Tuesday, December 12, 2006

Is A Photon (just) An(other) Object?

Fred Vaughan headshot by Fred Vaughan

Fred Vaughan back in the day
the author back in the day

Even very intelligent people tend to abandon logic in dealing with concepts of the special theory of relativity and especially with regard to those involving frame independence and mutual observability - the latter of which most have never even considered. These notions derive from a common sense presumption that a "ray of light" (read photon) emitted or detected at a given point in spacetime could have been emitted or detected by any other source or observer, respectively that happened to have been coincident at that particular instant in time. The presumption results from Einstein's insistence that Lorentz transformation "relations must be so chosen that the law of the transmission of light in vacuo is satisfied for one and the same ray of light (and of course for every ray) with respect to…"1coincident observers in uniform relative motion. Thus a photon was presumed to be a mutually observable real object. Well, it isn't.

Subsequent to Einstein's coining of this phrase concerning "the law of the transmission of light" in the first decade of the last century, much that was common sense about light had to be reevaluated and corrected because of light's notoriously non-commonsensical behavior. Einstein himself was a major contributor to that revised understanding that did not near completion for another twenty years. In fact, when he received the Nobel Prize for physics in 1921 it was for his powerful insights into the nature of light and the "photo-electric" effect in particular which involves the interaction of light and matter. In bestowing that honor, no mention was made of his more exhaustive efforts in relativity and most certainly not this "law" that gave rise to frame independence and mutual observability.

There have been notable challenges to the doctrine. For example, as early as 1926 in discussing the "nature of light" Gilbert Lewis who was the one who originally coined the term "photon," stated, "…we can no longer consider one atom the active agent and the other as an accidental and passive recipient, but both atoms must play coordinate and symmetrical parts in the process of exchange."2So that to presume that a photon of light is just an object that passes a point in spacetime available for inspection by any observer (rather than a specific emitter/absorber pair) had become extremely questionable within a very few years of Einstein's having coined his own catch phrase. Re-evaluation of whatever concepts depend upon it became an outstanding obligation, but in this case it was an obligation never addressed by those accepting the established interpretation of the Lorentz equations. But Lewis's position was notably cited by Wheeler and Feynman in their analyses of light as an inter-particle interaction in contrast to its being just another object or "wave/particle duality".3 But such interaction concepts with regard to the transmission of light do not seem ever to have been addressed specifically in the context of re-examining this cornerstone of the established interpretation of the Lorentz equations. Cramer did, however, address this misconception in his Transaction Interpretation of quantum mechanics.4

Einstein's and Minkowski's interpretation of the Lorentz equations postulates that events involving the emission, refraction or absorption of light in one frame of reference must be observable in these same senses by observers in any momentarily coincident frame of reference using their own equipment. This interchangeability insists not only on the possibility of coincident observation by relatively moving observers, but posits coincident observation of the very same events, which denies the unique role of the observer (absorber) in effecting Lewis's ultimate observation transaction. To instruct us with regard to the significance of this mutuality demand with respect to the interpretation of the Lorentz equations, Aharoni lays out the scheme very succinctly as follows: "Had an event not possessed absolute significance there could be no question of transforming its coordinates from one frame to another."5 So quite apart from the experimentally verified Lorentz relationship between observed events, a velocity addition formula was conjectured with no tests for refutation that ennobled the equations as a coordinate "transformation."6 So the very meaning of the Lorentz transformation equations as a transformation of one event rather than a correspondence between two events is what is at issue and resolution of this matter is of major epistemological significance.

Certainly, without experimental verification these equations ought not have been presumed, because of vague similarities to other mathematical forms, to fall into a category of coordinate conversion of identical events rather than a simpler correspondence between unique events related by the nature of observation. The latter is in more or less the same sense that observation is handled in quantum theories where the observer and what is observed are inextricably entwined. This interpretation would not violate other verified aspects of relativity; it would merely indicate that an event observable now by one observer corresponds to a different event on the world line of the source observable now by another. It would be in complete agreement with Einstein's insistence that the results of Lorentz calculations be considered as mensurable coordinate values. Both events would be observable by the other observer at some time, just not while in coincidence. This interpretation is similar to that of the parallax relationship of everyday experience. The Lorentz equations are at least as directly related to such a parallax translation of coordinates interpretation as they are to the usual didactic association with skew rotation employed in typical relativity texts.

The differences between these alternative interpretations of the mapping of events provided by Lorentz's equations must be subject to the usual refutation/verification procedures of experimental physics. So let us consider requirements on experiments that could determine whether such Lorentz-transformed events (more correctly "Lorentz-correspondent events") can possibly be the very same or must be distinct one from the other so as to comply with, or violate, the conjectured frame independence and mutual observability hypotheses.

An adequate test requires each of two relatively moving observers to obtain two types of data as shown in the figure below. The data must include that which an observer himself (or a relatively stationary synchronized assistant) observes directly and that observed and communicated at coincidence by the other observer or his synchronized assistant who will also be in uniform relative motion with the same velocity. The experiment will, furthermore, involve both measurements of electromagnetic emission and absorption events occurring exclusively within each observer's own apparatus and measurements involving interactive phenomena with the atoms and molecules of the apparatus of the other observer. Altogether this requires comparison of four categories of observation as shown.

The six relationships among these four types of experimental data pertinent to refutation of frame independence and mutual observability are also shown. Diagonally related observation types (I and IV, as well as II and III) pertain to observations of "common" events (or more explicitly to one specific event occurring on one particular object) by relatively moving observers and are presumed by theory to be related by the Lorentz equations. Note that these are the proper subject matter of the special theory but it has not been feasible to conduct such experiments. Horizontally related observation types (I and III, as well as II and IV) pertain to observations of analogous (i. e., similar but definitely not the same) events in the other frame of reference. Legitimacy of the assumed analogs depends upon the apparatus of each observer being constructed in accordance with identical drawings and that initiation of the identical experimental procedures by the observers be synchronized so as to maintain symmetry. These are sometimes erroneously assumed to exhibit a Lorentz relationship ostensibly pertaining to that between II and III (and presumably I and IV) and to have thereby confirmed length contraction and time dilation. Data obtained in horizontal categories (I and III as well as II and IV) require communication between observers with coincident assistants involved as appropriate for a definitive comparison. The relationship between I and III (and between II and IV) would seem by covariance to be an identity, but this is counter to the established interpretation in which the other's clocks are presumed dilated, etc.. Performing all these tests would substantiate or falsify the conjecture concerning light being just another object upon which so much of Einstein's and Minkowski's interpretation rests.

relativity observations possibilities
Four categories of observations possible in tests of relativity and their various relationships

Although experiments are still not feasible for comprehensively comparing all these measurements, one can at the very least use logical consistency as a criterion of validity for the various interpretations of Lorentz's equations. The author believes there to be a serious lack in the required consistency.

1 A. Einstein, Relativity - The Special and the General Theory, Crown, New York, p. 32. (1961)

2 G. N. Lewis, "The Nature of Light," Proc. N. A. S., Vol. 12, pp. 23-24 (1926)

3 J. A. Wheeler and R. P. Feyman, "Interactions with the Absorber as the Mechanism of Radiation," Rev. Mod. Phys., 17, 157 (1945); and J. A. Wheeler and R. P. Feynman, "Classical Electrodynamics in Terms of Direct Interparticle Action," Rev. Mod. Phys., 21, 425 (1949).

4 J. Cramer, "Transaction Interpretation of Quantum Mechanics," Rev. Mod. Phys., 58,3, 647-687 (1986).

5J. Aharoni, The Special Theory of Relativity, 2nd Ed., Dover, New York (1985), p. 38.

6 See R. F. Vaughan, Aberrations of Relativity (on sale through lulu publications on ReasonAndRhyme.com). The specific articles referenced are: "Are There Inevitable Uncertainties in Our Maps of the Universe," pp. 56-60; "The Certainty Principle," pp. 61-62; "Learning Addition All Over Again," pp. 63-68.

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