number of impacts. This is precisely what is referred to as a «hidden variables theory,» which we will examine in more detail below.
35 A. Einstein, B. Podolsky and N. Rosen, « Can Quantum-Mechanical Description of Physical Reality Be Considered Complete ? » , Phys. Rev., 47, 777 (1935).
36 We are not concerned here with the position observable of the particles.
37 The tensor product, denoted ⊗, is a mathematical operation that allows the combination of the quantum states of two (or more) distinct systems to form a global state describing the composite system
38 In a classical situation, this would correspond, for example, to the results of a coin toss (corresponding, for example, to for heads and for tails).
39 In the classical situation of a coin toss game, imagine you obtained, for example, the sequence (11) and your game partner obtained the sequence (12). The existence of sys-tematically opposing results between the two of you would naturally lead you to think that the coins are rigged. «Hidden variables» is the term used to describe this rigging, in the context of quantum mechanics.
40 We speak of counterfactual experiments in the case of experiments that are not actually conducted.
41 It should be noted that in quantum mechanics, very often, measurement destroys or makes the physical system unworkable.
42 J.S. Bell, « Speakable and unspeakable in quantum mechanics ». Cambridge University Press (1987).
43 For example, see A. Aspect, J. Dalibard, and G. Roger, «Experimental Test of Bell’s Inequalities Using Time-Varying Analyzers,» Phys. Rev. Lett., 49, 1804 (1982).
44 J.F. Clauser, M.A. Horne, A. Shimony and R. A. Holt, « Proposed experiment to test local hidden-variable theories », Phys. Rev. Lett., 23, 880 (1969).
45 B. Hensen et al. (2015) « Loophole-free Bell inequality violation using electron spins sep-arated by 1.3 kilometres » Nature, 526, 682 (2015).
46 The use of «large» and «small» avoids the terms «microscopic» and «macroscopic,» which implicitly assume a specific treatment for each of the two systems.
47 This was later named the «Schrödinger’s cat» paradox.
48 with respective weights α and β.
49 And of the quantum system.
50 This viewpoint is shared by contemporary authors affiliated with QBism (Quantum Bayesianism), for whom the state vector is also not an objective description of the system, but a mathematical tool that allows a given observer to structure their beliefs regarding the possible outcomes. For an introduction to the subject, see: C.A. Fuchs, N.D. Mermin, and R. Schack, «An Introduction to QBism with an Application to the Locality of Quantum Mechanics,» American Journal of Physics, 82, 749 (2014).
51 Still within the hypothesis where the state vector is considered as an objective attribute of a given quantum system.
52 The physicist Henry Stapp even described Bell’s inequalities as «the deepest discovery in science.» H. Stapp, «Bell’s theorem and the world process.» Il Nuovo Cimento B, 29, 270 (1975).
53 The most recent experiments report correlations between two photons over a distance greater than 1200 kilometers.
54 J. Maldacena and L. Susskind « Cool horizons for entangled black holes », Fortsch. Phys. 6, 781 (2013).
55 That is, the particles in an entangled state of type (9).
56 There is an extensive literature on this subject. Let us simply mention: M. Jammer, The Philosophy of Quantum Mechanics: The Interpretations of Quantum Mechanics in Historical Perspective, Wiley-Interscience, New York, 1974. B. d’Espagnat, Le réel voilé. Analyse des concepts quantiques, (Le temps des sciences), Paris, Fayard, 1994. F. Laloë, Comprenons-nous vraiment la mécanique quantique?, EDP Sciences/CNRS Editions, Paris, 2011.
57 In English : “Entities should not be multiplied without necessity.”
58 One can read the two enlightening articles by David Mermin, even though he has largely renounced them since: N.D. Mermin, ‘The Ithaca Interpretation of Quantum Mechanics,’ Pramana, 51, 549 (1998) and ‘What is quantum mechanics trying to tell us?’ American Journal of Physics, 66, 753 (1998).