I have only touched on the options people consider seriously for avoiding unpleasant consequences or conclusions of nonlocal correlations. An option that treats the mist as a physically real medium (with all the requisite weird properties necessary) is Bohm-de Broglie theory, Wikipedia has a decent exposition at De_Broglie–Bohm_theory.
If you start reading around this area there is a lot of confusion. For instance, people often conflate or equate the Einstein-Podolsky-Rosen paradox with Bell’s theorem. EPR’s paradox is about incompleteness, addressed in Part III, but it is more poorly explained than Einstein did on his own in other places. In fact all aspects of the EPR paradox can be reproduced in a local theory (as pointed out originally by Bell) and so it is distinct from Bell’s considerations. Because the EPR paper itself mashed up incompleteness with Heisenberg’s uncertainty principle, in Part III, I have chosen to use the much clearer argument for incompleteness Einstein gave in a letter (EA 47-22 at the Einstein archives) to Schroedinger.
Part III
More precise distinctions between types of explanations for the quantum state are elucidated by Harrigan and Spekkens at arxiv.org/abs/0706.2661. To read more on models with dynamical collapse, find the Stanford Encyclopedia of Philosophy’s (plato.stanford.edu) article qm-collapse. To read more on many-universe (non-collapse) explanations try their article qm-manyworlds or Wallace’s book, The Emergent Multiverse. The multiverse/many-worlds view is an example of taking the mist to be real, and taking it to be the only real state (the “first option” discussed in the text). An example where the mist is taken as real but there are other physical properties in the real states as well (the “second option”) is Bohm-de Broglie theory mentioned above.
If you want to read excerpts from the letter EA 47-22 to Schroedinger where Einstein made his argument most clearly (along with some musings on how Einstein or Schroedinger could have discovered Bell’s theorem) then try arxiv.org/abs/1411.4387. Gilder’s lovely book The Age of Entanglement seems to get the conceptual history mostly right, as do any of the papers by Howard (www3.nd.edu/~dhoward1/) upon which it is partly based.
Einstein also sometimes gave an argument along the lines that since a misty state of [W,B] sometimes looks like the “observably real” state W and sometimes like the “observably real” state B when we look at the ball, there is clearly more than one real state for a misty (i.e. quantum) state. This is an argument for the “second option” for taking the mist to be real, discussed in the text, namely that many different real states corresponding to a single misty state. It is a different form of “incompleteness”, and confusion with Bell’s theorem and the EPR paradox and Einstein’s letter to Schroedinger is rife.
Such a type of incompleteness would not alleviate us from all the “unphysical” properties of the real states when we take the mist to be real, for example that a measurement on one ball of the mist [WWWW,BBBB] in one location can change the purported real state of the world at arbitrarily distant locations. In the text I have focused on the stronger argument Einstein gave as to why misty and real states were not in “one to one correspondence”, because it is very often misunderstood, and, for reasons discussed in the Harrigan and Spekkens paper mentioned above, would have been much stronger in terms of ruling out various “realist interpretations” of quantum theory, had it not been found suspect by Bell’s discovery of nonlocality. Reading any of the writings of Fine, such as The Shaky Game, is a way of getting into this somewhat confusing topic.
In modern papers you will often read about “ontic states” (what I called real states) and the distinction between “the mist (quantum state) is real” versus “the mist (quantum state) is just knowledge/information about the real state” referred to as “psi-ontic” and “psi-epistemic” respectively.
Approaches to (and arguments for) understanding quantum states as epistemic can be found in Ballentine’s textbook Quantum Mechanics: A Modern Development, in Spekkens’ classic paper arxiv.org/abs/quant-ph/0401052, in Brukner and Zeilinger’s discussion arxiv.org/abs/quant-ph/0212084, and in any of the many papers on QBism by Fuchs and collaborators, for example arxiv.org/abs/1412.4211. QBism is an example of an approach that denies a connection between real states/physical properties and how we use the mist to explain our experiences and interactions with the world. There are also many great links and references in the article qt-issues at the Stanford Encyclopedia of Philosophy.
The “Pooh-Bear” argument is from arxiv.org/abs/1111.3328, but Leifer’s blog post can-the-quantum-state-be-interpreted-statistically is a good place to start if you want a clearer explanation. The very last sentence Pooh says to Einstein is direct quotation from Winnie-the-Pooh by A. A. Milne. The rest I made up.
Acknowledgements
My deep appreciation to Andrew Simmons, Naomi Nickerson and Jan Hazla for so many useful comments on very rough drafts, to Louisa Gilder for excellent, thoughtful micro- and macro-scopic editing, to Nic Harrigan for both technical help and encouragement (well, badgering) to engage in science communication and Ivan and Brenda Rudolph for proof-reading, great discussions, and life, all of which helped greatly in making this book possible.
Q is for Quantum Page 12