Abstract
Can we guess the shape of theories yet to come? History dampens our expectations, with quantum mechanics itself throwing the coldest water. But indulging in some harmless speculations can be entertaining and may help clarify some issues. Before the free-associating begins, however, there are some needed preliminaries, which will make this chapter a bit of a hodge-podge. First, a tighter focus on material from previous chapters about determinism and locality will be useful. Then we require a few additional points about quantum mechanics that did not fit conveniently into the historical narrative. Finally, we come to the shameless speculating.
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Notes
The “hidden assumption” in the impossibility theorems is the following. The theorems compare quantum mechanics to a theory of a (possibly multidimensional) hidden variable, call it λ, for which there is a universal probability law P(dλ). To each observable A, B,… (Hermitian matrices in quantum mechanics), there is assumed to be a corresponding random variable fA(λ), fB(λ),…. After making suitable additional assumptions about these random functions or their expected values, a contradiction is derived with some prediction of quantum mechanics (references in Chapter 8). But a statistician would object at the outset. Since different A’s may represent different experiments, possibly requiring different apparatus, the statistician’s instinct is to write PA,B,..(dλ) for the probability law and f(λ) for the outcome variable, as in the model in the text.
Some philosophers expressed the opinion that the “contextual/noncon-textual” distinction has to do with being versus observing, with “is” as opposed to “is found to be” (see Jammer, 1974). But I side with the statistician wrinkling her brows about these speculations. The experiments involve different situations, she thinks; metaphysics is not required.
Lumps and wires: the English mathematician Roger Penrose developed a similar idea for combining “spins”; see his article in Hawking and Israel (1987). He derived a discrete arithmetic of these spins, and a “principle of indifference” to explain the randomness, which reproduces all the quantum predictions for spin measurements. However, recovering the continuous four-dimensional space-time manifold from his discrete construction proved elusive. In his Princeton lecture, Böhm suggested something like the first speculation, if I understood him correctly.
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© 1995 Birkhäuser Boston
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Wick, D. (1995). Speculations. In: The Infamous Boundary. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-4030-3_20
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DOI: https://doi.org/10.1007/978-1-4612-4030-3_20
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