Abstract
Ever since Newton, two forms of influence or causation have vied for supremacy in physicist’s theories. Descartes and his followers thought local or contiguous action—material particles colliding and rebounding, for example—the essence of mechanical explanation; Newton evoked their wrath by advancing a form of action at a distance. In the 19th and 20th centuries, Maxwell and Einstein restored the local picture in their continuum theories of electromagnetism and gravity, and the cycle seemed to have come to an end—until Bell proved his theorem in 1964.
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Notes
Concerning relativity theory, I recommend General Relativity: From A to B by Robert Geroch (1978), from whom I learned Einstein’s theory in college. In this excellent book with a modest title, the reader will learn about the special and general theory from a man who collaborated with Steven Hawking and Roger Penrose on proving that black holes are inevitable in most cosmologies. Also recommended is Relativity for the Million (1962) by Martin Gardner; no one does this kind popular science writing better. The Principle of Relativity, by H. A. Lorentz et al., is the little book of translations mentioned in the Introduction; Minkowski’s 1908 lecture is included. For experimental tests of special relativity, which have attained an accuracy of 70 parts per million in direct tests of the constancy of the speed of light, see Science 30 (November 1990), pp. 1207–1208. As if to fulfill the journalistic requirement of “balanced treatment,” Science included a report on two heretics who are trying to disprove relativity. (Note: No heretic mentioned in this book tried to disprove quantum mechanics.) Just for the fun of it, take a look also at the chapter on relativity in one of the standard textbooks, say Halliday and Resnick (first edition, 1960; latest 1992). From their Hollywood version of the birth of relativity, one cannot help visualizing gray-bearded scientists in seminar lamenting their aether-drift experiments, when suddenly the young Einstein pops up from the audience with the shout: “I have a hypothesis!” The hypothesis contradicts what everyone has believed about velocity or time since grade school, yet the unknown proposer is lauded as a genius and his miraculous new “axiom” wins the day. The truth is that people who do that are called “cranks” and are shown quickly to the door. Einstein had very plausible principles (see Chapter 18 “Principles”) as well as convincing arguments backing up his proposals. This kind of presentation suggests that progress in science comes from wild hypothesizing rather than from painstaking analysis; perhaps the recent “cold fusion” and “fifth force” episodes can be partly blamed on such mythologizing. Of course, the standard textbook presentation of quantum mechanics is even worse than for relativity—but for this the writers cannot be held entirely responsible!
The Einstein anecdotes are from Pais, Subtle Is the Lord… (1982).
The ridiculous scenario is constructed by starting with a tachyon emitted by the first car at rest and making a Lorentz transformation to a new coordinate system in which the car is moving to the left and the tachyon is moving to the right and down (e.g., “backward in time”). For the second car, reflect this construction and move it down a bit; see Figure 21. Note that all time statements refer to a single reference frame.
The analyst for the Navy: see Mermin, Physics Today (April 1985).
References on local causality are: J. F. Clauser and M. Home, Phys. Rev. D 10 (1974), pp. 526–35; Bell’s articles “The Theory of Local Beables” and “Bertlmann’s Socks and the Nature of Reality” in Bell (1987); “An Exchange on Local Beables,” Epistemological Letters (Feb. 1977), reprinted in Dialectica 39 (1985);
J. F. Clauser and A. Shimony, Rep. Prog. Mod. Phys. 41 (1978), pp. 1881–1927.
Concerning Nelson’s distinction between active and passive locality, it is a remarkable fact that, as of 1994, the only theory known to satisfy the one but not the other is quantum mechanics. Of course, quantum theory accomplishes the trick by refusing to provide those missing variables (that is, it does not satisfy a realism principle). Efforts are underway to find a realistic, stochastic field theory that violates passive locality, especially by Nelson and his colleagues, but it is a very difficult business.
Nelson’s version of Bell’s Theorem is in S. Albeverio et al. (1986). The argument that perfect correlations plus independent stochasticity implies determinism (see the Appendix) was made by P. Suppes and M. Zanotti; see Suppes (1976). What I have called “passive locality” was first described by J. Jarrett, Nous 18 (1984), pp. 569–589, who called it the “completeness condition”; it was also discussed by Shimony under the name “uncontrollable nonlocality” or “outcome independence.” Shimony also coined a more picturesque phrase for this kind of nonlocality—less than action at a distance but more than mere correlation: “passion at a distance.” See Shimony (1993) and references therein. Michael Redhead has distinguished five forms of nonlocal influence (and three major interpretations of quantum mechanics); see Redhead (1987).
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Wick, D. (1995). Dice Games and Conspiracies. In: The Infamous Boundary. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-4030-3_12
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