This is a general introduction to and review of the philosophy of quantum mechanics, aimed at readers with a physics background and assuming no prior exposure to philosophy. It is a draft version of an article to appear in the Oxford Research Encyclopedia of Physics.He summarizes the interpretations, and concludes:
Among physicists, the (more operationalist versions of the) probability-based approach, and the Everett interpretation, are roughly as popular as one another, with different sub-communities having different preferences. (The modificatory strategies are much less popular among physicists, although they are probably the most common choice among philosophers of physics.) But more popular than either is the ‘shut-up-and-calculate’ approach : the view that we should not worry about these issues and should get on with applying quantum mechanics to concrete problems.There is some overlap here. The theory described in textbooks could be called probability-based, or shut up and calculate.
In its place, there is much to be said for ‘shut up and calculate’. Not everyone needs to be interested in the interpretation of quantum mechanics; insofar as a physicist working on, say, solar neutrinos or superfluidity can apply the quantum formalism without caring about its interpretation, they should go right ahead — just as a biochemist may be able to ignore quantum mechanics entirely, or a behavioral ecologist may be able to ignore biochemistry.
Wallace has sympathies to Everett many-worlds, but admits:
More productive criticisms4 of the Everett interpretation have mostly fallen into two classes, known collectively as the ‘preferred basis problem’ and the ‘probability problem’. ...I am coming around to the view that there are really just two interpretations: QM with and without the probabilities. With the probabilities, you can make predictions and do experiments. Without, you get many-worlds, and a lot of philosophers and physicists love it, but I don't see what it has to do with the real world.
It is fairly widely accepted that decoherence provides a solution to the preferred-basis problem. ...
The probability problem remains largely intact when decoherence is considered, and has been the main locus of controversy about the Everett in- terpretation in 21st-century discussions.