Experiments in Quantum Mechanics are often interpreted as a proof of non-local realism: the belief that, under certain conditions, particles can instantaneously affect physical properties of other particles, irrespective of the distance between them. Here I argue that the popular explanatory theses about quantum entanglement, non-local realism and other non-classical phenomena cannot be consistently deduced from the available empirical evidence.

The distinction between classical (local realist) behaviour of particles and Quantum Mechanics is typically demarcated by violations of Bell’s Inequality (Bell, J. S. (1964) “On the Einstein Podolsky Rosen Paradox”, Physics. p195–200). Bell’s Inequality (in the simplest, intuitive form) defines the maximum expected change, according to the classical model, in the probability of spin-correlation between two particles against a small change in the angle of measurement. The linked graph shows how the probability of spin-correlation varies according to the classical model vs. the quantum-theoretic model for the relevant angles of measurement.

Bell’s Inequality is consistently violated by experimental results in Quantum Mechanics. This is canonically interpreted as evidence of quantum entanglement: a state in which two particles originating from the same source maintain instantaneous sensitivity or reciprocity to each other’s state, whenever that state is measured, irrespective of the distance that separates them. Recently, an allegedly ‘loophole free’ test of Bell’s Inequality has been performed (PDF), confirming the quantum-theoretic prediction. I suggest that quantum entanglement, understood in the sense defined above does not follow from the accepted premises. The fact that the probability distribution for pairs of particles does not reflect classical probability is not evidence, let alone proof, of any specific explanatory thesis, such as non-local realism. The empirical findings of Gröblacher et al. (2006) published in Nature (PDF) and the analysis of Hardy’s formulation of Bell’s theorem by Arthur Fine give independent support for this accusation.

The canonical interpretation of Bell’s Inequality violations seems to take the absence of evidence (of local hidden variables) as the evidence of their absence, which is an excessive inferential step. Unless I radically misunderstand the formulation of Bell’s theorem, which on my reading assumes that the hypothetical hidden variable has uniform probability distribution over all directions (Ibid. Bell, p405), there is still logical space for the possibility of local variables with non-uniform probability distribution. It is not unthinkable that relativistic, tangential ‘stretching’ of the quantum space could occur at angles between 0 and 90 degrees from the longitudinal direction of motion, what would preserve the possibility of local realism. In other words, it may be the case that what appears to the human observer as the angle of 45 degrees between the axis of measurement and the direction of particles’ motion corresponds to a different angle (26.4 degrees, if my calculation is correct) in the reference frame of a moving particle, which would amount to the classical probability distribution being preserved in a distorted space. This is just a hypothesis, but it may indicate that legitimate explanatory possibilities are not yet exhausted with respect to what is canonically interpreted as quantum entanglement. I call this possibility the epistemic loophole.

The above limitation does not affect just the original formulation of Bell’s theorem but any consistent formulation of the problem, because no matter what probability distribution is predicted it is always possible to construct a hidden-variable function that will modify the predicted quantum-theoretic distribution to the classical distribution-function.

There are other speculative possibilities for defending local realism in quantum physics: faster than light communication would allow for local realist interpretations; existence of hidden spatial dimensions could explain appearance of one particle as multiple particles (a wormhole). For an accessible introduction to related ideas see the Clara Moskowitz’s article “Tangled Up in Spacetime” (Scientific American). The only thing we know for sure about violations of Bell’s Inequality is that we cannot explain the associated causal mechanism with any degree of confidence. All affirmative talk about ‘spooky’ action at a distance, teleportation and entanglement is just hollow speculation. We simply do not know why the world behaves the way it appears to behave at the quantum level.

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