# The Pusey, Barrett and Rudolph (PBR) theorem and "shut up and calculate"

I was looking around for a competent, recent, persuasive presentation of the "shut up and calculate" philosophy regarding interpretations of quantum mechanics, and google led me to Fuchs and Peres, "Quantum Theory Needs No 'Interpretation,'" Physics Today, March 2000. Although the article is paywalled, you can find PDFs online. They talk about interpreting quantum mechanics simply in terms of the information available to observers, and Copenhagen-style collapse as nothing more than updating one's estimates of probability based on new information.

But there is a 2011 paper by Pusey, Barrett and Rudolph (PBR), "On the reality of the quantum state," presenting what seems to be a no-go theorem for such interpretations.

Is it accurate to think of PBR as conflicting with Fuchs and Peres' particular brand of "shut up and calculate?" Are there other expositions of this approach that avoid all the Bayesian-sounding stuff, or that are recent enough to explicitly discuss PBR? It would be particularly helpful to have something that wasn't paywalled.

• Much as I'd like to know what modern psi-epistemic/non-realist interpretations look like, I find the piece you linked to be of little use. Fuchs and Peres are extremely non-committal on whether there is an underlying reality for the wavefunction's information to describe (so I'd counter that the piece doesn't really describe a particular brand of anything, really). To the degree that they do, they are indeed in territory ruled out by PBR, I should think; to the degree that they don't, they just describe an operationalist, non-realist model that's wholly outside the PBR framework. Jan 1, 2018 at 21:46
• I'm interested in see a really good article on the matter, too, but ... I've never really felt the need to go beyond 'well, applying these rules leads to correct predictions and all the attempts to "interpret" them have lead either to mistakes or impenetrable philosophical gobbledygook'. As a result I am in the habit of telling students that quantum foundations is a subject to take up after you have tenure. Jan 1, 2018 at 22:24
• @dmckee: I think it's fine if people don't worry about foundational issues, provided that they know what it is that they don't know. But many, many people seem to absorb some kind of half-baked version of the Copenhagen interpretation without realizing that it's an interpretation. E.g., if you ask, they will insist that there really is some physical process of wavefunction collapse, and quote a textbook to the effect that this belief is "standard." It would be nice to have a "shut up and calculate" philosophy that was actually well thought out, but I just haven't seen such a thing yet.
– user4552
Jan 1, 2018 at 23:01
• Not what the OP is asking for, actually rather the opposite, a quite enjoyable demolition of the "shut up and calculate" paradigm: arxiv.org/abs/1308.5619 Jan 1, 2018 at 23:05
• Closely related: physics.stackexchange.com/a/17186/3811 Jan 2, 2018 at 1:23

Frankly, I don't think "shut up and calculate" gets ruled out by PBR, simply because "shut up and calculate" isn't a (single) interpretation, at least in the sense of PBR.

The Fuchs and Peres piece you linked to is a good example of why I say this, but it's far from alone in that ground. The core problem is that "shut up and calculate" (SU&C) does not actually specify whether one should take some form of ontological viewpoint on the subject matter of quantum mechanics and, if so, which one. There are multiple choices there, several of which might be compatible with viewpoints that can be loosely grouped under SU&C; PBR rules out some of them, and it is entirely silent on others.

On the whole, though, I don't really think that the "shut up and calculate" school of thought is really an interpretation at all: quite on the contrary, the spirit it encapsulates is one that explicitly rejects the need for physics to even postulate an ontology for its subject matter. Is the act of actively not-even-trying-to-interpret and interpretation? That's ultimately semantics, but if you do call that an interpretation then I'll just agree to disagree (while quietly seething in a corner about the liberties some people take with language).

On somewhat more concrete grounds, though, if you try to formalize the strict dictum to leave ontology well alone, I would argue that what you get is an operationalist interpretation of quantum mechanics. The best exposition I know of is this talk by Rob Spekkens (starting at around the 51:20 mark, and continued here; Spekkens was aware of PBR at the time, and he gives a more direct response here), but the essence revolves around this mostly-uncontroversial statement about quantum mechanics:

In QM, (i) each preparation procedure $\mathsf P$ is associated with some density matrix $\hat \rho$, (ii) each outcome $m$ of some measurement procedure $\mathsf M$ is associated with a projection operator $\hat \Pi$, such that (iii) the probability of getting outcome $m$ through the measurement procedure $\mathsf M$ after the system has been prepared according to $\mathsf P$ is $P(m|\mathsf P,\mathsf M) = \mathrm{Tr}(\hat \rho\hat\Pi)$.

Most interpretations will then go on and invest the various elements with some form of ontology, but the operationalist approach will stop right at this statement, and hold that there is nothing else to say about the system, including such things as whether there is in fact some system that's produced by $\mathsf P$, and whether it has any properties at all.

If this is what you mean by SU&C, then PBR is completely silent on it. The PBR framework requires an ontological model to work, and the operationalist approach doesn't give it one.

Now, while it's a plausible philosophy to class under that banner, I don't really think that this is what's really meant by SU&C (again, even explicitly refraining from imbuing the mathematical components with any reality is already a good deal more waffling than what I associate with the SU part of SU&C), and indeed e.g. the Fuchs and Peres piece you link to does a great job at playing both sides of that boundary: they start off claiming that there is no need to provide anything beyond "an algorithm for computing probabilities", but then they go on to speak of Cathy's experiment like it actually "exists", and they do that in models that are quite $\psi$-epistemic in ways that are indeed liable to getting ruled out by PBR. However, I don't think that piece is specific enough with its models to tell what it's actually postulating, and by extension it's not specific enough to tell whether PBR impacts its conclusions.

What I think you really wanted to know, though, is not the relationship between PBR and "shut up and calculate", but its relationship to so-called $\psi$-epistemic interpretations: these are realist models that assume the existence of some form of system with some form of properties, which get described by the wavefunction in a strictly 'statistical' way.

If that's what you really wanted to ask, then I personally don't really know ─ but really, when people insist on things like "PBR doesn't rule out any statistical interpretations that are under active consideration", like Steve Byrnes and Ron Maimon (kind of) do here, I really have no idea what kinds of statistical interpretations they do think are worth considering, and I'd quite like to know what they are and how they interface with PBR.

However, if that's what you really wanted to ask, then I would definitely raise a pretty strong objection to the identification of statistical interpretations with the SU&C paradigm ─ which, again, isn't an interpretation.

"Shut up and calculate" (SUAC) is a philosophical doctrine and so can't be refuted by any experiment. SUAC holds that it doesn't matter what's happening in reality as long as you can predict experimental results. Advocates of SUAC would say that they can predict the results of the PBR experiment so it is irrelevant to SUAC.

SUAC is a special case of philosophical doctrine of instrumentalism applied to quantum mechanics. Instrumentalism is the idea that it doesn't matter what's happening in reality as long as you can make predictions. Instrumentalism was refuted more than 50 years ago by Popper (see his book "Conjectures and Refutations" Chapter 3) and has been criticised more recently by David Deutsch in "The Fabric of Reality" and "The Beginning of Infinity".

One problem is that you have to understand what's happening in reality to perform an experiment and understand its significance. If quantum mechanics isn't true, then it's a bit of a mystery why you would use it to make predictions.

Another problem is that if you use quantum mechanics to predict the result of experiment and then deny it represents reality, then all you have done is taken quantum mechanics and added an extra complication: a bunch of labels saying "this isn't real" about the wavefunction. This makes quantum mechanics more complicated and obscure and solves no scientific or philosophical problems.

SUAC has no scientific or philosophical value at all and should be discarded.

• Advocates of SUAC would say that they can predict the results of the PBR experiment so it is irrelevant to SUAC. There is no PBR experiment. There is a PBR paper, which presents a theorem...?
– user4552
Jan 3, 2018 at 17:17
• The theorem is about experimental predictions. This is a direct quote: "Here we present a no-go theorem: if the quantum state merely represents information about the real physical state of a system, then experimental predictions are obtained which contradict those of quantum theory." Jan 3, 2018 at 17:20