Tuesday 26 March 2019

Quantum Theory Confirmed Again


Last week, Justin Weinberg asked me and some other people whether we’d be willing to contribute to a group blog post commenting on a paper [1] that had been making the rounds on social media.  You can find our responses over at Daily Nous.

Justin asked that our contributions be relatively short, to get the discussion going.  So, of course, what I did was write a short piece, realize that it was about twice the length that Justin had asked for, and then applied surgery.  Here’s my full piece, which I’ve added to since then, explaining in a bit more detail what the de Broglie-Bohm theory says about the Wigner-Brukner thought experiment.

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Headline news!  Stop the presses!  A group of experimenters did an experiment, and the results came out exactly the way that our best physical theory of such things says it should, just as everyone expected. Quantum Theory Confirmed Again.

That’s what actually happened, though you’d never know it from the clickbait headline: A quantum experiment suggests there’s no such thing as objective reality [1].

The experiment [2] was inspired by a recent paper by Časlav Brukner, entitled “A No-Go Theorem for Observer-Independent Facts” [3]. The abstract of the paper reporting on the experiment proclaims, “This result lends considerable strength to interpretations of quantum theory already set in an observer-dependent framework and demands for revision of those which are not.”

Here’s a convenient feature of claims of this sort: when you see one, you can be sure, without even going through the details of the argument, that any conclusion to the effect that the predictions of quantum mechanics are incompatible with an objective, observer-independent reality, is simply and plainly false. That is because we have a theory that yields all of the predictions of standard quantum mechanics and coherently describes a single, observer-independent world.  This is the theory that was presented already in 1927 by Louis de Broglie, and was rediscovered in 1952 by David Bohm, and is either called the de Broglie-Bohm pilot wave theory, or Bohmian mechanics, depending on who you’re talking to.  You can be confident that, if you went through the details of a thought-experiment, then (provided that the thought-experiment is sufficiently well-specified), you would find that the de Broglie-Bohm theory gives a consistent, observer-independent, one-world account of the goings on in the experiment, an account that is in complete accord with standard quantum mechanics with regards to predictions of experimental outcomes.

The way that the de-Broglie Bohm theory achieves this is interesting. It is a theory on which the world consists of well-localized particles that obey a non-classical law of motion. There’s always a matter of fact about where things are, on this theory. It’s a deterministic theory, so, given initial conditions, the result of any experiment is determined. But what that result is can depend on what other experiments are performed at the same time; it’s what is called a contextual hidden-variables theory. Moreover, it’s a nonlocal theory: the result of an experiment will sometimes depend on what other experiments are performed at a distance.  This is no accident; Bell’s theorem (see [4]) shows that any theory of this sort has to be nonlocal.

There are other theories, known as dynamical collapse theories, which also yield accounts of a single, observer-independent reality.  These theories yield virtually the same predictions as standard quantum mechanics for all experiments that are currently feasible, but differ from the predictions of quantum mechanics for some experiments involving macroscopic objects.

Much of the confusion surrounding quantum mechanics, which leads smart people to say foolish things, stems from the fact that, in the usual textbook presentations, we are not presented with a coherent physical theory. Typical textbook presentations incorporate something that is called the “collapse postulate.”  This postulate tells you that, when an experiment is done, you dispense with the usual rule for evolving quantum states, and replace the quantum state by one corresponding to the actual outcome of the experiment (which, typically, could not have been predicted from the quantum state). This is call “quantum state collapse.” There is some ambiguity as to its status, which reflects ambiguity as to the status of quantum states. Sometimes collapse is taken to be a real physical process (which it would have to be, if a quantum state represents something physically real); sometimes, collapse is taken to involve mere updating of information (which would be appropriate if a quantum state represents nothing more than an agent’s knowledge about a system). Confusion arises if the two views of collapse are conflated.

If we want to apply the collapse postulate, we need guidance as to when to apply it, and when to use the usual quantum dynamics, and textbooks are inevitably vague on this. In practice, this vagueness tends not to matter much.  But a thought-experiment devised by Eugene Wigner [5] imagines a situation in which it does matter. Brukner’s thought-experiment is a combination of Wigner’s thought-experiment and tests of Bell inequalities.

In the variant of Wigner’s thought-experiment invoked by Brukner, a friend of Wigner’s, named Friend, who is locked in a hermetically sealed lab, does an experiment, with two possible results, which we will call up and down, on a particle that is prepared in a particular, known quantum state, chosen so that the two outcomes of the experiment have equal probability. Wigner considers the quantum state of the content of Friend’s lab. If the collapse postulate is applied at the end of Friend’s experiment, the quantum state of the lab should be the one corresponding to the result that Friend obtained,  up or down.  If, on the other hand, the no-collapse rules of quantum state evolution apply, the quantum state is a state that is represented as a sum of up and down states.

Fig. 1. Wigner's Friend thought-experiment. From [3].


Moreover, if Wigner has unlimited powers of manipulation and no qualms about doing violence to his friend, the question of whether the quantum state is collapsed when Friend does her experiment can be decided experimentally.  The easiest way to do this would probably be to precisely reverse the velocity of everything inside Friend’s lab and wait a while, so that the experiment is undone, removing any trace, in Friend’s memory, her lab equipment, and any system that might carry a record of the experimental result, of the outcome of the experiment. For the sake of argument suppose this could be done.  Then, if no collapse has occurred, this would restore the original state of the particle that Friend experimented upon, and we could then do an experiment to test for this state.  Label the results of this experiment yes or no.  If no collapse occurs when Friend does her experiment, the result will be yes with certainty, and, if Friend’s experiment collapses the state, the result will be yes with probability ½ and no with probability ½. A Wigner with the powers we are imagining him to have could do the experiment repeatedly, and so determine whether or not Friend’s experiment collapses the quantum state.

What do the two observer-independent theories we have mentioned would say about this thought experiment? The de Broglie-Bohm theory says that the quantum state always obeys the usual, no-collapse law of evolution. However, the quantum state isn’t an exhaustive description of physical reality; at the end of Friend’s experiment, there is an objective matter of fact about which result she obtained. Wigner can verify that the quantum state has not collapsed, but only at the expense of erasing Friend’s memory and any other trace of the outcome. None of this is an ad hoc adjustment of the theory to handle cases like this, it’s what the theory, as we have it, tells us about this case.
A collapse theory would also say that Friend has obtained a definite result. But, on a theory like that, when Wigner does his experiment to determine whether the quantum state has collapsed, he would find that it has.

Obviously, Proietti et al. have not achieved a full-blown realization of the Wigner-Brukner thought-experiment. The equivalent of the Friend, in their experiment, is a single photon. The set-up of their experiment, unlike that of the full-blown Wigner’s Friend thought-experiment, is one in which collapse theories predict no collapse.

Puzzlement about the Wigner thought-experiment stems from the conjunction of (1) an assumption that, if the quantum state hasn’t collapsed, there’s no matter of fact about what the result of Friend’s experiment is (false on the de Broglie-Bohm theory) and (2) an assumption that Wigner will find that the state has not collapsed (false on a collapse theory).  Any theory according to which there is an objective, observer-independent world must violate one of these assumptions.

Brukner’s version of the thought-experiment involves a pair of hermetically sealed labs, each containing an observer playing the role of Wigner’s friend, and an observer outside each of these labs.  The external observers, named, Alice and Bob, each have a choice of two experiments that they can perform on the contents of the two labs (which, of course, include the internal observer,  who are named Charlie and Debbie).  The possible experiments of Alice (carried out on Charlie’s lab) are labelled A1 and A2, and the possible experiments of Bob (carried out on Debbie’s lab) are B1 and B2. The experiments A1, B1 are chosen so that they amount to asking Charlie and Debbie what they saw.  The experiments A2, B2 are chosen to be equivalent to the sort of experiment that Wigner is imagined to do, in the Wigner’s friend thought experiment.

Fig. 2. Brukner's thought-experiment. From [3].

Charlie and Debbie perform their experiments on a pair of particles prepared in a quantum state that is chosen so that (on the assumption that the usual rule of quantum evolution applies to their experiments, and there’s no collapse), the predicted quantum statistics for Alice and Bob’s experiment violate a Bell inequality. This has the consequence, via a theorem due to Arthur Fine [6], that we can’t think of these statistics as arising from a probability distribution over definite values of A1, A2, B1, B2, that are merely revealed upon measurement.

What does the de Broglie-Bohm theory say about this experiment?  First, that Charlie and Debbie will observe definite outcomes, and that Alice and Bob can learn these outcomes by performing experiments A1 and B1.  Second, if an A2 experiment is performed on Charlie’s lab, all trace of Charlie’s result will be erased, and if a B2 experiment is performed on Debbie’s lab, all trace of her result will be erased. 

The quantum state used in the experiment predicts correlations between the outcomes of the experiments, and the de Broglie-Bohm theory will get these right.  If A1 B1 experiments are performed in a repeated series of tests, Bob’s result will be correlated with Alice’s result, and hence with Charlie’s result, which is reflected in Alice’s.  If A1 B2 experiments are performed, again, Bob’s result will be correlated with Alice’s, and hence also with Charlie’s.  If A2 B1 experiments are performed, Alice’s result will be correlated with Bob’s, and hence also with Debbie’s.  It’s at this point that it looks like there’s a conflict with quantum mechanics.  If A2 B2 experiments are performed, the de Broglie-Bohm theory predicts that the results are correlated, just the way quantum mechanics says that they should be.  You might be tempted to conclude that, in this case, Alice’s result is still correlated with Debbie’s, and Bob’s with Charlie’s, on the (reasonable-seeming) assumption that Alice’s result is still the same as it would have been if Bob had done the B1 experiment, and Bob’s result is the same as it would have been if Alice had done the A1 experiment.

But (as I already mentioned) this can’t be done: there’s no way to maintain all four of the pairwise correlations:

1. The correlation between the results obtained by Charles and Debbie.
2. The correlation between the results of Alice’s A2-experiment and Bob’s B2-experiment.
3. The correlation between the result of Alice’s A2-experiment and Debbie’s result, which we would have found if Bob had done a B1-experiment.
4. The correlation between the result of Bob’s B2-experiment and Charlie’s result, which we would have found if Alice had done an A1-experiment.

For the cases in which Alice does an A2-experiment and Bob does a B2-experiment, the de Broglie-Bohm theory is obliged to respect the quantum correlations in (2).  Since Charlie and Debbie actually do their experiments, and obtain results (and, in principle, could have compared them if Alice and Bob had not intervened), the theory also respects the quantum correlations in (1).  It predicts that, in the cases in which Alice does an A2-experiment and Bob does a B2-experiment, at least one of the correlations (3) and (4), represented by blue lines in Figure 3, will be broken. Exactly how will depend crucially on the details of how the experiments are done (for example: if Alice does her experiment first, and then Bob, Alice’s results will still be correlated with Debbie’s, but Bob’s resuls won't be correlated with Charlie’s).

Figure 3. In the cases in which A2 and B2 experiments are done, the de Broglie-Bohm theory yields the quantum correlations between Charlie’s and Debbie’s results, and between Alice’s and Bob’s, at the expense of the correlations indicated by the blue lines. 

Could we check to see whether, in this case, the correlations (3) and (4) are maintained? No, because, as we’ve emphasized, Alice’s A2-experiment requires erasing all trace of Charlie’s result, and Bob’s B2-experiment requires erasing all trace of Debbie’s result.  The de Broglie-Bohm theory promises only to recover quantum probabilistic predictions for all records of experimental results that exist at a given time.  And it does that.

References
  
[1] “A quantum experiment suggests there’s no such thing as objective reality.MIT Technology Review, March 12, 2019.

[2] Proietti, Massimo, et al. , “Experimental rejection of observer-independence in the quantum world.” arXiv:1902.05080v1 [quant-ph].

[3] Brukner, Časlav , “A No-Go Theorem for Observer-Independent Facts,” Entropy 20 (2018), 350.

[4] Myrvold, Wayne, Marco Genovese, Marco and Abner Shimony, “Bell’s Theorem.” The Stanford Encyclopedia of Philosophy (Spring 2019 Edition), Edward N. Zalta (ed.).

[5] Wigner, Eugene, “Remarks on the mind-body question,” in The Scientist Speculates, I. J. Good (ed.).   London, Heinemann, 1961: 284–302.

[6] Arthur Fine, “Hidden variables, joint probability, and the Bell inequalities.Physical Review Letters 48 (1982): 291–295.

Thursday 3 January 2019

Actual philosophers talking about particle physics

In yesterday's Backreaction post, Sabine Hossenfelder takes on a paper by Bernardo Kastrup that argues for a form of panpsychism. Neither panpsychism nor Kastrup will receive any defense from me. What interests me is the way she summarizes her post at the end:
Summary: If a philosopher starts speaking about elementary particles, run.
Now, some people enjoy ridiculing philosophers who talk about things they don't understand. Those who want to engage in it will surely be disappointed to learn that Kastrup is not a professional philosopher. According to his website, his Ph.D. is in computer engineering. He lists no affiliation with any academic department of philosophy (though he does say that he has worked at CERN and at the Philips Research Laboratories).

This may leave readers wondering what sorts of things actual professional philosophers say when they talk about particle physics. If you're interested, I have two suggestions.