Outline of this series:
I. The Impetus for This Series
II. Special Relativity: The Standard Explanation
IV. A Further Look at Simultaneity
VI. Getting Light Right
VII. Further Thoughts on the Meaning of Spacetime and the Validity of STR
VIII. Mettenheim on Einstein’s Relativity
Bibliography (appended to each part of the series)
“Part III: A Fatal Flaw?” exposes the erroneous thought experiment used by Einstein (1920) to demonstrate the (supposed) relativity of simultaneity. “Part V: The Velocity Conundrum” points out inconsistencies in the way that the special theory of relativity (STR) treats velocity. Here I consider a misleading interpretation of the speed of light, to which Einstein contributed.
Light purportedly moves at the same (constant) speed (in a vacuum) regardless of the motion of its source or sensor. (Aside: The speed of light may actually vary; that is, it may not be a universal constant.) As I will discuss in this section, the meaning of that (purported) fact has been misinterpreted, and then used to draw incorrect conclusions about relativity. Even Einstein did it.
I begin with my own thought experiment. Consider the case of an observer who is standing by a railroad track. On the track, coming toward him from the left, is an open train car — an extra-long one — on which a pitcher throws a ball to a catcher standing 132 feet away. (The pitcher is throwing in the observer’s direction.) Assuming away the problem of air resistance, the observer sees the ball coming toward himself at the sum of two speeds: the speed of the ball (relative to the catcher) and the speed of the train car (relative to the observer). Thus, if the pitcher throws the ball at 90 miles per hour (mph) in a train car that is moving toward the observer at 60 mph, the ball approaches the observer at 150 mph.
In feet per second (fps), the ball moves toward the catcher at 132 fps, the train car moves toward the observer at 88 fps, and the ball therefore moves toward the observer at 220 fps. If the pitcher releases the ball when he is 220 feet from the observer, the catcher is then 88 feet from the observer (220 feet from pitcher to observer – 132 feet from pitcher to catcher). In the 1 second that it takes the ball to reach the catcher, the train moves 88 feet toward the observer. The ball is therefore caught when the catcher is adjacent to the observer. Thus takes the ball 1 second to travel 220 feet from its release point to the observer’s position. This is another way of saying that the ball approaches the observer at 150 mph, which is 220 fps (pitch moving relative to pitcher at 132 fps + train car moving relative to observer at 88 fps). This is the classical addition of velocities according to Galilei-Newton relativity.
I will now rerun the thought experiment, making a slight modification. Instead of a baseball, the pitcher throws an exceedingly slow “ball” of light at the same 132 fps. If light were an ordinary object like a baseball, it would approach the observer at 220 fps. But light isn’t like a baseball in that its apparent speed is the same for every observer: 132 fps. (Remember, this is a thought experiment, and I’m using a very slow speed of light just to keep it simple. I know that light really travels at 2.99792 x 10^8 meters per second in a vacuum.)
At this point I must introduce the crucial misconception about the speed of light. Here is what Einstein says in the second paragraph of the 1905 paper in which he introduces STR:
[T]he phenomena of electrodynamics as well as of mechanics possess no properties corresponding to the idea of absolute rest. They suggest rather that, as has already been shown to the first order of small quantities, the same laws of electrodynamics and optics will be valid for all frames of reference for which the equations of mechanics hold good. We will raise this conjecture (the purport of which will hereafter be called the “Principle of Relativity”) to the status of a postulate, and also introduce another postulate, which is only apparently irreconcilable with the former, namely, 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.
Clearly, Einstein does not say that the speed of light is the same relative to all observers. He merely says that it is always the same for all observers. I will illustrate the subtle distinction with another thought experiment, which begins with a “true” fact.
Albert A. Michelson and others built a mile-long vacuum tube in which a beam of light was bounced back and forth by an arrangement of mirrors, resulting in a 10-mile journey that could be timed with precision. The experiment was conducted many times from 1930 to 1935. And in 1935, four years after Dr. Michelson’s death, his collaborators reported an estimate of the speed of light that was more than 99.99 percent of the value now deemed correct. (That’s better than Ivory Soap, which was advertised as 99.44 percent pure, though pure of what I don’t know.)
Imagine that there was a construction road parallel to the mile-long tube (which there probably was). Suppose that the road wasn’t used during experiments, with one exception. One fine day, Dr. Michelson hopped in his car and was driving parallel to the tube, reaching a steady speed of 50 mph as a beam of light was sent on its 10-mile journey. Imagine, further, that the top of the tube was made of glass, so that Dr. Michelson could catch a glimpse — a truly fleeting one — of the beam of light as it zoomed by him. Did his presence cause the beam of light (however fleetingly) to speed up so that it was going 2.99792 x 10^8 meters per second (the “correct” value) relative to Dr. Michelson? Or, if Dr. Michelson had been able to measure the speed of light at the moment it passed him, would he have found that it was moving at the same 2.99792 x 10^8 meters per second, even though he was moving at 50 mph?
It seems obvious to me that the second possibility in the correct one. The first possibility not only requires light to behave weirdly, but it also requires light to move faster than its own (supposedly limiting) speed. In sum, the speed of light would remain the same for Dr. Michelson (despite the speed of his car). But relative to Dr. Michelson, it would be moving at a speed of 2.99792 x 10^8 meters per second minus the speed of the car (50 mph = 22.35 meters per second).
The moral of the thought experiment: Light (in a vacuum) moves at the same, constant speed for all observers. But it must move at different speeds relative to various observers, depending on the speeds at which they are moving.
I have gone out of my way to make this point because it evidently eluded Einstein. This is from Einstein (1920):
Let us suppose our old friend the railway carriage to be travelling along the rails with a constant velocity v, and that a man traverses the length of the carriage in the direction of travel with a velocity w. How quickly, or, in other words, with what velocity W does the man advance relative to the embankment [on which the rails rest] during the process?… As a consequence of his walking, … he traverses an additional distance w relative to the carriage, and hence also relative to the embankment, … the distance w being numerically equal to the velocity with which he is walking. Thus in total he covers the distance W = v + w relative to the embankment in the second considered.
That is, by the classical addition of velocities formula, the man in the train car is moving at speed v + w relative to a an observers standing by the railroad track. But …
Einstein continues:
If a ray of light be sent along the embankment [in an assumed vacuum], … the tip of the ray will be transmitted with the velocity c relative to the embankment. Now let us suppose that our railway carriage is again travelling along the railway lines with the velocity v , and that its direction is the same as that of the ray of light, but its velocity of course much less. Let us inquire about the velocity of propagation of the ray of light relative to the carriage. It is obvious that we can here apply the consideration of the previous section, since the ray of light plays the part of the man walking along relatively to the carriage. The velocity W of the man relative to the embankment is here replaced by the velocity of light relative to the embankment. V is the required velocity of light with respect to the carriage, and we have
V = c − v .
The velocity of propagation of a ray of light relative to the carriage thus comes out smaller than c .
But this result comes into conflict with the principle of relativity set forth in Section V. For, like every other general law of nature, the law of the transmission of light in vacuo must, according to the principle of relativity, be the same for the railway carriage as reference body as when the rails are the body of reference.
(I have taken the liberty of making a minor change in Einstein’s notation to avoid some confusion, but I haven’t changed his discussion or the relationship depicted by the resulting equation.)
Einstein contradicts himself. He insists that the speed of light relative to the train car should be c. But it can’t be, as I argue above. The speed of light is unaffected by the speed of the train car. It remains c, even though the train car is moving at v. The movement of the train car at v doesn’t affect the actual speed of light, which remains constant — the same for all observers. Therefore, Einstein wrongly rejects V = v – c as the formula for the speed of light relative to the train car. It is exactly the right formula. Rearranging, it says that c = v + V , which preserves the constancy of c (much like preserving its virtue).
I am taking this long detour from the route of my original thought experiment (which I will rejoin) because clarity demands it. So does the evidence, insofar as I am familiar with it. The speed of light has been measured by two basic methods. One kind of measurement involves a stationary apparatus, where the light source and sensor are fixed relative to each other; there is no motion of emitter or observer to account for. The other kind of measurement takes advantage of natural occurrences (e.g., light reflected from distant, moving moons). But in such cases the location of the distant object is accounted for in the computation of the speed of light; what is measured is the speed of light during its transit from a distant object to an earth-bound sensor. This is no different, in principle, than the measurement of the speed of a baseball thrown between pitcher and catcher in a moving train car; there is no “stationary” observer to add the speed of the baseball and the speed of the train car. In other words, such observations do not confirm that the speed of light is independent of the speed of its emitter. But they are consistent with the view that the speed of light “in flight” is constant.
And if the speed of light is constant, it moves at various speeds relative to objects in its vicinity. (For example, if it is emitted from or observed by an object which is moving at 0.9c, it is simply moving 0.1c faster than that object, and so on.) It doesn’t assume different speeds at a whim, or at the whim of whatever it happens to be moving near it. It is one thing to say that the speed of light is constant, regardless of the motion of its source or observer. It is quite another thing — and a prescription for chaos — to say that the speed of light is always greater by c than that of its source or observer (which implies that light somehow travels faster than light). But that is precisely what Einstein implies in his later explanation of STR, and that misstatement — which has been propagated by many expositors of STR — must not be allowed to stand.
I now return, at last, to the thought experiment involving the pitcher, catcher, train car, and observer standing next to the railroad track. The pitcher is throwing a “ball” of (exceedingly slow) light at 132 fps in the direction of the observer while he (the pitcher) is moving toward the observer on a train car that is moving toward the observer (from the observer’s left) at 88 fps. At the point of release, the “ball” of light is 132 feet from the catcher and 220 feet from the observer. But the catcher is moving away from the release point at 88 fps. The “ball” must therefore reach the catcher before it passes by the observer.
The same order of events would obtain in the case of a real beam of light, though many orders of magnitude faster. The constancy of the speed of light is preserved, even though it appears move at less than c relative to the pitcher and catcher, who are moving in the same direction as the “ball” of light.
Here’s the clincher: Einstein’s thought experiment about the relativity of simultaneity, which I discuss in “A Fatal Flaw?,” is built on the same premise. In that thought experiment, the person (at M’) who is analogous to the catcher of my thought experiment, is moving toward the source of light instead of away from it. As a result, he sees a flash of light before the stationary observer (at M) sees it. I am therefore puzzled as to why, in the thought experiment quoted above, Einstein insists that light must move at c relative to the moving train car.
BIBLIOGRAPHY
Online courses in special relativity
Lecture 1 of “Special Relativity”, Stanford University
All lectures of “Special Relativity”, Khan Academy
All lectures of “Understanding Einstein: The Special Theory of Relativity”, Standford University
Selected books, articles, and posts about special relativity
Barnett, Lincoln. The Universe and Dr. Einstein. New York: Time Incorporated, 1962.
Bondi, Hermann. Relativity and Common Sense: A New Approach to Einstein. New York: Doubleday & Company, 1946.
Buenker, Robert J. “Commentary on the Work of Thomas E. Phipps, Jr. (1925-2016)”. 2016.
Einstein, Albert. “On the Electrodynamics of Moving Bodies”. Annalen der Physik, 322 (10), 891–921 (1905).
———. Relativity: The Special and General Theory. New York: Henry Holt, 1920.
Epstein, Lewis Carroll. Relativity Visualized. San Francisco: Insight Press, 2000.
Hall, A.D. “Lensing by Refraction…Not Gravity?“. The Daily Plasma, December 23, 2015.
Marrett, Doug. “The Sagnac Effect: Does It Contradict Relativity?“. Conspiracy of Light, 2012.
———. “Did the Hafele and Keating Experiment Prove Einstein Wrong?“. Conspiracy of Light, 2013.
von Mettenheim, Christoph. Popper versus Einstein. Heidelberg: Mohr Siebeck, 1998.
———. Einstein, Popper and the Crisis of Theoretical Physics (Introduction: The Issue at Stake). Hamburg: Tredition GmhH, 2015.
Noyes, H. Pierre. “Preface to Heretical Verities [by Thomas E. Phipps Jr.]”. Stanford: Stanford Linear Accelerator Center, Stanford University, June 1986.
Phipps, Thomas E. Jr. “On Hertz’s Invariant Form of Maxwell’s Equations”. Physics Essays, Vol. 6, No. 2 (1993).
———. Old Physics for New: A Worldview Alternative to Einstein’s Relativity Theory. Montreal: Apeiron, first edition, 2006.
———. Old Physics for New: A Worldview Alternative to Einstein’s Relativity Theory. Montreal: Apeiron, second edition, 2012 (The late Dr. Phipps — Ph.D. in nuclear physics, Harvard University, 1950 — styled himself a dissident from STR, for reasons that he spells out carefully and exhaustively in the book.)
Rudolf v. B. Rucker. Geometry, Relativity, and the Fourth Dimension. New York: Dover Publications, 1977.