is to say - in plane view - as a trapezoid appended to the trailing edge of the contracted, lens-bearing face of the “moving” upper cube. These combined effects have been represented as a “rotation in space-time” of the laterally-viewed object, but, unfortunately for geometricians who see theirs as a dimensionally-elevated and thus superior viewpoint, this illusion/analogy is incomplete in the absence of a trapezoidal tapering of the lens-bearing face balancing the trailing face in mimicry of perspective view. (Note: spherical objects would not, and experimentally do not, betray this incompletion.) In any case, it remains to be explained how the lower cube can likewise appear to the upper cube so as to maintain the symmetry of relativistic effects.
This was the challenge that our professor could not meet, except with the dogmatic assertion that he was not confronted with a paradox for failure to explain the upper cube’s reciprocation of the lower cube’s viewpoint. It should be mentioned that this explanation was necessary in order to maintain the inertial equivalence which is itself the axiomatic Special Principle of the Special Theory and which is, as illustrated below, the optical and/or calculational implication of the “asynchronicity” of events along the axis of motion of a reference framework. The professor was theoretically, if not demonstrably, correct in standing his ground against the imputation of paradox, but his incapacity beyond that point again illustrates the pedagogical shortcoming of the orthodox emphasis on geometry as opposed to physics. What then is the physical explanation for the moving cube’s image of a “quasi-pseudo-rotated” stationary cube, when the latter is not physically contracted and cannot emit photons laterally from its trailing face? The physical answer lies in optical asynchronicity, as shown during completion of our “thought experiment” below.
The upper, moving cube perceives the lower cube as laterally aligned with itself when the former is sufficiently displaced rightwardly to permit photons, which have entered its lens earlier, to then “intercept” the image-sensitive plate behind the lens (thus generating an impression of an aligned lower cube when in fact the moment of physical alignment is immediately past). This phenomenon, known as aberration, can be represented in our sketch by: drawing a dotted-line cube exactly to the right of the upper cube; drawing a line from the northwest corner of the lower cube, bisecting the lens-bearing face of the D-L cube, ending on an imaginary line extending rightward from the northwest-northeast square sides/cube faces of the upper cubes; drawing a line from the northeast corner of the lower cube, bisecting the lens-bearing face of the D-L cube and intersecting the previous line at the same point, ending on the same imaginary line; drawing another D-t cube rightward of the first, positioned along the axis of motion so that the “light rays” just drawn through the lens of the first will plant a now-inverted image on the image-sensitive plate of the second. This latest cube represents the point in time and space when the upper cube perceives itself as laterally aligned with the lower cube, and it permits us to draw the line/light ray from the southeast corner of the lower cube, through the lens of the first D-L cube and on to the image-sensitive plate of the second, which now registers an impression of the “trailing” face of the lower cube exactly equivalent to the image created by the photons emitted laterally in the wake of the trailing face of the upper cube! Now we have only to compensate for the contraction of the moving upper cube in order to complete our requirement for symmetry.
Note the different lengths of the “light rays” drawn from the northwest and northeast corners of the lower cube and reflect upon the fact that this implies that the rays do not arrive on the plate at the same time. Thus the coincident ray from the northwest corner of the lower cube must originate when the upper cube is less rightwardly displaced than when the ray from the northeast corner starts out. Therefore, the coincident rays intersect at a point inside the cube that is proportionally closer to the back-wall plate, so producing an image that is “contracted” or more narrow than it would have been had synchronicity prevailed. Note the operation again of an overcompensatory effect in the reduction of the width of the image to the square of the fraction of the width to which the upper cube is itself reduced. Note also that focus is preserved (for those who are alert to that consideration) by the longer ray entering the lens earlier, as we said, when the upper cube is less rightwardly displaced. That consideration, by the way, vindicates such emphasis as is placed upon recognition and reconciliation of non-simultaneities and asynchronicities in relativistic contexts, while at the same time indicting the obscurity of such discussion for failure of our expert professor to contribute anything to this analysis.
Are there indications that a similar incapacity afflicts speculation about, and investigation of, phenomena on the frontier of the discipline? One example comes to mind of relativistic premises possibly held beyond the point of theoretical utility or reason. This particular problem relates to “renormalization” procedure as applied to electrodynamics - specifically the adjustment required to deal with the field strength of an electron which is to interact with other quanta. If this student correctly understands this much, computations of the mass/field strength produce infinite quantities, in part because of an infinitude of virtual quanta influencing the mass, and in part because of the requirement for regarding the electron itself as an unextended, “point-like” object. This requirement is understood to be the implication of the apparent instantaneity of transmissions across the electron, which could not be so if L is indeed a limit and if the electron has extension in space. Thus the question: why retain c as a limit in this instance when the fundamentals of quantum mechanics, as formulated in Bell’s theorem and as confirmed in the upholding of his inequality by the EPR-inspired experiments, directly imply non-locality in quantum-dynamic phenomena? The answer in part seems to be that locality powerfully appeals to the mind-set of classical, deterministic physics (of which relativity is the crowning glory) and so the implications of Bell’s experiment are ignored or denied, based upon actually irrelevant requirements for verification of a definite polarization state in “twinned” particles and for evidence of communication potential in the implicit non-local influences therebetween.
Then has “relativism,” indeed, struck again? Perhaps, since one is reminded (by EPR, if nothing else) of Einstein’s own resistance to the physics of indeterminacy. However, imputations of motive or metaphysical premise ought cautiously to be made in regard to matters in the vanguard of theoretical research. Based on his own experiences with persons and papers addressing matters which ought, in contrast, to have been well settled, this student has come to realize, nevertheless, that physics is not the pristine realm of dispassionate discussion and research that it ought to be, but is, rather, a jungle - where dinosaurs still walk the earth.