Various and Sundry

A few recent items of interest:

  • Martin Greiter has put together a written version of Sidney Coleman’s mid-1990s lecture Quantum Mechanics in Your Face, based on a recording of one version of the lecture and copies of Coleman’s slides.

    It’s often claimed that leading physicists of Coleman’s generation were educated in and stuck throughout their careers to a “shut up and calculate” approach to the interpretation of quantum mechanics. Coleman’s lecture I believe gives a much better explanation of the way he and many others thought about the topic. In particular, Coleman makes the crucial point:

    The problem is not the interpretation of quantum mechanics. That’s getting things just backwards. The problem is the interpretation of classical mechanics

    He ends with the following approach to the measurement problem:

    Now people say the reduction of the wave packet occurs because it looks like the reduction of the wave packet occurs, and that is indeed true. What I’m asking you in the second main part of this lecture is to consider seriously what it would look like if it were the other way around—if all that ever happened was causal evolution according to quantum mechanics. What I have tried to convince you is that what it looks like is ordinary everyday life.

    While some might take this and claim Coleman as an Everettian, note that there’s zero mention anywhere of many-worlds. Likely he found that an empty idea that explains nothing, so not worth mentioning.

  • For the past year the CMSA has been hosting a Math-Science Literature Lecture Series. The talks have typically been excellent surveys of areas of mathematics, given by leading figures in each field. To coordinate with Tsinghua, the talks have often been at 8am here in NYC, and several times the last couple months I’ve made sure to get up early enough to have breakfast while watching one of the talks. All of the ones I’ve seen were very much worth the time, they were the ones given by Edward Witten, Andrei Okounkov, Alain Connes, Arthur Jaffe and Nigel Hitchin. Jaffe’s covered some of the ideas on Euclidean field theory that I’ve been spending a lot of time thinking about. For a more detailed version of his talk I highly recommend this article.
  • Peter Scholze has posted at the Xena blog a challenge to those interested in formalizing mathematics and automated theorem proving (or checking): formalize and check the proof of a foundational result in his work with Dustin Clausen on “condensed mathematics”. As part of the challenge, he provides an extensive discussion of the motivation and basic ideas of this subject, which attempts to provide a replacement (with better properties) for the conventional definition of a topological space.

    Spending a little time reading this and some of the other expositions of the subject convinced me this is a really thorny business. Scholze explains in detail his motivation for making the challenge in part 6 of the posting. My suspicion has always been that most of the value of computer theorem checking lies in forcing a human to lay out clearly and unambiguously the details of an argument, with that effort likely to make clear if there’s a problem with the theorem. It will be fascinating to see what comes of this project.

    I see there’s also a blog posting about this at the n-category cafe.

  • On the topic of theorems that definitely don’t have a clear and unambiguous proof, supposedly PRIMS will be publishing Mochizuki’s IUT papers in 2021. Mochizuki and collaborators have a new paper claiming stronger versions of Mochizuki’s results.
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43 Responses to Various and Sundry

  1. Michael Weiss says:

    Peter,
    I write to provide a nuance to your inference that Sidney Coleman’s question–“what it would look like if it were the other way around, if all that ever happened was causal evolution according to quantum mechanics?”– was unrelated to Everett’s Many Worlds Interpretation (MWI).

    I believe that MWI was in fact the starting point for Sidney’s line of thought. The evidence comes from his final lecture in Physics 143 in May, 1977 at Harvard College. (You took this class a year earlier, I think, with Ed Purcell.) Prof. Coleman ended this wrap-up lecture by asking the class exactly the above question and suggesting an answer: “It would look like ordinary everyday life.” We sat in silence for a minute, trying to make sense of this insight.

    Frank DeLucia (a few years later to develop the DeLucia-Coleman Theorem) was TA that semester and (if he reads this blog) may have further insight. John Preskill was TA in 1976 with Ed, and may also remember how Sidney’s thoughts evolved.

  2. Peter Woit says:

    Michael Weiss,

    Coleman explicitly does refer to Everett, and yes, he’s an Everettian in the sense of seeing no reason QM without a reduction postulate can’t describe the world as we know it. My point was just that he doesn’t invoke a splitting into “many worlds” to replace wave-function reduction.

    I’d be curious to know if his views evolved, whether exposure to Everett changed an earlier, different point of view. The point of view he’s taking (reduction of the wave-function is apparent, arising out of properly treating Sidney Coleman as a quantum system and the emergence of classical mechanics and our consciousness built around that) seems to me what I would have thought was the conventional one of the mid-1970s era when we were learning the subject. On the other hand, at that time I remember never hearing about Everett, hearing a lot about Copenhagen.

    Coleman explicitly says that arguing over a Copenhagen vs. Everett interpretation of QM is “getting things just backwards”, ignoring the real problem of how we get classical out of quantum. He refers to “vernacular quantum mechanics”, which is a “looser and sloppier” Copenhagen interpretation. That may be a better way than “shut up and calculate” to refer to a standard QM course’s approach to “interpretation”.

  3. John McAndrew says:

    I’m a little disappointed that the questions he answered from the audience at the end aren’t recorded in the text. He’s asked if he’s a follower of Everett’s Many Worlds interpretation at 1:04:20:

    Sidney Coleman, Quantum Mechanics in Your Face [1994]
    https://youtu.be/EtyNMlXN-sw?t=3853

    ‘Everett wrote a truly wonderful paper, then everyone got on their horse and rode off in all directions”

    I’m guessing this is: Relative State’ Formulation of Quantum Mechanics”, Reviews of Modern Physics, 29: 454–462, cited here: https://plato.stanford.edu/entries/qm-everett/

  4. Peter Woit says:

    John McAndrew,

    Thanks for pointing that out. Does anyone know what he had in mind by the “everyone got on their horse” comment?

  5. S says:

    It’s nice that Coleman doesn’t bring in “many worlds,” but on the other hand, it seems to me that his solution of “Where does Born come from?” is going to suffer from the same thing as any Everettian theory — some (possibly hidden) additional axiom or measure that is not clearly any better motivated or more coherent than collapse.

    (The problems with Coleman’s own approach to getting Born’s rule have been documented by, e.g., David Albert. I can dig up the reference if anybody is sufficiently interested; otherwise I’ll spare myself the hassle.)

  6. Peter Woit says:

    S.
    Coleman was explicitly not claiming to be saying anything original.

    I’m curious to hear if others know more specifically about Coleman’s views, but don’t want to start a rehash of the usual arguments over interpretations.

  7. Coleman’s complete course on QFT, from the 1975-76 academic year at Harvard, is online here: https://www.physics.harvard.edu/events/videos/Phys253

  8. James Smith says:

    Your suspicion “..that most of the value of computer theorem checking lies in forcing a human to lay out clearly and unambiguously the details of an argument…” is spot on in my opinion.

  9. Michael Weiss says:

    Peter,
    Please forgive my lack of clarity: I left out that that in his last lecture in 1977 Sidney Coleman explicitly defined and discussed Everett and the MWI–but as a topic of enrichment not on the final exam. I guess he was unusual among the Harvard Physics faculty at that time in including this material even as a bonus topic.

    I believe that Prof Coleman ended Physics 143 with these conceptual issues because he simply loved playing with ideas and engaging young minds.

    Curiously, you may remember that Sidney late in his life gave an interview in which he claimed to have disliked teaching. If so, he sure fooled my classmates and me! We loved him.

  10. Peter Woit says:

    Michael,
    Thanks! I’m sorry I missed that version of Physics 143. The version I took a year earlier was taught by Norman Ramsey, using David Saxon’s textbook. It’s been far too long for me to really remember, but if he discussed interpretational issues, I don’t recall that.

    I’ll take a longer look at the Saxon book later, but from a quick look online, there’s nothing like a “Copenhagen interpretation” discussion, and what is there isn’t inconsistent with Coleman’s Everettian viewpoint that in principle the state of the observer should also be described by QM.

    Sorry for my continual negative reaction to the “Many-Worlds” terminology. As I’ve written about here far too often, I think it’s a really bad terminology to use to refer to the ideas Coleman was discussing, especially given recent publicity campaigns for the idea that invoking multiple worlds explains things that it doesn’t. I’d be very curious to hear what Coleman thought of this, it’s a shame he’s no longer with us to discuss.

  11. Jon101 says:

    There seems tobe some renewed interest in Mochizuki’s work: he gave a colloquium at Berkeley in november https://mathoverflow.net/questions/375889/berkeley-mathematics-department-colloquium-by-s-mochizuki and there is a joint Rims-Lille seminar where several people from both inside and outside Mochizuki’s circle are giving talks http://www.kurims.kyoto-u.ac.jp/~bcollas/IUT/index.html

  12. martibal says:

    Off topic but could be of interest for Peter: the last paper of Penrose, together with Marcolli, about twistors and noncommutative geometry
    https://arxiv.org/abs/2012.02823

  13. Peter Woit says:

    Frank Wilhoit,
    Perhaps more useful than the videos, Coleman’s QFT lectures are now available as a book, see
    https://www.math.columbia.edu/~woit/wordpress/?p=10799

    Jon101,
    I’ve seen no evidence of increased interest in IUT recently, quite the opposite. Mochizuki and his circle have dealt with the problem pointed out by Scholze and Stix essentially by ignoring it based on a claim that Scholze and Stix are ignorant incompetents. It’s striking (and actually, disturbing) that neither in Mochizuki’s talk nor anywhere in the Lille/RIMS program is there any mention of the Scholze-Stix argument that the proof is flawed. Until Mochizuki or someone else comes up with a convincing rebuttal to Scholze/Stix, very few experts will pay attention to this.

  14. John Baez says:

    Peter Woit wrote:

    Does anyone know what he had in mind by the “everyone got on their horse” comment?

    I don’t know what he meant, but Everett did write a wonderful Ph.D. thesis on the relative state interpretation, which said very little if anything about “worlds” or “branches” — and then Bryce DeWitt and John Wheeler and others got into the act and introduced, or at least popularized, those terms. You can see the whole process of degradation in the book The Many Worlds Interpretation of Quantum Mechanics, edited by DeWitt and Neill Graham, which includes Everett’s thesis followed by essays by DeWitt, Wheeler, Graham and others. It’s sad how Everett gets blamed for other people’s interpretations of his work. I don’t know how much he went along with it.

  15. Jack Morava says:

    Re: theorems that definitely don’t have a clear and unambiguous proof

    Physics is very interesting. There are many, many interesting theorems. Unfortunately, there are no definitions.
    David Kazhdan.

    (stolen from https://www.jmilne.org/math)

  16. John Baez says:

    That’s why category theory and physics work together so synergetically: category theory has tons of great definitions but no interesting theorems. 😜

  17. Low Math, Meekly Interacting says:

    I stumbled on this a while back because I was a big fan of the Eels, long before I knew Mark Oliver Everett was Hugh Everett’s son.

    A letter Hugh Everett wrote to Bryce DeWitt…

    https://www.pbs.org/wgbh/nova/manyworlds/orig-02.html

  18. John McAndrew says:

    John Baez and Peter,

    you might be interested in Everett’s amoeba analogy from an early draft of Hugh Everett’s doctoral dissertation at Princeton Universty:
    https://www.pbs.org/wgbh/nova/manyworlds/orig-01.html

    “The same is true of [sic] one accepts the hypothesis of the universal wave function. Each time an individual splits he is unaware of it, and any single individual is at all times unaware of his “other selves” with which he has no interaction from the time of splitting.”

    How does one interpret this?

    It looks to me that Everett was the first to get on a horse and ride off in some bizarre, speculative direction, eventually crafting the paper that Coleman admires after Wheeler and co reigned in some of his ‘not even wrong’ ideas.

  19. Peter Woit says:

    John McAndrew,

    Thanks. I should make clear that I don’t think the problem with the “splitting into multiple worlds” business is that it’s bizarre or speculative, it’s that it’s meaningless, and pretends to solve a problem that it doesn’t. I’d be curious to hear what Coleman thought of this, but the fact that he doesn’t mention multiple worlds and does explain that the hard problem is understanding how to interpret classical mechanics makes me guess he would have agreed that multiple worlds explain nothing.

  20. TonyK says:

    Peter, this is from the Wikiquote page on Stephen Leacock:

    “Lord Ronald said nothing; he flung himself from the room, flung himself upon his horse and rode madly off in all directions.”

    “Gertrude the Governess”, Nonsense Novels (1911)

    Coleman realised that this quote could be interpreted literally in an Everettian world (or worlds? — syntax fails me here).

  21. Low Math, Meekly Interacting says:

    I am myself struck by the similarity between the quote from Coleman’s lecture and Everett’s expressed point of view, in regards to human experience. In fact, in essence their positions appear to be identical almost down to the wording. The only possible distinction seems a purely philosophical one, i.e. whether or not the notion of a single “reality” is justifiable if one agrees there is nothing but “causal evolution according to quantum mechanics”.

  22. Peter Woit says:

    LMMI,
    Unlike Everett, I don’t see Coleman anywhere mentioning “splitting”. The only place the term “reality” occurs is once in the combination “Quantum Reality”, part of a proposed title for the talk. He seems to have no interest in the usual arguments over “reality”.

    My quantum education was very conventional for the early-mid-seventies, no exposure to Everett, directly or indirectly through Coleman. I distinctly recall being well aware that the obvious and simplest way to interpret QM (without wave-function reduction) was as a theory that applied to everything, including the observer and the observer’s consciousness, that there was nothing about our experience of the world in conflict with this.

  23. Low Math, Meekly Interacting says:

    Hi, Peter,

    I probably should have expressed myself better: They appear to be in 100% in agreement about the scientific content. All that’s left to disagree about appears to be the “reality” of other possible experiences, including whether or not that’s even something worth pondering.

  24. S says:

    I guess, Peter, that I’m confused about how one could take a unitary-only / Everettian / Colemannian approach to QM and *not* talk about many “worlds” or at least, if the “worlds” seem confusing, about many parallel non-interacting observers who all think that they are the same person. You end up with a wave function on configuration space that is extremely sharply peaked over various “classical” configurations, each of which corresponds to a different observer + environment, and if one takes each of those observers seriously, then there are a bunch of different Peters, who will have made (say) different moderation decisions about the value of this comment.

    Call it worlds or don’t — and I can see where talk of “branching” is maybe not helpful (although it’s a reasonable description of decoherence in the Everett model, no?) — but this feature seems unavoidable at that point.

    And so do problems with getting the Born rule out of the picture.

    One thing I’ve wished is that I understood better what your — Peter’s — alternative to this view is when you talk about unitary-only without many-worlds.

  25. Peter Woit says:

    S,
    I just don’t think saying “my initial more or less classical state branched into multiple other more or less classical states and I’m in one of them, other mes are in the others” explains anything about anything, or answers any kind of meaningful question. You can think about the world that way if you want, but you haven’t solved any problem by doing so.

    There are endless problems with making any sense out of “branching”, in practice that’s nothing but a meaningless word standing in for not understanding the measurement problem. What you’re doing is trying to recover a classical description of reality, by ignoring the quantum nature of reality except at these mysterious places where classical reality “branches”. I take Coleman as saying it’s a mistake to try to describe reality classically, there is only quantum reality. Put differently, classical behavior is a complex, hard to understand emergent phenomenon. If you take that as the fundamental nature of reality and try and express everything in terms of it, you’re going to end up with a confusing and paradoxical conceptual framework.

  26. Peter Shor says:

    Some questions that I think show that many-worlds doesn’t actually solve the “measurement problem”.

    How do two photons in an Aspect-type experiment that are well separated in space know whether they’re supposed to be in the same “world” or not? Do the “splits” between worlds happen everywhere in the universe at once (and does this violate the theory of relativity?) or do they start at a single point and radiate out like waves the speed of light (and in this case how do two world-splitting waves approaching each other know which worlds in one of these waves should be merged with which worlds in the other?)?

  27. Jim Akerlund says:

    Peter,
    Of all your comments on the Coleman lecture, I at least expected a comment about this statement from the lecture.

    “There’s no point in trying to wow him with the anomalous
    magnetic moment of the electron or the behavior of
    artificial atoms that we just heard about or anything like
    that, because he is so deeply opposed to quantum mechanics
    and so old and stubborn that as soon as you
    start putting a particular quantum mechanical equation
    on the board his brain turns off, rather like my brain in
    a seminar on string theory.”

  28. Homodyne says:

    Coleman’s derivation has an analogue in terms of classical probability.

    If we imagine a system, say a coin, that is probability p to be heads and 1-p to be tails we could write it as:
    p[H] + (1-p)[T]

    Then imagine a detector which enters the state D or E depending on whether it sees heads or tails.
    Well then after measurement we have:
    p[H,D] + (1-p)[T,E]

    Nobody would read this as “two separate worlds”. As Peter Woit says it doesn’t really solve anything. It’s just tortuous semantics for a basic probability assignment.

    What Coleman then goes on to describe is say we do this again with more and more coins then the probabilities essentially go to 1 for histories where the ratio of heads events to the total number of event is p and converges to 0 for other histories. In essence it’s the law of large numbers.

    The only mystery/issue is that in the case of a quantum system and recording device we would have:
    c|H,D> + d|T,E>
    where c and d square to p and 1-p.

    The issue/thing to be explained is that we only recover the same probabilistic reading provided we can only measure the device in the |D>,|E> basis and that other “interference” bases are non-physical such as {|D>+|E>,|D>-|E>}.

    This indeed seems to be the case from empirical evidence, but we need a detailed explanation as to why. Roland Omnes’s famous 1994 book has a good sketch in Chapter 8 (although one would need Chapters 6 and 7 to fully understand it) and I’d also recommend Allahverdyan et al’s paper here:
    https://arxiv.org/abs/1303.7257
    It’s a summary of a much longer paper by them from 2011.

  29. Moshe says:

    One of the issues I have with MWI is that (like many other interpretational issues) it is not specific to quantum mechanics. In fact there is already an old approach to probability called modal realism which is essentially the same as the MWI. The fascinating thing about quantum mechanics is that it is not equivalent to a classical probabilistic system. Focussing on issues that already exist for classical stochastic systems misses all the real mysteries. Another common example is attributing some mystery (like conflict with relativity) to quantum entanglement that already exists for plain statistical correlations.

  30. Homodyne says:

    Moshe,

    Thanks for that. It’s what I was clumsily getting at above. If you treat the classical probability distribution as “real” then one essentially has many worlds for classical probability. I wasn’t aware that it had a formal name, i.e. “modal realism”.

    Of course Spekkens toy model shows that many of the features people commonly say are quantum can be reproduced in a classical theory. For example super dense coding, teleportation, entanglement, no cloning, interference.

    Thus allowing one to focus on what classical probability cannot replicate: Kochen-Specker contextuality and CHSH violating correlations.

  31. John Baez says:

    “Focussing on issues that already exist for classical stochastic systems misses all the real mysteries.”

    Not all of them. Classical probability theory is already deeply mysterious – witness the Bayesian/frequentist arguments about what probabilities actually mean. Any mystery one doesn’t get straightened out in classical probability theory is likely to come back with redoubled force when you start thinking about probabilities in quantum mechanics.

    But yes, quantum theory holds new mysteries.

  32. J Frager says:

    In the paper mentioned above (http://www.kurims.kyoto-u.ac.jp/~motizuki/Explicit%20estimates%20in%20IUTeich.pdf), Mochizuki et al. seem to propose an entirely new proof of Fermat’s last theorem for prime exponents large enough. Has this been checked/confirmed/peer-reviewed? I haven’t seen much discussion on that, although such a claim would seem to warrant it. Have the people involved in the original proof of FLT (Wiles, Taylor, Conrad etc.) expressed an opinion?

  33. Peter Woit says:

    J. Frager,
    It has long been known that a proof of abc can be used to prove Fermat in this way. The problem is that this new paper depends crucially on the part of Mochizuki’s IUT-based arguments which Scholze/Stix have convincingly argued can’t work. As far as I can tell, essentially no one outside of RIMS and Nottingham thinks there is a proof, either in the original work, or in this new one.

    The new work does imply much stronger claims than the earlier IUT papers. Perhaps the most interesting aspect of these is whether any of them can be shown to not be true, providing a direct disproof of Mochizuki’s original work.

  34. Peter Woit says:

    For an example of what the problem is with the multiverse publicity campaign for MWI, check out the latest New Scientist
    https://www.newscientist.com/article/mg24833122-100-if-the-multiverse-exists-are-there-infinite-copies-of-me/
    where you’ll learn that the way to think about quantum mechanics is this:
    “The startling upshot of this view is that there are potentially squillions of versions of you going about their (your?) business in parallel universes.

    Well, sort of. Those other versions of you aren’t really copies, says Sean Carroll, a physicist at the California Institute of Technology: they are individuals who used to be you, but at some point split off and became separate. “You are not spread out over worlds,” says Carroll. “You are here in this world, and there are a lot of other people in other worlds who are closely related to you.”

    As to how many other-worldly relations you have, it is impossible to say. “The number could be infinite or there could be a continuum of worlds rather than a discrete set,” says Carroll. “But the number might also be finite. We’re not sure.””

  35. Moshe says:

    John Baez, I think you know what I mean. But as an aside, it is an interesting sociological phenomena how philosophical discussions of scientific subjects can be completely decoupled from the scientific ones. My impression that people that use probability for a living, for an example as reflected in graduate texts in statistical learning theory, are uniformly Bayesian for well articulated reasons. Similar phenomena can be observed in discussions of quantum mechanics, general relativity, etc. etc.

  36. John Baez says:

    Yes, one great thing about working at the Centre for Quantum Technologies part-time is that when I’m there, I never hear the usual tiresome arguments about interpretations of quantum mechanics.

  37. Godfrey says:

    Anent Mochizuki, Scholze and Stix’s paper seems to have gone?

    http://www.kurims.kyoto-u.ac.jp/~motizuki/SS2018-08.pdf

  38. Peter Woit says:

    Godfrey,
    The links may have changed. Mochizuki’s page discussing this is here
    http://www.kurims.kyoto-u.ac.jp/~motizuki/IUTch-discussions-2018-03.html
    and it links to the Scholze-Stix paper as
    http://www.kurims.kyoto-u.ac.jp/~motizuki/protectedpdf-2018-08/SS2018-08.pdf

  39. random reader says:

    That Mochizuki’s claimed results imply effective ABC was known and published on the arxiv in 2016, by Vesselin Dimitrov. This goes back to Dimitrov’s MathOverflow postings in 2012 on the implications of (incorrect, overly strong) claims in earlier versions of Mochizuki’s papers, https://mathoverflow.net/questions/106560/philosophy-behind-mochizukis-work-on-the-abc-conjecture . Back then, Mochizuki acknowledged correspondence with Dimitrov and (independently) Venkatesh about those problems in 2012, and apparently revised his papers in response.

    Now in the new article by Mochizuki et al, they elliptically refer to someone who must be Dimitrov as a mysterious “one mathematician” who had some related results (which they disparage) using Belyi maps (which are indeed used in the 2016 arxiv paper) but whose work they say they cannot find written down anywhere. As though Mochizuki and company could not get back in touch with Dimitrov or do a web search for any papers he might have written about this.

    Not naming the person gives some not very plausible deniability, but it sure looks like Team Kyoto has graduated from denial of problems to outright erasure of work outside their clique.

  40. David Yager says:

    Fermilab’s Muon g-2 pages have been updated recently – they had been left unchanged since 2015! Is the announcement near to hand? Probably not this year …
    https://muon-g-2.fnal.gov/

    Still no leaks to here or to Resonaances – it’s just a shame how information no longer wants to be free.

  41. Anot Heran Dom says:

    @random reader,

    I was thinking it might have been Taylor Dupuy, but you’re right, Dimitrov seems more likely. I think it extremely bad form to not even name the person, let alone the disparaging remarks, verging on academic dishonesty. Imagine if people went around merely alluding to others’ prior results but not naming them or giving a citation.

  42. F. Zaldívar says:

    Vesselin Dimitrov’s 2016 preprint: https://arxiv.org/abs/1601.03572

  43. random reader says:

    Footnote on Mochizuki from last week’s arxiv.

    Jakob Stix, who together with Peter Scholze went through the Mochizuki ABC papers and diagnosed the mistake, has found an error that went unnoticed since 1997 in a famous paper by Caporaso-Harris-Mazur. Stix also contributed a lemma to the article by C-H-M announcing and fixing the mistake.

    https://arxiv.org/pdf/2012.14461.pdf

    Interesting data point on Stix’ ability to find errors.

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