Why a Quantum Field Theorist is the wrong person to ask about Quantum Mechanics

Quantum Mechanics is quite possibly the sexiest, most mysterious thing to come out of 20th century physics. Almost a century of evidence has confirmed that the world is fundamentally ambiguous and yet deeply predictable, that physics is best described probabilistically, and that however alien this seems the world wouldn’t work without it. Quantum Mechanics raises deep philosophical questions about the nature of reality, some of the most interesting of which are still unanswered to this day.

And I am (for the moment, at least) not the best person to ask about these questions. Because while I specialize in Quantum Field Theory, that actually means I pay very little attention to the paradoxes of Quantum Mechanics.

It all boils down to the way calculations in quantum field theory work. As I described in a previous post, quantum field theory involves adding up progressively more complicated Feynman Diagrams. There are methods that don’t involve Feynman Diagrams, but in one way or another they work on the same basic principle: to take quantum mechanics into account, add up all possible outcomes, either literally or through shortcuts.

That may sound profound, but in many ways it’s quite mundane. Yes, you’re adding up all possibilities, but each possibility is essentially a mundane possibility. There are a few caveats, but essentially each element you add in, each Feynman Diagram for example, looks roughly like the sort of thing you could get without quantum mechanics.

In a typical quantum field theory calculation, you don’t see the mysterious parts of quantum mechanics: you don’t see entanglement, or measurements collapsing the wavefunction, and you don’t have to think about whether reality is really real. Because of that, I’m not the best person to ask about quantum paradoxes, as I’ve got little more than an undergraduate’s knowledge of these things.

There are people whose work focuses much more on quantum paradoxes. Generally these people focus on systems closer to everyday experiments, atoms rather than more fundamental particles. Because the experimentalists they cooperate with have much more ability to manipulate the systems they study, they are able to probe much more intricate quantum properties. People interested in the possibility of a quantum computer are often at the forefront of this, so if you’ve got a question about a quantum paradox, don’t ask me, ask people like WLOG blog.

A final note: there are many people (often very experienced and elite researchers) who, though they might primarily be described as quantum field theorists, have weighed in on the subject of quantum paradoxes. If you’ve heard of the black hole firewall debate, that is a recent high-profile example of this. The important thing to remember is that these people are masters of many areas of physics. They have taken the time to study the foundations of quantum mechanics, and have broadened their horizons to the tools more commonly used in other subfields. So while your average grad student quantum field theorist won’t know an awful lot about quantum paradoxes, these guys do.

10 thoughts on “Why a Quantum Field Theorist is the wrong person to ask about Quantum Mechanics

  1. Lucas Vieira

    Maybe that is because the typical field theorist will not ask the right questions for the foundations of QM. You could certainly ask what happens if slow moving particles whose spin are entangled are accelerated to high energies.
    Also, the field theorest deals mostly with pure states, whereas the information theories must look at mixed states.
    You can always think of QM though, from the point of view of effective field theory, or as a one dimensional quantum field theory.

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  2. Madeleine Birchfield

    A quantum field theorist is the right person to ask about questions of quantum mechanics. It is quite simple, quantum mechanics is simply a approximation for when a semiclassical particle picture makes sense, an effective field theory in 0+1 dimensions. For example, wavefunction collapse occurs in quantum mechanics when particles start interacting with each other and the environment, because then one has to take into account the complex quantum field interactions between the “particle” and the quantum fields in the environment. Wave/particle duality exists because both waves and particles are simply two different approximations of certain field configurations. None of the debate over various interpretations of quantum mechanics (Everett, Copenhagen, et cetera) are even necessary because they all postulate that the particle picture is reality, rather than being an approximation of quantum field theory.

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    1. Madeleine Birchfield

      And I should add that the quantum field theory picture is quite classical in nature. Position is, like in classical mechanics and classical field theory and unlike in traditional quantum mechanics, a parameter and not an operator obeying the uncertainty principle; there is no uncertainty inherent in the physical location of point particles. The uncertainty is instead an result of the interactions between the quantum fields of the detectors and the measured phenomena.

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      1. 4gravitons Post author

        I think your attention was drawn to this post by my “Classicality has Consequences” post, which should explain why the second part of your comment doesn’t follow from the first. Yes, in QFT position is a parameter, not an operator. However, the rest depends on precisely how you handle the matching to a point-particle 0+1 worldline EFT. You certainly don’t have to invoke specific detector fields to do it. For example, the papers I linked there calculate expectation values with wavepacket wavefunctions that smoothly go to point particles in the classical limit.

        In general, once you’ve conceded that QM is just an EFT for QFT, then you can’t make definite statements about where one thing or another comes from in QM…there can be more than one EFT that gets the job done! 😉

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    2. 4gravitons Post author

      Wave-particle duality indeed becomes super obvious from the perspective of QFT (and isn’t all that “cool” by itself anyway), but the impression I had is that measurement/”wavefunction collapse” remains an issue. In particular, your statement that

      “For example, wavefunction collapse occurs in quantum mechanics when particles start interacting with each other and the environment, because then one has to take into account the complex quantum field interactions between the ‘particle’ and the quantum fields in the environment.”

      seems equivalent to the statement that decoherence solves the “measurement problem”, and I’d gotten the pretty thorough impression that that’s false, it just postpones it. I don’t think that’s an artifact of them all just being stuck at first order in a worldline EFT.

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      1. Madeleine Birchfield

        Actually, I don’t think in quantum field theory the wavefunction ever actually “collapses”, because quantum field theory postulates that the entire universe is just a giant quantum field (read: wavefunction). The actual problem, and what I meant to say, is that any subsystem of quantum “particles” in the real world isn’t ever closed or complete, since it doesn’t take into account the quantum fields of the detectors and/or the rest of the world, so once the subsystem interacts with the rest of the world, of course the original state of the quantum subsystem is destroyed, and one has to move to the a larger subsystem of the universe for a wavefunction/quantum field description to be restored.

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        1. 4gravitons Post author

          Ok, at that point you’re just reproducing (more modern versions of) Everett, though, and you’re vulnerable to all the normal objections there. I don’t think that’s necessarily an invalid perspective, but QFT isn’t buying that much for you here…maybe it makes Bohmian perspectives specifically look dumber, but they’re somehow at peace with not being able to reproduce QFT regardless. It doesn’t distinguish between Everett and QBism anyway. (“QFT postulates that the entire universe is just a giant quantum field” is if anything harder to defend from the formalism alone than “QFT is a tool used by agents to compute correlation functions”.)

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          1. Madeleine Birchfield

            What I meant by the “wavefunciton is real and covers the entire universe” is not Everett’s many-world interpretation, where all particles are real and all measurements of all particles exist in some multiverse fashion. My interpretation is more like the following: suppose you have a system traditionally described as the following: a beam of particles moving in one direction, with an associated uncertainty, and you can make measurements of the locations of the particles. What is actually real is the beam or wavefunction or quantum field, which evolve deterministically according to the rules in quantum mechanics, the probabilistic nature of the measured “particles” are simply a result of the statistical measurements of the properties of the wavefunction/field. The important variables here which define the evolution of the wavefunciton/field are the quantum expectation values and the quantum variance for the wavefunction/field, which arise from some sigma-algebra associated with the wavefunction/field. The uncertainty in the quantum expectation and so forth arises from the fact that wavefunctions and quantum fields aren’t point particles, but extended objects, and so one cannot exactly measure the quantum expectation values and quantum variance of a wavefunction, just as one cannot exactly measure the centre of mass for a ball of putty in classical mechanics, it comes with an expected value and variance.

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            1. 4gravitons Post author

              I mean, you absolutely can measure the center of mass of a ball of putty exactly in classical mechanics, if you’re modeling the putty with fluid mechanics. You can’t measure it if you’re modeling the putty with statistical mechanics, but that’s because statistical mechanics is probabilistic, not because extended objects are.

              More generally, I think your perspective still lands you on something like Everett (if, again, one of the more modern versions of it). More modern commentators on Everett (Deutsch etc.) generally don’t think that the particle picture is correct. They think the universe has a wavefunction which evolves deterministically, and that any individual person experiences part of that wavefunction, with the whole wavefunction “existing” in some sense.

              In particular, your perspective seems like it would give exactly the same “gee whiz” kinds of imagery that Everett does. Suppose someone has a radioactive atom, and makes a decision to buy a car based on whether it decays in a time equal to its half-life. Under your perspective, the wavefunction of the universe is real and evolves deterministically, so it certainly sounds like reality contains both outcomes: the person both buys and does not buy the car. That’s Everett.

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        2. Madeleine Birchfield

          I should add that classical behaviour isn’t a result of wavefunctions/quantum fields “collapsing” into a pure classical state upon observation, it is the result of the thermodynamic limit of quantum statistical mechanics when N goes to infinity.

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