I've completed a full year QM course (undergraduate level) and I am left confused on where to draw the line between quantum mechanics theory and its interpretation(s). I would personally like to stick to no interpretation at all, but since I do not know what is interpretation and what isn't, it is extremely hard to stick to this rule. Many introductory books do not mention if they use a particular interpretation at all, and I suspect they do use some interpretation(s) here and there, without any warning nor notice.
From what I have read on the Internet, the "collapse" or "reduction" of the wave function, is part of interpretations of QM. Not all interpretations assume there is even such a thing as a collapse of $\Psi$. Good, that's an easy one.
But what about what $\Psi$ represents for example? I've commonly read that its modulus squared represents the probability density of finding the particle(s) at a particular position(s) and time(s). But does such a description already assume an interpretation?
What about the QM postulates? Is there any interpretation hidden in one or more of these postulates?
I've read several Lubos Motl's posts (here on PSE and on his own blog) and to him (and apparently many others such as John Rennie and Zurek), $\Psi$ is entirely subjective and two observers of the same quantum system need not to use the same $\Psi$ to describe the system. But no mention of any interpretation is ever done. I suspect they use some interpretation to make such claims, but I couldn't get the information from skimming through many books (including one by Zurek called "Quantum theory and Measurement" which is a package of many QM papers and one such paper by London around page 250 seemed to agree with the Motl's description).
I have heard of the "Shut up and calculate!" approach, but I have read on Wikipedia that it's associated to the Copenhagen interpretation. Is that really so?
I have read from the member alephzero that QM works perfectly well without any interpretation. Quoting him:
"Wave function collapse" is not part of QM. It is only part of some
interpretations of QM (in particular, the Copenhagen interpretation).
The fact that this interpretation is used in a lot of pop-science
writing about QM doesn't make it an essential part of QM – to quote
David Mermin, "just shut up and calculate!" Note: AFAIK there is no
so-called "standard interpretation" of QM – it works perfectly well as
a theory of physics with no "interpretation" at all.
My question is, how on Earth do we draw the line between QM theory and its interpretations? The books seem completely blurry in that aspect and almost any other sources I could find too.
Best Answer
Interpretation is whatever people don't have to agree on to have the same accurate predictions about the observable.
Classical mechanics is empirically wrong in ways quantum mechanics isn't. For example, only quantum mechanics predicts discrete energies for atomic electrons, and discrete changes in these energies from the absorption and emission of radiation. How do you get these energies? Empirically, you measure them; theoretically, you reduce it to a calculus problem. These agree; there's no "interpretation" at work there.
Meanwhile, there are experiments you can do that vary in their results from time to time, and the frequencies of the results are, again, available both empirically and theoretically. The latter comes from the same calculus apparatus. What's that? You have a formula for something called $\psi$, whose square modulus gets us the answers we want? Great, our theory is predictive (insofar as anything probabilistic deserves that label.)
But what's this $\psi$ that crops up in both of those exercises? Well, it's not a thing classical mechanics makes claims about, or experiments detect; so whatever answer you give to that question, it amounts to an interpretation of quantum mechanics. Oh, you need $\psi$ or some alternative to get the predictions, and the predictions are right; no-one disputes either of those statements. But when you ask what these items "are", or "what they do unobserved", that's interpretation.
Get 20 QM experts in the room, each of them subscribing to a different interpretation. They'll all make the same predictions about experiments' observable outcomes. And if, in an experiment that leaves an electron's position unmeasured, one of these experts says the electron is "somewhere specific we don't know", and another says the electron is "everywhere at once", and another that it "doesn't have a location", they've found something they disagree on. It's just not an observable thing.
This doesn't mean interpretation is bunkum, or interpretations are wrong, or you shouldn't think about interpretations. (Fun fact: philosophy of physics is not limited to awkward questions about quantum mechanics.) But since your question is about where the line exists between interpretations and the rest of a QM textbook's contents, well... see the bold sentence up top.
Trust me, I understand the urge to put as little philosophy into things as possible. I do, I love me some number-crunching. But that should cut both ways, i.e. you don't want too many philosophical opinions about how little philosophy physicists should be doing either. For example, "shut up and calculate" doesn't have to mean "don't have an interpretation"; to me it means, "it's 9 am and we're predicting experimental outcomes; you can wonder what's going on 'behind the scenes' when we're at the bar". (Or vice versa!)
"Philosophy" isn't necessarily worse than "physics". It's just you can discern which is which from the fact that we know better how to get everyone on the same page for some questions than for others. Maybe that's not a bad thing. You don't have to agree the lack of an interpretative consensus is "embarrassing", but it's worth knowing that consensus is lacking.