Time, Reality and Bell’s Theorem

Featured image: John Bell with a Schneekugel (snowing ball) made by Renate Bertlmann; in the Bells’ flat in Geneva, 1989. © Renate Bertlmann.

Lorentz Center workshop proposal, Leiden, 6–10 September 2021

As quantum computing and quantum information technology moves from a wild dream into engineering and possibly even mass production and consumer products, the foundational aspects of quantum mechanics are more and more hotly discussed. Whether or not various quantum technologies can fulfil their theoretical promise depends on the fact that quantum mechanical phenomena cannot be merely emergent phenomena, emerging from a more fundamental physical framework of a more classical nature. At least, that is what Bell’s theorem is usually understood to say: any underlying mathematical physical framework which is able, to a reasonable approximation, to reproduce the statistical predictions made by quantum mechanics, cannot be local and realist. These words have nowadays precise mathematical meanings, but they stand for the general world view of physicists like Einstein, and in fact they stand for the general world view of the educated public. Quantum physics is understood to be weird, and perhaps even beyond understanding. “Shut up and calculate”, say many physicists.

Since the 2015 “loophole-free” Bell experiments of Delft, Munich, Vienna and at NIST, one can say even more: laboratory reality cannot be explained by a classical-like underlying theory. Those experiments were essentially watertight, at least as far as experimentally enforceable conditions are concerned. (Of course, here is heated discussion and criticism, too).

Since then however it seems that even more energy than ever before is being put into serious mathematical physics which somehow gets around Bell’s theorem. A more careful formulation of the theorem is that the statistical predictions of quantum mechanics cannot be reproduced by a theory having three key properties: locality, realism, and no-conspiracy. What is meant by no-conspiracy? It means that experimenters are free to choose settings of their experimental devices, independently of the underlying properties of the physical systems which they are investigating. In the case of a Bell-type experiment, a laser aimed at a crystal which emanates a pair of photons which arrive at two distant polarising photodectors, ie detectors which can measure the polarisation of a photon in directions chosen freely by the experimenter. If the universe actually evolves in a completely deterministic manner, then everything that goes on in those labs (housing the source and the detectors and all the cables or whatever in between) was determined already at the time of the big bang, the photons can in principle “know in advance” how they are going to be measured.

At the present time, highly respectable physicists are working on building a classical-like model for these experiments using superdeterminism. Gerard ’t Hooft used to be a lonely voice arguing for such models but he is no longer quite so alone (cf. Tim Palmer, Oxford, UK). Other physicists are using a concept called retro-causality: the future influences the past. This leads to “interpretations of quantum mechanics” in which the probabilistic predictions of quantum mechanics, which seem to have a built in arrow of time, do follow from a time symmetric physics (cf. Jaroslav Duda, Krakow, Poland).

Yet other physicists dismiss “realism” altogether. The wave function is the reality, the branching of many possible outcomes when quantum systems interact with macroscopic systems is an illusion. The Many Worlds Interpretation is still very alive. Then there is QBism, where the “B” probably was meant to stand for Bayesian (subjectivist) probability, in which one goes to an almost solipsistic view of physics; the only task of physics is to tell an agent what are the probabilities of what the agent is going to experience in the future; the agent is rational and uses the laws of quantum mechanics and standard Bayesian probability (the only rational way to express uncertainty or degrees of belief, according to this school) to update probabilities as new information is obtained. So there only is information. Information about what? This never needs to be decided.

To the right, interference patterns of waves of future quantum possibilities. To the left, the frozen actually materialised past. At the boundary, the waves break, and briefly shining fluorescent dots of light on the beach represent the consciousness of sentient beings. Take your seat and enjoy. Artist: A.C. Gill
On the right, interference patterns of waves of future quantum possibilities. On the left, the frozen actually materialised past. At the boundary, the waves break, and briefly shining fluorescent dots of light on the beach represent the consciousness of sentient beings. Take your seat and enjoy. Artist: A.C. Gill

Yet another serious escape route from Bell is to suppose that mathematics is wrong. This route is not taken seriously by many, though at the moment, Nicolas Gisin (Geneva), an outstanding experimentalist and theoretician, is exploring the possibility that an intuitionistic approach to the real numbers could actually be the right way to set up the physics of time. Klaas Landsman (Nijmegen) seems to be following a similar hunch.

Finally, many physicists do take “non-locality” as the serious way to go; and explore, with fascinating new experiments (a few years ago in China, Anton Zeilinger and Jian-Wei Pan; this year Donadi e al.), hypotheses concerning the idea that gravity itself leads to non-linearity in the basic equations of quantum mechanics, leading to the “collapse of the wave function”, by a definitely non-local process.

At the same time, public interest in quantum mechanics is bigger than ever, and non-academic physicists are doing original and interesting work, “outside of the mainstream”. Independent researchers can and do challenge orthodoxy, and it is good that someone is doing that. There is a feeling that the mainstream has reached an impasse. In our opinion, the outreach from academia to the public has also to some extent failed. Again and again, science supplements publish articles about amazing new experiments, showing ever more weird aspects of quantum mechanics, but it is often clear that the university publicity department and the science journalists involved did not understand a thing, and the newspaper articles are extraordinarily misleading if not palpably nonsense.

In the Netherlands there has long been a powerful interest in foundational aspects of quantum mechanics and also, of course, in the most daring experimental aspects. The Delft experiment of 2015 was already mentioned. At CWI, Amsterdam, there is an outstanding group led by Harry Buhrman in quantum computation; Delft has a large group of outstanding experimentalists and theoreticians, in many other universities there are small groups and also outstanding individuals. In particular one must mention Klaas Landsman and Hans Maassen in Nijmegen; and one must mention the groups working in the foundations of physics in Utrecht and in Rotterdam (Fred Muller). Earlier we had of course Gerard ’t Hooft, Dennis Dieks and Jos Uffinck in Utrecht; some of them retired but still active, others moved abroad. A new generation is picking up the baton.

The workshop will therefore bring a heterogeneous group of scientists together, many of whom disagree fundamentally on basic issues in physics. Is it an illusion to say that we can ever understand physical reality? All we can do is come up with sophisticated mathematics which amazingly gives the right answer. Yet there are conferences and Internet seminars where these disagreements are fought out, amicably, again and again. It seems that perhaps some of the disagreements are disagreements coming from different subcultures in physics, very different uses of the same words. It is certainly clear that many of those working on how to get around Bell’s theorem, actually have a picture of that theorem belonging to its early days. Our understanding has enormously developed over the decennia, and the latest experimentalists have perhaps a different theorem in mind, to the general picture held by theoretical physicists who come from relativity theory. Indubitably, the reverse is also true. We are certain that the meeting we want to organise will enable people from diverse backgrounds to understand one another more deeply and possibly “agree to differ” if the difference is a matter of taste; if however the difference has observable physical consequences then we must be able to figure out how to observe them.

The other aim of the workshop is to find better ways to communicate quantum mysteries to the public. A physical theory which basically overthrows our prior conceptions of time, space and reality, must impact culture, art, literature; it must become part of present day life; just as earlier scientific revolutions did. Copernicus, Galileo, Descartes, Newton taught us that the universe evolves in a deterministic (even if chaotic) way. Schrödinger, Bohr and all the rest told us this was not the case. The quantum nature of the universe certainly did impact popular culture but somehow it did not really impact the way that most physicists and engineers think about the world.

Illustration from Wikipedia, article on Bell’s Theorem. The best possible local realist imitation (red) for the quantum correlation of two spins in the singlet state (blue), insisting on perfect anti-correlation at 0°, perfect correlation at 180°. Many other possibilities exist for the classical correlation subject to these side conditions, but all are characterized by sharp peaks (and valleys) at 0°, 180°, and 360°, and none has more extreme values (±0.5) at 45°, 135°, 225°, and 315°. These values are marked by stars in the graph, and are the values measured in a standard Bell-CHSH type experiment: QM allows ±1/√2 = ±0.7071…, local realism predicts ±0.5 or less.

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