Abstract
We have seen that it is easy to obtain a score of 3 in Bell’s game. For example, we need only agree beforehand to produce the same result each time. But we have also seen that it is impossible to specify any local strategy that could be applied independently by Alice and Bob and that would allow them to win more often than 3 times out of 4. But if two players were to win Bell’s game more often than 3 times out of 4, what must we conclude in this case?
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Notes
- 1.
In this sense, the image of twin photons often used to speak of entangled pairs of photons, which can in fact be used to win Bell’s game, is extremely misleading.
- 2.
I do not intend to assert that the explanation in terms of nonlocal randomness is complete and definitive. However, I would say that scientists will always try to find explanations, and that any explanation for this must necessarily be nonlocal. The explanation that history will eventually adopt will be the one that allows us to go beyond the physics of today and leads us to the discovery of a new physics that incorporates quantum physics as an approximation. This new physics will still allow us to win Bell’s game, otherwise it will not be in agreement with experimental results. For this reason, it will also be nonlocal.
- 3.
In classical physics, the result of any measurement is predetermined. In a sense, it is written into the physical state of the system being measured. Probabilities come in only through our ignorance of the exact physical state. This ignorance compels the scientist to resort to statistical methods and probabilistic calculations obeying Kolmogorov’s axioms. In quantum physics, the result of a measurement is not predetermined, even if the state of the system is known perfectly. Only the propensity of such and such a result to manifest itself is written into the physical state of the system being measured. These propensities do not obey the same rules and do not satisfy Kolmogorov’s axioms. But note that certain results in quantum physics are nevertheless predetermined. The structure of the mathematical theory of quantum physics (Hilbert space) is such that, for states allowing no ignorance, the so-called pure states, the set of all predetermined results uniquely characterises the propensity of all other possible results. In this sense, the propensities of quantum physics are a logical generalisation of classical determinism. (N. Gisin: (N. Gisin: Propensities in a non-deterministic physics, Synthese 89, 287–297, 1991; see also arXiv:1401.0419.)
- 4.
Ferrenberg, A.M., Landau, D.P., Wong, Y.J.: Monte Carlo simulations: Hidden errors from ‘good’ random number generators, Phys. Rev. Lett. 69, 3382 (1992); Ossola, G., Sokal, A.D.: Systematic errors due to linear congruential random-number generators with the Swendsen–Wang algorithm: A warning, Phys. Rev. E 70, 027701 (2004).
- 5.
Popescu, S., Rohrlich, D.: Nonlocality as an axiom, Found. Phys. 24, 379 (1994).
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Gisin, N. (2014). Nonlocality and True Randomness. In: Quantum Chance. Copernicus, Cham. https://doi.org/10.1007/978-3-319-05473-5_3
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DOI: https://doi.org/10.1007/978-3-319-05473-5_3
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