**Comment on recent articles published in Nature and Physical Review Letters**

Louis Vervoort, 10.02.2016

*Minkowski Institute, Montreal, Canada*

In recent articles [1-3], three research teams, led by Anton Zeilinger at the University of Vienna, Austria [1], Lynden Shalm at NIST in Boulder, Colorado [2], and Ronald Hanson at the Delft University of Technology in the Netherlands [3] have reported on the untimely death of local realism. These teams have succeeded in the experimental *tour-de-force* to close, in a Bell experiment, the most relevant loopholes for local hidden-variable theories. ‘Realism’ is ‘the assumption that objects have physical properties independent of measurement’, and ‘locality’ is the assumption that there are no influences traveling faster than the velocity of light [1]. The general content of these publications is thus that one of these cornerstones of physics must be given up. If true, such a conclusion would surely represent a landmark in our intellectual history. However, I believe this conclusion is quite premature.

Upon closer inspection the authors appear to be more cautious. In fact, it appears that only a *certain class* of hidden-variable theories is eliminated by the experiments. Ref. [1] is maybe most explicit, by describing how the experiment would close the ‘freedom-of-choice’ loophole: “This loophole can be closed only under specific assumptions about the origin of [the hidden variables]. Under the assumption that [the hidden variables] are created with the particles to be measured, an experiment in which the settings are generated independently at the measurement stations and spacelike separated from the creation of the particles closes the loophole.”

Now, it is certainly very natural to consider the hidden variables as ‘pertaining’ only to the particle pair, more generally as created at the source with the particles, in the sense of [1]. But it is not the only possibility that is allowed by logic and physical law. My point is that the class of hidden-variable theories still exploiting the freedom-of-choice loophole is vast and natural. For instance, the hidden variables could, besides the particles, also describe a background field or medium in which the particles move and that interacts with particles and analyzers. In this case the full dynamics of the hidden variables is crucial, as I have recently investigated in detail in Ref. [4] (the background field may refer to vacuum fluctuations, an ether, a dark field,…). In [4] it is shown that such background-based theories can reproduce the quantum correlation of the Bell experiment.

Background-based hidden-variable theories are inspired by spectacular recent experiments by Couder, Fort, Bush and co-workers, which demonstrate that background fields (or pilot waves if one prefers) can lead to a surprisingly wide range of quantum-like phenomena in fluid mechanical systems [5-6]. Such background-based theories therefore remind one of Louis de Broglie’s pilot-wave theory. There is a whole series of physicists working on modern variants of this theory, attempting to derive quantum mechanics from a deeper level. One can also refer here to the Cellular Automaton Theory of quantum mechanics of Nobel Laureate Gerard ‘t Hooft [7].

In conclusion, the crucial experiments [1-3] do eliminate a wide and natural class of local-realistic models. But when more general claims are made (‘By closing the freedom-of-choice loophole […] we reduce the possible local-realist explanations to truly exotic hypotheses’ [1]), I disagree. There is a wide and natural class of local-realist theories that is not eliminated by [1-3]. Not only is local realism far from dead; I believe that by prematurely proclaiming its passing one has closed a promising road to finally reconcile quantum mechanics and relativity theory. Some more info can be found in [8].

*Acknowledgements. I thank Ronald Hanson for his kind willingness to discuss his group’s experiment and its interpretation*.

[1] M. Giustina et al., ‘Significant-loophole-free test of Bell’s theorem with entangled photons’, Phys. Rev. Lett. **115**, 250401 (2015)

[2] L. Shalm et al., ‘Strong loophole-free test of local realism’, Phys. Rev. Lett. **115**, 250402 (2015)

[3] B. Hensen et al., ‘Loophole-free Bell inequality violation using electron spins separated by 1.3 kilometers’, Nature **526**, 682 (2015)

[4] L. Vervoort, ‘No-go theorems face background-based theories for quantum mechanics’, Found. Physics **45**, 1 (2015), doi: 10.1007/s10701-015-9973-7

[5] A. Eddi, J. Moukhtar, S. Perrard, E. Fort, and Y. Couder, ‘Level-Splitting at a macroscopic scale’, Phys. Rev. Lett. **108**, 264503 (2012)

[6] J. Bush, ‘The new wave of pilot-wave theory’, Phys. Today, Aug. 2015, 47

[7] G. ‘t Hooft, ‘Models on the boundary between classical and quantum mechanics’, Phil. Trans. R. Soc. **A 373**, 20140236 (2015)

[8] L. Vervoort, Comment on ‘Significant-Loophole-Free Test of Bell’s Theorem with Entangled Photons’, arXiv preprint, http://arxiv.org/abs/1602.01859 (2016)

I enjoyed reading this commentary article! It has a number of striking strengths.

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Indeed, and there is a very classical counterexample to the conclusions that the Bell test crowd want to draw. If a magnetic line of force could be modeled as a flux tube in a fluid, as James Clerk Maxwell argued in the 1861 paper in which he first presented his equations, and photons are perturbations of this flux tube, then they not only obey Maxwell’s equations but also are polarised, and where two of these perturbations are generated equal and opposite by the same process, remote measurements of the correlation of their polarisation will be exactly the same cos 2\phi that is predicted by quantum mechanics and observed in the Bell tests. See 1502.05926 for the details and here for more. This may not be the only possible model: see the liveblog of EMQM 2015 which is the specialist conference for this and where many such ideas are discussed.

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Indeed, Ross, I agree that these sub-quantum theories from which QM might emerge deserve full attention. Of course, my aim was just to elucidate how this is allowed in principle; it is widely believed that no local sub-quantum theory can be compatible with quantum mechanics. In my view the simplest way to understand this is by invoking a background medium; it seems to be the common denominator between all feasible (and therefore local) theories underlying QM. The second ingredient such theories need is sufficient correlation between far-apart subsystems, but that occurs in many systems, fluid-mechanical ones (e.g. the droplet systems investigated by Couder, Fort, Bush and others; or the vortices that you studied); spin-lattices; etc.

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