Sixty Symbols on Quantum Mechanics

I’m currently working hard to finish a paper on the Everett (Many-Worlds) approach to quantum mechanics, collaborating with Charles (“Chip”) Sebens from the University of Michigan. It’s an area that lies at the intersection of “foundations of quantum mechanics” and “philosophy of physics,” and neither of those is really my expertise — but I’m trying to learn! More when the paper comes out, hopefully quite soon.

Meanwhile, I end up posting a lot of videos rather than really blogging, until the larger crush of work is lifted a bit. While I was in Nottingham I had the pleasure of sitting down to record for their series of Sixty Symbols videos, which is a terrific series that I’m happy to recommend. Here’s me chatting about the different approaches to quantum mechanics.

Forthcoming: me chatting about the Higgs boson, and me chatting about the arrow of time. My time in England involved a lot of chatting, it’s true.

This entry was posted in Science. Bookmark the permalink.

38 Responses to Sixty Symbols on Quantum Mechanics

  1. Matt Leifer says:

    I find it very hard to believe that the reason that 42% of the participants at a quantum foundations conference prefer the Copenhagen interpretation is because they haven’t really thought about the foundations of quantum mechanics. Why else would they be at a foundations meeting?

    The Copenhagen interpretation is not the thing that you described in the video. That sounds more like the orthodox or Dirac/von-Neumann interpretation, which is the thing that we actually teach to undergraduates. The main difference is that the orthodox interpretation accepts the eigenvalue-eigenstate link, which says that if a system is in an eigenstate of an observable A then A is a property of the system. This implies that the orthodox interpretation is realist about the wavefunction, since every wavefunction is an eigenstate of some set of observables, and specifying that set is mathematically equivalent to specifying the wavefunction. Therefore, on the orthodox view, we have to accept that there is some real physical transformation going on in wavefunction collapse, since the real physical properties of the system change. The conflict between collapse and unitary dynamics is therefore a flat out contradiction on the orthodox view, so the measurement problem shows that the interpretation is inconsistent and should be rejected, despite the fact that we are still teaching it to undergrads.

    In contrast, the Copenhagen interpretation does not accept the eigenvalue-eigenstate link. In fact, it is pretty clear that it endorses an epistemic attitude towards the wavefunction, much like the “information theoretical” view described in the video. I can dig up the usual quotes from Bohr to back this up, but I am pretty Bohred of doing that, so I’ll wait to see if someone disagrees with me first. On the Copenhagen view, there need be no dramatic transition in the physical properties of Schroedinger’s cat when we look in the box. The wavefunction, both before and after the measurement, is just a description of our knowledge of the state of the cat and is not a property of the cat itself.

    This confusion about Copenhagen is common. It arises because Dirac and von Neumann both thought they were outlining the Copenhagen interpretation when they wrote their famous books and that is where most physicists learned quantum theory from in the early days so this error got repeated in many textbooks. However, if you look into the writings of Bohr, Heisenberg, Pauli et. al. you will see no statement indicating that they thought the wavefunction is real and plenty of staements that indicate they thought it was epistemic.

    Things like the “information theoretic” interpretation and Quantum Bayesianism are really just modern variants of Copenhagen, and as such I personally call them neo-Copenhagen interpretations. They only differ from Copenhagen in that they try to state the position more precisely and they correct some errors that Bohr et. al. made by virtue of the fact that they did not envision macroscopic superpositions or applying quantum theory to the whole universe. In particular, they usually clear up the mess that Bohr made by insisting that there must always be some system that is treated classically. Nevertheless, the interpretations are all so close in spirit that we should arguably lump them all together as saying roughly the same thing. If this had been done in the poll then neo-Copenhagen may well have scored more than 50%, although it is difficult to tell as people were obviously allowed to pick more than one answer.

  2. charles pervo says:

    Thank you!

  3. Sean Carroll says:

    Matt– I’ll agree that my offhand phrasing in the video about why Copenhagen got so much support was certainly not the best; I could have given a more sympathetic interpretation. (I would stand by my words with respect to physicists-on-the-street, which is the context I usually talk about, but this was a meeting of experts on foundations.) Apologies for that.

    But I’m interested in the claim that most self-professed believers in the Copenhagen interpretation take a purely epistemic view of the wave function. That might be true, especially among this audience, but I suspect that a fraction of those who voted for Copenhagen would also say the wave function is real. In Question 9 of the Schlosshauer et al poll, only 27% said the wave function was epistemic, although admittedly 33% voted for “a mixture of epistemic and ontic,” and I’m not sure what that is supposed to mean. I wish there had been a sub-question so that people voting for Copenhagen could have indicated what they meant.

    I’d be happy to stop using the phrase “Copenhagen interpretation” entirely, and distinguish between “real collapse” approaches and purely informational approaches.

  4. john naddaf says:

    thanks for the talk,,,i feel like studying it ,taking notes,and preparing an in depth reply to provide the adequate information,,,,For now ill say this:
    the splitting of of the quantum system,is required as the most fundamental law of nature…in a totality of one singularity,where the singularity is total,and the totality is single,the singularity system must oppose(split) in order for one to observe one…a stable system of one unopposed is as we know non interacting a singularity,therefore unable to observe or be observed,and would never exist,so it must oppose in order to be observed…
    what is lacking in quantum mechanics is a deeper understanding of time,,,time orders the universe,space merely observes the order,measuring the observation…
    im just leaving it at that for now,i have to stop somewhere,,,but i will say the quantum spin of time(polarity),matches that of dark matter,,,dilating/condensing…while the quantum spin of space,matches that of dark energy,,,entropy/inflation…

  5. AI says:

    Not only wavefunction is a mixture of epistemic and ontic components but pretty much everything else too. Take electron mass for example, it is centered around it’s “true” value (ontic component) but it also contains uncertainty related to our state of knowledge (epistemic component.)

    A purely epistemic concept could not have any relation to physical reality at all and therefore would be pretty useless. Conversely a purely ontic one would be an idealization since our descriptions of reality cannot be complete.

    Whether the change of the state of the cat when we open the box falls on the ontic or epistemic side the fact that in both cases we have a cat means the wavefunction has an ontic component but since the concept of a cat is not a complete description it is also epistemic.

  6. Gizelle Janine says:

    Many-worlds interpretation
    From Wikipedia, the free encyclopedia:

    “The many-worlds interpretation is an interpretation of quantum mechanics that asserts the objective reality of the universal wavefunction and denies the actuality of wavefunction collapse. Many-worlds implies that all possible alternative histories and futures are real, each representing an actual “world” (or “universe”). It is also referred to as MWI, the relative state formulation, the Everett interpretation, the theory of the universal wavefunction, many-universes interpretation, or just many-worlds.”

    “The original relative state formulation is due to Hugh Everett in 1957.[2][3] Later, this formulation was popularized and renamed many-worlds by Bryce Seligman DeWitt in the 1960s and 1970s.[1][4][5][6] The decoherence approaches to interpreting quantum theory have been further explored and developed,[7][8][9] becoming quite popular. MWI is one of many multiverse hypotheses in physics and philosophy. It is currently considered a mainstream interpretation along with the other decoherence interpretations and the Copenhagen interpretation.[10]”

    “Before many-worlds, reality had always been viewed as a single unfolding history. Many-worlds, however, views reality as a many-branched tree, wherein every possible quantum outcome is realised.[11] Many-worlds claims to reconcile the observation of non-deterministic events, such as the random radioactive decay, with the fully deterministic equations of quantum physics.”
    “In many-worlds, the subjective appearance of wavefunction collapse is explained by the mechanism of quantum decoherence, which resolves all of the correlation paradoxes of quantum theory, such as the EPR paradox[12][13] and Schrödinger’s cat,[1] since every possible outcome of every event defines or exists in its own “history” or “world”.

    “In lay terms, there is a very large—perhaps infinite[14]—number of universes, and everything that could possibly have happened in our past, but did not, has occurred in the past of some other universe or universes.”

    Sorry Sean, can’t say I agree with eloping with this idea. You might as well deny the existance of music theory and vibrations. Something about every theory that’s thrown in my face to learn, always has some inconsistancy to locality, specifically. It works, I do agree. But saying wavefunction collapes happen sometimes in special instances is just as annoying to me as calling the higgs “The God Particle” to you. Wouldnt superposition of elections be a kind of collape even though its a probablitiy in QM? I mean you guys don’t even know what makes someone’s perception real, so how can you say anything except Many-Worlds needs to be fixed too? Science is like a f$&*@$! broken tea pot.

    Scientists are mind-boggling to me, it always seems they think so hard they lack common sense. I knew you were unlikeable for a reason. I said it last year I think, but I’ll never buy your book. 😀

  7. Gizelle Janine says:

    By the way, for Sean’s sanity since he gets asked so often, I will always strike out “The God Particle” When refering to it as such. It is really annoying. He also looks like he wants to murder the interviewers when asked why. Please don’t end up a court case like O.J, Sean. We love you and are here for you. 😀

  8. Tony Rz says:

    I think if the cat is dead or alive depends on if the cat is dead or alive, and has nothing to do with observation, observation can only confirm reality. I think that in the many worlds view that if another universe splits off from this one that it takes with it the information that is contained in this one, this one would be the parent, while the split universe, like a child may appear to be different, though very little, the same laws would apply. While the universe that we can see may be an atom compared with the entire Cosmos it still would be connected on all sides sharing information. QM is beginning to sound like Alice down the rabbit hole. I realize I don’t know the math, but still I try to use the abilities I have. So, Help me.

  9. Gizelle Janine says:

    Ok, well Tony, perception is something that is an unobservable observable in many instances, even with equations. If scientists knew what made up human perception, it would solve violations in physics, specifically QM. Many violations have to do with the idea that in many experiments, you are unable to tell if perception is even a probability for being relevant. Locality and non locality are ways of observing, not thinking. Additionally I was not talking about that particular thought experiment, which is a great fun way to think about ways of observing in QM so I wasn’t even responding to anything you said previously. I was talking about how I do not agree that you can say many worlds is relevant without including collapse of the wave function and it’s specifically because of the cat-in-a-box experiment and also a lot because of Euclidean space. Which wasn’t specified specifically, but suggested quietly.

  10. Gizelle Janine says:

    Sorry about the spelling. I did mean which as opposed to with. I type on an ipad mini, and editing doesnt always work. So sorry about the painful inconsistancy.

  11. Gizelle Janine says:

    Oh, by the way, Tony:

    When I hear “sharing information” I think ten to the google years of hawking radiation, which is me at my most optimistic. 😀

  12. Matt Leifer says:

    “But I’m interested in the claim that most self-professed believers in the Copenhagen interpretation take a purely epistemic view of the wave function. That might be true, especially among this audience, but I suspect that a fraction of those who voted for Copenhagen would also say the wave function is real. In Question 9 of the Schlosshauer et al poll, only 27% said the wave function was epistemic…”

    I’ll admit that even amongst this audience, there is a great deal of confusion about what the word “Copenhagen” means. Some mistake it for the orthodox interpretation and some for “shut up and calculate”. It is possible that this accounts for the discrepancy with the epistemic wavefunction question. However, it seems unlikely to me that many of the respondents meant the orthodox interpretation, as people attending such a conference would be very familiar with the fact that the measurement problem is a flat out contradiction for this view. Therefore, foundationally inclined people who think that orthodox=Copenhagen are likely to view the measurement problem as ruling out Copenhagen, so they are unlikely to pick it as their favourite option. It also seems unlikely that many people at a foundations conference would favour shut up and calculate.

    There is also another possible resolution of the discrepancy, which is that perhaps some people object to ever using the term “epistemic” for a state in the context of physics. It does presuppose a broadly Bayesian account of probability theory in which probabilities represent knowledge, information or belief. Frequentists may prefer the term “statistical”, which is equivalent as far as most of the implications of the epistemic/ontic distinction go. Whether you say that the wavefunction is “epistemic” or “statistical” you are still saying that it is not an intrinsic property of an individual system. It makes a difference if you are someone who believes that taking the correct foundation for probability theory is important for understanding quantum foundations, as the Quantum Bayesians do for example, but not if you think that the two problems are independent. However, the fact that 0% of people picked the “statistical interpretation” lends some doubt to this view.

    It is probably useless to speculate upon what people actually meant in their responses to this survey. If I were being cynical, I would say that the whole excercise was an attempt to undermine Max Tegmark’s frequent rhetorical use of his earlier poll, which came out in support of Everett. You can see that in the way the questions are phrased. For example, respondents were allowed to pick multiple responses and were given multiple oppportunities to say that they agreed with Copenhagen-type ideas, but only one opportunity to say that they like Everett. I guess what we have learned from this survey is that if you conduct a survey about favourite interpretations at a conference organized by Tegmark then Everett will come out top whereas if you conduct one at a conference organized by Zeilinger then Copenhagen-type ideas will come out top. Is this really a surprise to anyone?

  13. Igor says:

    If you asked 18th-century physicists about their favorite explanation of gravity, you’d also get a lack of consensus. Various accomplished physicists would advocate different explanations, but from the 21st-century perspective, the majority of the answers would be complete misses.

    18th-century physicists would find the theory of gravity to be very accurate and useful in their daily work. They would also find it unsettling because there is no accepted explanation of its counterintuitive properties, such as non-locality. Doesn’t that sound a lot like quantum mechanics today?

    Ultimately, until there is an experiment that can distinguish between the different interpretations, they are all just speculations.

  14. Mike Bacon says:

    “I guess what we have learned from this survey is that if you conduct a survey about favourite interpretations at a conference organized by Tegmark then Everett will come out top whereas if you conduct one at a conference organized by Zeilinger then Copenhagen-type ideas will come out top.”

    Well, not exactly. I think you may be implying (even if in jest) more equivalence between the polls than actual exists. If I’m not mistaken the result of Tegmark’s poll had the MWI coming in second, not on top. Actually, Copenhagen came in on top!!

    Do you think that the bias you noted in the recent poll’s questions was evident in the Tegmark poll? Take a look at the choices.

    Speaking of bias, I guess mine is showing. :)

  15. Jeff Lassahn says:

    Thanks, Sean, for this and many other lucid explanations.

    Although I have some philosophical queasiness with the Many Worlds interpretation, my biggest problem is that I haven’t yet seen a convincing demonstration of the core claim: that a large quantum system settles over time into an observer-like portion that looks like a set of noninteracting classical possibilities and an environment-like portion that is correlated with the observer.

    I’ve seen a few papers claiming to prove this, but they fall into two categories: 1) completely impenetrable, and 2) making dubious assumptions that seem like they might be taking the desired conclusion as an axiom (a typical example is assuming that the “observer” system is localized in a small region of space).

    Can anyone recommend a good survey of Many Worlds, Decoherence, etc. at, say, the introductory graduate school level for those of us who are confused?

  16. Mitchell Porter says:

    Sean Carroll, or anyone: how can you be a realist about wavefunctions, and yet also believe in special relativity? Wavefunctions are defined with respect to a particular spacelike surface. If they are just (mysteriously effective) constructs for the purpose of making predictions, that might be OK, but if you reify them, it seems you must also be reifying the space-time foliation with respect to which they are defined.

  17. vmarko says:

    @ Mitchell Porter:

    Special relativity is not a problem. There is this thing called “relativistic quantum mechanics” (actually, it’s a simplistic view on the more elaborate thing called “quantum field theory”), which takes special relativity into account. Simply put, there is the “wavefunction of the vacuum”, which is invariant wrt. Lorentz transformations, and then you can build other wavefunctions from that one by acting on it with creation operators for various fields. These transform covariantly under Lorentz transformations, so consequently different observers will use “different but compatible” wavefunctions. And so on.

    Now, when you start looking at general relativity, the vacuum wavefunction cannot even be defined, and *that’s* where all the fun starts… 😉

    HTH, :-)

  18. Ray Gunn says:

    No worries, Sean. Elsewhere on the Wave Function you finished your paper early, and got a morning call from the Nobel committee.

  19. Mitchell Porter says:

    @ vmarko:

    The “Everett worlds” of the many-worlds interpretation are supposed to be “parts” of a global quantum state – a component of a superposition, a reduced density matrix for a local set of degrees of freedom… But the states in quantum field theory are either asymptotic (located at past infinity or future infinity) or they are defined on specific spacelike surfaces within space-time. So it seems that Everett-worlds will only be defined asymptotically, or they will be pinned to a particular foliation.

    The one serious attempt to resolve this problem within MWI that I know about, is by Wallace and Timpson. They start in the Heisenberg picture, with a particular state on a particular hypersurface, and then construct states with consistent predictions, for every mutually spacelike collection of points in space-time. So now they have a family of quantum states, one for every slice of every foliation. But they don’t go on to explain how Everett decompositions of those states will map onto each other. MWI already has a problem – on which MWI advocates are divided – of whether one should regard only the worlds resulting from a particular preferred basis as real, or whether the worlds resulting from every decomposition relative to every possible basis are just as real as what we see. (The latter choice would seem to imply, for example, that “cat half dead and half alive” is a world in itself, and not just a superposition of worlds.) Wallace and Timpson face this same dilemma – either endorse all possible decompositions as equally real, including deadalive cats, or else pick out just one set of mathematical possibilities as physically/ontologically special – but generalized to the relativistic domain.

    An alternative approach might be to prefer the configuration basis from the beginning, think of superpositions located at individual space-time points as the ontological building blocks, and try to build up everything else from that. Or, one might try to reify the coarse-grained histories in a particular set of consistent histories… I have been discussing MWI with advocates for several years, and repeatedly the feeling I get is that I have to do their homework for them: I have to suggest various ways that they could try to get their theory into shape, before it is even fit to be critiqued. MWI advocates are just incredibly sloppy in defining their theory with any exactitude, and in specifying how it is supposed to connect with reality.

    Well, either they’re sloppy, or they veer into outright nonsense, such as Wallace and Deutsch’s “decision-theoretic” justification of the Born rule, according to which worlds can’t be counted, but observed frequencies behave as they do because if they didn’t, we couldn’t behave rationally in the multiverse… But mostly, when a physicist advocates MWI, it’s just because they’re conceptually sloppy, in ways inherited from the Copenhagen interpretation’s cavalier attitude towards notions of existence and reality. So if a real physicist like Sean Carroll is going to stand up and say that MWI is an option or makes sense, then I would like to hear him make a few comments about a basic matter like the relationship between Everett worlds and special relativity. It’s the least he can do.

  20. Matt says:

    Gizelle Janine

    You need to stop drinking the bong water……….

  21. Gizelle Janine says:

    Matt: I sincerely hope your joking.

  22. Gizelle Janine says:

    …did I mention I’m not a b$&@*? 😀

  23. Hakon Hallingstad says:

    I think the Everett interpretation is basically correct, but the preferred basis problem has not yet been solved. Decoherence may resolve the issue in practice, but doesn’t help with the interpretational problem. For instance, what is the exact condition for when a particular decomposition becomes real compared to other decompositions?

    The major reason there’s still no consensus on the interpretation is because the Everett interpretation cannot be used to give a concise description of QM like the Copenhagen interpretation can. Also, the interpretation struggles with its past for ending up with irrelevant discussions about the world-splitting and derivation of the Born rule.

  24. Jens says:

    Totally out of my league here, but what do you (Sean) mean that the Universe “splits”? You mean an instant copy of our Universe is created somehow, separate from our own, whenever a quantum event occurs which could have two outcomes? A copy of our entire Universe?? What mechanism has been proposed for this? Is that even science? I mean presumably these instant copies, which must spring up zillions of times per second just in my backyard, are not “knowable” to us in this timeline, right? Can a theory for how this occurs or how it could be tested, even exist? Or is this not actually science but, well, something else?

  25. C.Takacs says:

    Jens: MWI is not science, since it can’t be tested or falsified by experiment, and NO, mathematical jiggling with computer models or simulations does not qualify as experiment. MWI is akin to the worst of metaphysics at best, such as: “how many angels can dance on the head of a pin?” except in this case it’s how many divergent universes can be created without energy or mass in an infintisimal of time with no regard for conservation of either energy or mass? Reality check: Take a one dollar bill, place it on the table in front of you. Multiply the one dollar bill by the number two. How many dollar bills do you have on the table now? If you are in reality you should still have only one dollar bill, as the dollar bill does not multiply by pulling mass/energy from the void just because you conjecture it multiplying in abstraction…(no, I am not going to include the chairman of the federal reserve in this analogy.) I think many in the High Energy Physics community are somehow willfully oblivious to the fact that all mathematical abstraction (or fantasy) is a subset of reality, not the other way around.