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 [167]: 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.

A probability isn't the 'real' world either, it's a second hand calculation entirely instigated by humans (no probability ever naturally occurred without someone to perform it) and hopefully based on relatively accurate measurements taken in the real world. Much like an average, it's still a mathematical fiction that uses one system of abstraction to mimic actual physical properties of an entirely different kind of system. The problem with this mimicry is that it is always diverging from reality unless you constantly tinker with it outside of the algorithm itself, much like the idea of God intervening to dictate the fall of every sparrow, the human must intervene for the math to even remotely resemble the reality it is supposed to model.

ReplyDeleteEpistemologically, the universe is not made of decimal numbers, much less reiterative calculations based on those same numbers. If a decimal number is involved, it can at best be 'approximately about' the measurements of something it is being compared to, not the something itself.

Interesting paper. Hadn't read it before. (Even now, just looked at the first few pages.)

ReplyDeleteWallace says:

> ``It is through the Born rule --- and only through the Born rule --- that the formalism is connected to experiment and observation.''

Well, not quite.

Before you can apply the Born rule, you have to prescribe (and usually, also evolve in time) the ket for the state of the system. Prescribing the ket --- the QMcal modelling of the IC of the system using the QMcal formalism --- is a necessary part of using QM; Born's rule can't be applied otherwise. All other postulates of the formalism, therefore, also come into the picture.

In other words, the formalism gets connected to experiment and observation also via translating the initial (physically existing) state of the system into the initial ket of the formalism.

There is some art involved in correctly modelling the initially existing state as the initial ket of the QM formalism, just the way it is in pre-QMcal theories too. It involves questions like: what kind of assumptions are to be made about the (a) domain (finite? infinite? homogeneous? isotropic? etc.); (b) boundary conditions (field condition? flux (or first time-derivative) condition? mixed condition? periodic? absorbing? reflecting? partially reflecting? how about time-dependent changes in them? etc.); (c) the ``shape'' of the wavefunction (because, in connecting to reality, position representation necessarily kicks in); etc.

In fact, in QMcal modelling, in addition, you have to also prescribe certain aspects pertaining to the *final* condition: the quantities to be measured, the kind of detectors and their configuration (e.g. position), etc.

[Another point, in another comment below. Couldn't fit the two points in one comment]

Best,

--Ajit

Dear Roger,

ReplyDelete> ``I am coming around to the view that there are really just two interpretations: QM with and without the probabilities.''

Ummm... Yes, this distinction is useful, in a way, but not *very* useful. See, Stat. Mech. has the combination of probabilities *and* deterministic state evolution too, but it doesn't suffer from the measurement problem. (This is a point that Wallace too touches on, at least indirectly, within the first few pages which I read.)

IMO, more useful criteria might be these: (a) the presence or absence of hidden variables; (b) ontological soundness of the scheme; and (c) whether the measurement problem is acknowledged as a problem to solve or not.

There are many different theories all of which have hidden variables in some or the other form: Superdeterminism has its own kind of extra variables that in principle remain hidden; Bohmian Mechanics has its hidden potential (and people have argued that even their particle is a hidden variable, because Bohmians don't give any independent means to observe it nor any physics for precisely how the particle and ``wave'' or the potential ``guide'' it --- with what PDE for the detail of the *particle-wave* interaction); MWI has at least one *entire* world as hidden (and by implication, an infinity^infinity^infinity... number of them, where the exponentiation is to be conducted an infinity of times.)

The most basic problem with all the hidden variable theories is that they fail to even acknowledge that they need to provide that extra (independent) body of phenomenology which would justify the inclusion of their hidden variables into the QM theory (so as to solve the measurement problem). If they were to present such extra phenomenology, then, the variables could have been taken as actually existing, and hence proper, but remaining as hidden only within the narrower scope of the *QMcal* phenomenology. [As an example, just to illustrate this point: Electrical charge remained hidden in Newtonian and Continuum mechanics because roughly equal amounts of +ve and -ve charges come packed in the kind of objects which are studied in these kind of mechanics, and the packing is such that on the gross scale these bodies *are*, effectively, electrically neutral. But charge had to be included when the phenomenology underlying EM was brought into physics, which in turn led to relativity. Both EM and SR include NM as a special limiting case.] Hidden variable theories present no additional phenomenology which might suggest such hidden variable.

Ontological soundness is a general requirement, and MWI is at the most extreme end of violating it. (Refer to the infinite number of exponentiations referred to above.)

Copenhagen has neither hidden variables nor explicit ontology. And, it does not solve the measurement problem. It *also* does *not* reject the very existence of this problem as a problem. [The idea of outright rejecting the measurement problem as a proper problem to be solved, is of very recent origins.]

Best,

--Ajit

Wow!

ReplyDeleteThe change of the email ID makes such a huge difference to the hits at my blog?

Obviously, Roger, rich folks in your country believe in tracking email IDs than the objectivity of the replies at blogs such as yours.

Cheers, Roger, cheers! I don't get any replies at my own blog, so their objectivity cannot ever be in question, you know!

Best,

--Ajit

[PS: 1,057,036. That's the number of hits this blog by Roger had, when I posted this comment, at around 02:17 IST, 07/12/2023.]