## Quantum Madness

A very busy day lies in store so I only have time for a quick morning visit to the blog. If you enjoyed the recent guest post on the “hidden variables” interpretation of Quantum Mechanics, then you will probably enjoy reading a paper that recently appeared on the arXiv with the abstract:

Motivated by some recent news, a journalist asks a group of physicists: “What’s the meaning of the violation of Bell’s inequality?” One physicist answers: “It means that non-locality is an established fact”. Another says: “There is no non-locality; the message is that measurement outcomes are irreducibly random”. A third one says: “It cannot be answered simply on purely physical grounds, the answer requires an act of metaphysical judgement”. Puzzled by the answers, the journalist keeps asking questions about quantum theory: “What is teleported in quantum teleportation?” “How does a quantum computer really work?” Shockingly, for each of these questions, the journalist obtains a variety of answers which, in many cases, are mutually exclusive. At the end of the day, the journalist asks: “How do you plan to make progress if, after 90 years of quantum theory, you still don’t know what it means? How can you possibly identify the physical principles of quantum theory or expand quantum theory into gravity if you don’t agree on what quantum theory is about?” Here we argue that it is becoming urgent to solve this too long lasting problem. For that, we point out that the interpretations of quantum theory are, essentially, of two types and that these two types are so radically different that there must be experiments that, when analyzed outside the framework of quantum theory, lead to different empirically testable predictions. Arguably, even if these experiments do not end the discussion, they will add new elements to the list of strange properties that some interpretations must have, therefore they will indirectly support those interpretations that do not need to have all these strange properties.

You can download a PDF of the full paper here. It’s a short piece, but with a very good list of references for further reading.

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January 21, 2021 at 8:17 pm

There have been many posts on this wonderful blog about quantum theory, but this seemed like one of the more recent ones.

For anybody interested in this area I would very much advise reading up on the more recent no-go theorems. Most expositions on the subject of Quantum Foundations only mention Bell’s theorem or possibly the Kochen-Specker. So they are essentially stuck in the 1960s. Even moderately stronger results like the Legget (note: Not Leggett-Garg) inequalities from the 80s are very rarely discussed.

Modern no-go theorems are very powerful and remove essentially any realistic chance for there to be a hidden variable account beneath the non-commutative probability theory of QM.

I would start with:

1. Non-signaling deterministic models for non-local correlations have to be uncomputable Phys. Rev. Lett. 118, 130401 (2017)

2. Causation does not explain contextuality, Quantum 2, 63 (2018). Which also is nicely explained in: Evans, Peter W (2020) The End of a Classical Ontology for Quantum Mechanics? Entropy, 23 (1). p. 12.

3. No extension of quantum theory can have improved predictive power. Colbeck, R., Renner, R. No extension of quantum theory can have improved predictive power. Nat Commun 2, 411 (2011)

Basically they show the hidden variable theory would:

1. Have to be uncomputable, in a sense its dynamics would involve Gödelian undecidable sentences.

2. Playing around with causation does not get you out of this

3. Regardless the Hidden Variable theories are not scientifically usable. This is an older result.

So essentially one is stuck with a model for the statistics of observation, there doesn’t seem to be a model for observation independent properties. In the spirit of this blog one can only model the epistemic situation. There’s no valid ontic model possible.