Is quantum mechanics irrational?

Hans Halvorson

The following is an opinionated reading guide for students who want to get started thinking about the philosophical issues that arise in quantum mechanics.

It was claimed from the very start (1910s and 20s) that the attempt to push physical theory into the subatomic realm meets some challenging philosophical issues. These issues engaged the pioneers of quantum mechanics for two decades – until the European scientific community, with its rich history of philosophical debate, was decimated by a hateful political movement. When the balance of power in institutional science moved to North America, the more conceptual discussions of physics were mostly left behind. Whatever conceptual innovations were achieved in the 1920s and 30s seem not to have survived into the physics of the latter half of the 20th century. (In contrast, the technical and even mathematical innovations survived and flourished.)

Thankfully, the fact that quantum physics isn’t just “physics as usual” was clearly realized by John Bell, David Bohm, and Hugh Everett. (Unfortunately this second wave of quantum philosophers never got to talk things through with Niels Bohr and the other conceptually minded physicists of the previous generation. They might have found the discussions to be rather fruitful, in the same way that Einstein and Schroedinger found it fruitful to talk with Bohr and Heisenberg.) At present – nearly a third of the way through the 21st century – there is rather small minority of physicists who think actively about the foundations of quantum physics, alongside a small community of philosophers who are savvy about physics. Unfortunately, disciplinary boundaries have often impeded conceptual progress, and I hope that this document will be of some small help in overcoming that problem.

Wake up call

For a “wake-up call” about what’s wrong with textbook quantum mechanics, see (Albert 1994). Albert’s book is a locus classicus for the quantum measurement problem, and he also describes some of the main ways of attempting to solve this problem – i.e. interpretations of quantum mechanics.

There are quite a few things in Albert’s book that are tendentious — but that’s why it’s exciting! I would say that it’s a bit uncharitable to treat QM as a “statistical algorithm” that only makes predictions. Perhaps that is the way that some, or even many, physicists use QM. But perhaps others manage to use it in a way that leads them to make true descriptions of things that happen before or after measurements, or more generally, of things that cannot be seen by the human eye. So to say that QM is only a statistical algorithm seems a bit uncharitable.

For an even more clear statement of what the measurement problem is supposed to be, see (Maudlin 1995). Maudlin’s derivation of the measurement problem gives a convenient way of classifying interpretations of QM based on which assumption they give up. He argues that the following three assumptions are inconsistent:

  1. Linear dynamics

  2. The wavefunction is complete

  3. Measurements have outcomes

Collapse interpretations give up the first, hidden variable interpretations give up the second, and the Everett interpretation gives up the third.

The work by Albert, Maudlin, et al. develops themes that begin the articles by John Bell in the 1960s and 70s. These articles are collected in (Bell 2004). But I don’t buy into the narrative – so popular in recent years – that John Bell uncovered problems in QM that were shoved aside by the pioneers of the field – i.e. the narrative the Bohr et al. ignored these problems, and silenced those who raised them. (This narrative can be found in books by Beller (1999) and Becker (2018), and is presupposed in rather a lot of the journal articles published by philosophers.) Every bit of historical evidence suggests that Bohr, in particular, would have been happy to renegotiate the philosophical issues into all eternity.

Does quantum mechanics break the rules of logic (or probability theory)?

In the early days of quantum theory it did certainly seem like the laws of logic were in danger of being broken. There were experiments that seemed to indicate that the underlying material was wavelike, and other experiments that seemed to indicate that the underlying material was particulate. But waves are not particles, so it looked like the world simply didn’t make sense to human logic. (Heisenberg’s “solution” – at first! – was to be silent about things that cannot be observed.)

There are other ways in which the quantum world seemed to defy the laws of rationality. Take, for example, the idea that every event must have a cause. Well, quantum theory said that an electron might spontaneously transition from one energy level to another with no antecedent cause. So that seems like yet another sense in which quantum mechanics defies the laws of rationality. (Bohr himself had contemplated giving up on the conservation of energy, but he eventually decided that QM does not violate that principle.)

Or take more recent experiments that indicate that two things that are distant in space from each other can be “entangled” in a way that simply doesn’t make sense according to common sense intuitions. One can even sometimes find people saying things like “a particle can be in two places at one time”. But that kind of claim really goes beyond what the theory actually says. It doesn’t say that one thing can be in two places at a single time. It only says that two things can behave in a way that is hard to explain by treating them as separate individuals. See nonlocality

For a student who has learned some formal logic, there is a more precise question to be asked, viz. whether QM demands that we revise the rules of logic. That is a real live debate, and people have some quite strong opinions about it. I would say that the recent consensus is that quantum mechanics doesn’t say anything that directly impinges on the laws of classical formal logic. But that wasn’t always the favored opinion. In an infamous article, Hilary Putnam argued that QM demands a revision of logic (Putnam 1968). If you look (e.g. on Google scholar) at all the responses to that article, then you will see not only that many people have argued against it, and even Putnam himself eventually decided it was misguided.

There has been a bit of a recent flareup in discussions about quantum logic. See (Maudlin 2005; Kripke 2023; Williamson 2018)

For a rigorous approach to quantum logic, without much philosophical drama, see (Gibbins 1987). There are interesting technical questions here as well – in particular, about the relationship of quantum logic to other substructural logics (such as linear or relevance logic). Some people have seem interesting parallels between quantum mechanics and intuitionistic logic, but nobody seems yet to have found a rigorous formal correspondence.

Nonlocality

As a formal, quantifiable feature of models, the notion of quantum nonlocality was born with the proof of Bell’s theorem in 1965. (Bell’s paper “On the Einstein-Podolsky-Rosen paradox” is reprinted in his book (Bell 2004).) The underlying issue of entanglement had been identified at least thirty years prior by Schroedinger and Bohr, and was exploited in the infamous Einstein-Podolsky-Rosen argument.

There is one clear sense in which Bell’s inequality is a consequence of classical probability theory. One might be tempted then to conclude that the violation of Bell’s inequality in QM shows that classical probability theory is false. There was some debate along these lines in the 1970s and 80s, with the work of Arthur Fine, Itamar Pitowski, etc. However, others insist that the violation of Bell’s inequality is about locality and not at all about probability theory.

Adopting an interpretation

If one starts to get serious about a particular interpretation of QM, then the question is: what to do with it? At risk of grossly caricaturing, Bohmians have a scientific task: develop extensions of Bohmian mechanics to capture more real physical situations. (David Wallace is not optimistic about their chances (Wallace 2023).) In contrast, Everettians have a philosophical task: explain how we can get our heads around this metaphysical picture that is so alien to common sense.

Hot topics

Everett (Many Worlds)

To call Everett a “hot topic” is about 15 years behind the times. The topic got hot again in the early 2000s, thanks to (among others) David Wallace. It has now moved into a more stable development and articulation phase, I would say. There are lots of problems and sub-problems still to be worked out. My sense is that of all the interpretations on offer, Everett is the closest to a “worldview”.

Wavefunction realism

The idea is simple: the quantum wavefunction is a real thing. This view has been developed by Alyssa Ney (Ney and Albert 2013), and defended by Sean Carroll. I myself have criticized the view in print (Halvorson 2019).

QBism

A radical, and potentially interesting idea, propelled forward by the growth of quantum computing and information theory. What if the whole point of the quantum revolution is that physics should no longer try to say how things are? I haven’t been following the latest in QBism, but if you google it, and also keyword “Chris Fuchs”, you’ll find plenty to read. One very interesting thing about QBism is that it makes you think hard about the interpretation of probability – i.e. when you say that an event has a 50% chance of occurring, what exactly are you saying about the world? QBism also requires one to think about big issues regarding objectivity and subjectivity, and the goals of science. (In this sense, John Bell would have called QBism a “romantic interpretation” of QM – which for him was a derogatory term.)

Relational quantum mechanics

This is the bespoke interpretation of Carlo Rovelli. There is much more to say about it, both in terms of why it’s such an interesting idea, and in terms of skepticism about whether it works.

Healey’s pragmatic turn

Richard Healey has been doing some creative thinking about what quantum physics means. For a start, see his book (Healey 2017). The view has now been further developed in several articles. Healey’s view shares features in common with Bohr, Rovelli, and QBism.

Since quantum physics is so exotic, there is quite a lot of interesting popular science literature about it. While this genre does not generally encourage philosophical rigor, the philosopher can still benefit quite a lot from these perspectives. One older book that I find to be quite good is (Herbert 2011).

Additional resources

References

Albert, David Z. 1994. Quantum Mechanics and Experience. Harvard University Press.
Becker, Adam. 2018. What Is Real?: The Unfinished Quest for the Meaning of Quantum Physics.
Bell, John Stewart. 2004. Speakable and Unspeakable in Quantum Mechanics: Collected Papers on Quantum Philosophy. Cambridge university press.
Beller, Mara. 1999. Quantum Dialogue: The Making of a Revolution. University of Chicago Press.
Gibbins, Peter. 1987. Particles and Paradoxes: The Limits of Quantum Logic. Cambridge University Press.
Halvorson, Hans. 2019. “To Be a Realist about Quantum Theory.” In Quantum Worlds: Perspectives on the Ontology of Quantum Mechanics, 133–63. Cambridge University Press.
Healey, Richard. 2017. The Quantum Revolution in Philosophy. Oxford University Press.
Herbert, Nick. 2011. Quantum Reality: Beyond the New Physics. Anchor.
Kripke, Saul A. 2023. “The Question of Logic.” Mind 133 (529): 1–36. https://doi.org/10.1093/mind/fzad008.
Maudlin, Tim. 1995. “Three Measurement Problems.” Topoi 14 (1): 7–15.
———. 2005. “The Tale of Quantum Logic.” In Hilary Putnam, 156–87. Cambridge University Press.
Ney, Alyssa, and David Z Albert. 2013. The Wave Function: Essays on the Metaphysics of Quantum Mechanics. Oxford University Press.
Putnam, Hilary. 1968. “Is Logic Empirical?” Boston Studies in the Philosophy of Science 5.
Wallace, David. 2023. “The Sky Is Blue, and Other Reasons Quantum Mechanics Is Not Underdetermined by Evidence.” European Journal for Philosophy of Science 13 (4): 54.
Williamson, Timothy. 2018. “Alternative Logics and Applied Mathematics.” Philosophical Issues 28 (1): 399–424.