Abstract
What has been said so far is all well and good, but the implications of the quantum phenomena and the measurement problem of orthodox quantum mechanics are far from conclusive. We appear to be left with many options: determinism (Bohm, Everett) or indeterminism (GRW), many worlds or a single one, particles or flashes or the wave function alone—all these possibilities could, in principle, fit physical reality as we know it. And now we turn to something new, something fundamental, in fact, an eternal truth: the nonlocality of Nature. We will make the concept more precise as we go along, but in a nutshell, nonlocality means that the fundamental laws of Nature must involve some sort of action at a distance, i.e., distant events sometimes influencing each other instantaneously.
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Notes
- 1.
“Instantaneous” provides the right intuitive understanding, but we should note that it is no longer well defined when we come to relativistic physics. “Superluminal” would be a more precise way of speaking, but it actually fails to express just how radical this new feature is (see footnote 10).
- 2.
H.P. Stapp, Bell’s theorem and world process. Nuovo Cimento B 29, issue 2, 270–276 1975.
- 3.
A more complete quote can be found in Einstein’s letter to Cornelius Lanczos: “It seems hard to sneak a look at God’s cards. But that he plays dice and uses ‘telepathic’ methods (as the present quantum theory requires of him) is something that I cannot believe for a moment.” The “ telepathic methods” are a reference to the action at a distance that Einstein identified in quantum mechanics.
- 4.
A. Einstein, B. Podolsky, and N. Rosen, Can quantum-mechanical description of physical reality be considered complete? Physical Review 47, 777 (1935).
- 5.
When Stern first proposed these experiments, he suggested using a magnet which was oriented from the floor to the ceiling of the lab. This may be responsible for the terminology “up” and “down”.
- 6.
Reprinted in: J.S. Bell, Speakable and Unspeakable in Quantum Mechanics, 2nd edn, Cambridge University Press, 2004, Chap. 16.
- 7.
The parameters a, b, etc., still represent the orientations a, b, etc., of the spin measurements, as in the previous section. However, we shall drop the vectorial notion from now on, since it is usual to think of the relevant parameters as angles in the plane of rotation of the Stern–Gerlach magnets (orthogonal to the flight trajectory of the particles).
- 8.
Note that the probabilities in (10.12) could all be 1 or 0, which would be the case for deterministic theories in which a complete state description λ uniquely determines the measurement outcomes.
- 9.
B. Hensen et al., Loophole-free Bell inequality violation using electron spins separated by 1.3 kilometres. Nature 526, 682–686 (2015).
- 10.
Since the relevant experiments exclude only influences that propagate at most with the speed of light, we could ask, at least as long as we think non-relativistically, whether nonlocal influences have to be truly instantaneous or whether they could act with a finite (though superluminal) velocity. The answer is that they could not, at least not if superluminal communication is excluded; see N. Gisin, Quantum correlations in Newtonian space and time. In: D. Struppa and J. Tollaksen (Eds.), Quantum Theory: A Two-Time Success Story, Springer, 2014.
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Dürr, D., Lazarovici, D. (2020). Nonlocality. In: Understanding Quantum Mechanics . Springer, Cham. https://doi.org/10.1007/978-3-030-40068-2_10
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DOI: https://doi.org/10.1007/978-3-030-40068-2_10
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