Outline of this series:
I. The Impetus for This Series
II. Special Relativity: The Standard Explanation
IV. A Further Look at Simultaneity
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)
THE IMPETUS FOR THIS SERIES
Why am I, a mere amateur, writing about Einstein’s special theory of relativity (STR)? First, it has long intrigued me because it seems to me counterintuitive, as it does to most people who know at least a little bit about it. If it’s true that the speed of an object affects its length and the rate at which it ages, what is the physical explanation for such phenomena? If there is one, is is buried deeply under reams of mathematical derivations that assume the rightness of STR. Similarly, there are tons of books and articles that take STR as gospel and merely present illustrations of its mysterious effects, without ever really explaining the underlying physical phenomena.
Second, deeper reading into STR has led me to dissidents — not just crackpots, but real scientists who have uncovered flaws in STR. If there are flaws, why is STR and its successor, Einstein’s theory of general relativity (GR), still almost universally accepted and taught as “the truth”? In other words, how dare those skeptics question a “scientific consensus”?
Real science isn’t about consensus, of course, it’s about finding the best possible explanations for what happens in the observable world — without ever knowing with certainty that the most recent explanations represent the “truth”. In fact, the explanations have changed drastically over time because old explanations have been challenged by the facts and logic of newer explanations, often despite what some would have called a “consensus” in favor of the old explanations. (See “The Science Is Settled”.)
In the case of STR, two real scientists (among many) who have uncovered flaws are the late Thomas E. Phipps Jr. and Christoph von Mettenheim. I begin with Mettenheim (2015), who says that
opinions on the meaning of a word can vary even if the word remains the same. The approach thus opens the possibility of ostensibly solving a problem by using some concept in one meaning at the beginning of an investigation and using it in a different meaning at its end…. Einstein repeatedly reached his results by that method…. At this point an example from his mathematics may serve to show its consequences…. The only mathematical knowledge needed for understanding the following is that if we do something on one side of an equation, then we must do the same also on the other side.
In his famous paper “On the Electrodynamics of Moving Bodies,” containing the first presentation of his Special Theory of Relativity, Einstein violated that principle. After introducing the premise that the speed of light is always constant, independent of the motion of its source, he considered a system with the ends A and B and defined the synchronism of two ‘clocks’ located at those points…
Mettenheim then walks through Einstein’s derivation. I will quote here only the key points made by Mettenheim:
The purport of equation (1) is that assuming the speed of light to be constant, a light signal travelling in a system at rest from A to B and back to A will take equal time on both ways….
Two pages further down, in § 2 of his paper, he introduced the following equations [(3) and (4)] for defining the time taken by light in a moving system on its single ways from A to B and back from B to A after reflection in B….
The expressions on the left sides of equations (3) and (4) are the same as those on either sides of (1). Einstein did not introduce new definitions of his symbols. Equation (1) therefore implies that the left sides of (3) and (4) are equal. Their right sides must then also be equal which gives us [equation (5)]….
One glance will show that equation (5) cannot possibly be correct. The numerators on both sides are identical whereas the denominators differ only in the symbols ‘+’ and ‘-’….
This shows that Einstein’s equations either violate the definition of ‘=’ or, alternatively, one of those of ‘+’ or ‘-’. The origin of that self-contradiction lay in equation (2), where he shifted the meaning of one of the symbols he used.
Mettenheim continues:
The fact that a mistake of that importance could have remained undiscovered so long is more interesting than the mistake itself. It casts a strange light on the state of theoretical physics in the past century. Even if Einstein’s self-contradiction were explicable somehow, one still would expect some other physicist to have discussed or even published that explanation somewhere. But that never happened….
… The fact that Einstein had based his special theory of relativity on the mathematical self-contradiction shown above gave me a new argument supporting my own explanation of gravity. And the fact that his mistake had remained undiscovered in a whole century gave me a new argument for demonstrating the weakness of the tradition of theoretical physics in the 20th Century. If a mathematical mistake as obvious as the one just shown could remain undiscovered for a whole century, then what are we to think of the far more complicated calculations of quantum theory or of the general theory of relativity?…
Though criticizing Einstein severely in this essay, I am doing my utmost to be fair to his memory. By neither styling him a genius nor accusing him of dishonesty I think I am not only doing him more justice but also being fairer to him than his uncritical admirers are. All those following him blindly put on him alone the responsibility for leading theoretical physics astray in more than a century. They fail to see that the far more important reason for that crisis is not in Einstein but in his followers. It is in their lack of critical faculties and of independence of thinking, in their exaggerated desire for geniality and in the barren intellectual soil which that attitude left over for permitting creativity to survive also in the field of science.
Here is what Phipps (2012) says about Mettenheim’s Popper versus Einstein:
This seems to me a deeply thought-out critique of Einstein’s theories from an unexpected quarter — that is, from a purely philosophical viewpoint. Von Mettenheim’s approach to time bears essential similarities to the one advanced here, but is supported by entirely different and independent arguments. I find it remarkable that by the application of purely philosophical principles a non-physicist can arrive at a deeper and more practically useful conception of “time” than the physicists have succeeded in doing….
The fallacy … evidently lies in analogical thinking, of the sort Einstein himself employed on many occasions…. [But] the only test of [theory] is empirical…
Philosophers as a profession seem more or less supinely to have joined the chorus of Einstein adulation — he being a thinker [i.e., analogous] after their own heart…. It is good to find an exception…. Apparently not all philosophers stand clueless under the aspect of modern physics.
I must underline Phipps’s point about analogical thinking:
An analogy is a comparison between two objects, or systems of objects, that highlights respects in which they are thought to be similar. Analogical reasoning is any type of thinking that relies upon an analogy. An analogical argument is an explicit representation of a form of analogical reasoning that cites accepted similarities between two systems to support the conclusion that some further similarity exists. In general (but not always), such arguments belong in the category of inductive reasoning, since their conclusions do not follow with certainty but are only supported with varying degrees of strength….
… Steiner (1989, 1998) suggests that many of the analogies that played a major role in early twentieth-century physics count as “Pythagorean.” The term is meant to connote mathematical mysticism: a “Pythagorean” analogy is one founded on purely mathematical similarities that have no known physical basis at the time it is proposed….
… [N]obody has yet provided a satisfactory scheme that characterizes successful analogical arguments. This strategy would face an additional problem even if we could find such a characterization: the appeal to past triumphs provides no insight or explanation for the fact that a certain class of analogies has often been successful. [Paul Bartha, “Analogy and Analogical Reasoning”, The Stanford Encyclopedia of Philosophy, June 25, 2013]
Einstein’s thought experiments are a kind of analogical thinking. In what follows I will sometimes essay a thought experiment of my own, though mainly to suggest the inadequacy of Einstein’s thought experiments or reasoning. The reader, in evaluating what Einstein and I say, should keep this in mind:
[T]hought experimenting seems to be constrained only by relevant logical impossibilities and what seems intuitively acceptable. This is indeed problematic because intuitions can be highly misleading and relevant logical impossibilities fairly ungrounded if they cannot be supplemented by relevant theoretical impossibilities based on current science in order to avoid the jump into futile fantasy. [James Robert Brown and Yiftach Fehige, “Thought Experiments”, The Stanford Encyclopedia of Philosophy, August 12, 2014]
In other words, it ain’t empirical.
As Phipps (2012) puts it, STR
is the precise modern counterpart of Ptolomy’s [geocentric] theory [of the universe]; it is not physics, but mathematical science based on a philosophy picked up in the street — that of spacetime symmetry, which has exactly as much physical legitimacy as Ptolemy’s divinity of the perfect circle. Both “philosophies” are pre-shaped molds into which the human mind, because it likes symmetries, has decided to pour experience.
Stay tuned for the next episode in this series. Comments may be sent to the following email address: the Germanic nickname for Friedrich followed by the surname of the 1974 Nobel laureate in economics followed by the 3rd and 4th digits of his birth year followed by the usual typographic symbol followed by gmail.com .
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.