The Mathematical Question From Which All Answers Flow

I’m beginning to suspect that there are actually (at least) two different theoretical HEP physicists named Nima Arkani-Hamed out there. One of them (who I’ll call Nima1) believes the way to understand the fundamental nature of physical reality involves extremely complicated extensions of the Standard Model, with large numbers of parameters tuned to avoid conflict with observation, and possibly hundreds or thousands of extra fields thrown in for good measure. He also seems to like the multiverse and anthropic explanations. I have a lot of disagreements with Nima1, most recently discussed here.

The second Arkani-Hamed (Nima2) has a completely different point of view, one quite close to my own, although he may be even more of a mathematical mystic than I am. Natalie Wolchover has recently talked to Nima2 and written about it for the New Yorker. Nima2 is in love with the deep mathematical structure of physics and the way it appears in different aspects:

Nima Arkani-Hamed, a physicist at the Institute for Advanced Study, is one of today’s leading theoreticians. “The miraculous shape-shifting property of the laws is the single most amazing thing I know about them,” he told me, this past fall. It “must be a huge clue to the nature of the ultimate truth.”

Wolchover expands on this idea of multiple ways of expressing the same underlying mathematical structure:

The existence of this branching, interconnected web of mathematical languages, each with its own associated picture of the world, is what needs to be understood.

This web of laws creates traps for physicists. Suppose you’re a researcher seeking to understand the universe more deeply. You may get stuck using a dead-end description—clinging to a principle that seems correct but is merely one of nature’s disguises. It’s for this reason that Paul Dirac, a British pioneer of quantum theory, stressed the importance of reformulating existing theories: it’s by finding new ways of describing known phenomena that you can escape the trap of provisional or limited belief. This was the trick that led Dirac to predict antimatter, in 1928. “It is not always so that theories which are equivalent are equally good,” he said, five decades later, “because one of them may be more suitable than the other for future developments.”

Today, various puzzles and paradoxes point to the need to reformulate the theories of modern physics in a new mathematical language. Many physicists feel trapped. They have a hunch that they need to transcend the notion that objects move and interact in space and time. Einstein’s general theory of relativity beautifully weaves space and time together into a four-dimensional fabric, known as space-time, and equates gravity with warps in that fabric. But Einstein’s theory and the space-time concept break down inside black holes and at the moment of the big bang. Space-time, in other words, may be a translation of some other description of reality that, though more abstract or unfamiliar, can have greater explanatory power.

Nima2 is obsessed with exactly the same mystical mathematical issue that I am: what’s the right mathematical question that has as answer the Standard Model and GR?

To Arkani-Hamed, the multifariousness of the laws suggests a different conception of what physics is all about. We’re not building a machine that calculates answers, he says; instead, we’re discovering questions. Nature’s shape-shifting laws seem to be the answer to an unknown mathematical question…

Arkani-Hamed now sees the ultimate goal of physics as figuring out the mathematical question from which all the answers flow. “The ascension to the tenth level of intellectual heaven,” he told me, “would be if we find the question to which the universe is the answer, and the nature of that question in and of itself explains why it was possible to describe it in so many different ways.” It’s as though physics has been turned inside out. It now appears that the answers already surround us. It’s the question we don’t know.

I’m not sure the Amplituhedron is the right path to the “tenth level of intellectual heaven” and finding the “mathematical question from which all the answers flow”, but I’m completely sympathetic with Nima2’s motivation and quest.

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16 Responses to The Mathematical Question From Which All Answers Flow

  1. Warren Siegel says:

    Nima2 = Douglas Adams?

  2. Maybe this provides the first compelling evidence in favor of the existence of the multiverse?

  3. Peter Woit says:

    Francois Loeser,
    What’s confusing here is the continual tunneling back and forth between the two different Nima1/Nima2 universes.

    All,
    I’m wondering: has anyone ever seen Nima1 and Nima2 in the same place at the same time? He gives a lot of talks. Has anyone ever seen one containing both an inspirational segment on the existence of a deep mathematical answer to all our questions AND a segment on how split SUSY is the way to go?

  4. Low Math, Meekly Interacting says:

    Maybe he’s normally in a superposition, and only collapses into one form or the other depending on the kind of question he’s answering.

    When you posted that latest entry, I wondered immediately what happened to all the amplitude stuff. Guess this sort of answers the question.

    The article makes a lot of references to Feynman. I recall from watching the videos (and from reading QED) Feynman’s frustration with getting answers out of QCD using the methods he’d helped invent. I gather there are lots of better ways to do it nowadays, but they don’t seem to get to the heart of what was bothering him, namely his intuition that the approach was simply wrong on some level, and only good as an approximation. He found it hard to believe that nature really does all these calculations, and that there must be a better way that doesn’t involve accounting for an infinite number of “paths” to get to the result.

    Even if the radical interpretation of the amplituhedron is totally off, if it produced a way to do calculations in a realistic theory a lot easier, that seems like such a great use of one’s time. Odd we don’t hear about this version of the man more often in the pop-sci press.

  5. Peter Woit says:

    LMMI,
    Everyone would like a more insightful formulation of QCD, I have no idea if the amplitudes program has anything promising in that direction. The over-the-top claims I’ve seen tend do be of the “we’re going to replace space-time”, not “we’re going to solve QCD” variety.

    As for the invocation of Feynman, the peculiar thing is that both Nima1 (complicated BSM models that evade experiment) and Nima2 (the mathematics-physics mystic) seem very far away from what Feynman would find congenial.

  6. Martin S. says:

    When you interact with him, you measure him. He is clearly macroscopic, thus don’t be surprised that actual superpositions are not seen. May be if you would put him close to zero temperature, there would be a chance. Though I do not suggest it…
    Hm, the transitions suggest superpositions in between, i.e. a possibility of him approaching really low temperatures. Polar vortex?

  7. Sam Hopkins says:

    Do you know of any examples before the recent scattering amplitudes stuff in which total positivity had important connections to physics?

  8. Amitabh Lath says:

    Do I contradict myself?
    Very well then I contradict myself,
    (I am large, I contain multitudes.)

    -Walt Whitman, Song of Myself.

  9. ay says:

    Are the multiple perfect descriptions a profound property of physics or a mundane property of mathematics – namely that there’s lots of it and it’s all interrelated.

  10. Peter Woit says:

    ay,
    An excellent question. One problem with this essay is that since it’s aimed at such a non-technical audience, there’s no indication of what exactly Arkani-Hamed has in mind, so hard to tell what the origin might of the particular multiplicity of descriptions that he’s interested in

  11. Low Math, Meekly Interacting says:

    Perhaps I misunderstood something, which is not unlikely. The amplituhedron’s heritage (summarized far better than I ever could hope in the link below, so I won’t even try) suggested notable relevance to the difficulties of QCD, specifically its roots in ideas (BCFW) being put to real use for, say, calculating backgrounds in hadron collisions (I’m aware there are many others). Regardless of what it all “means” about space-time and so on, if the amplituhedron work is to some extent a simplification or a generalization, then presumably it could be of some benefit for very real-world problems in cutting-edge experimental particle physics. To me that overall story, of how people got from Feynman diagrams to the present tools, is nothing short of heroic, with a lot of contributors doing great physics that makes demonstrable contact with experiment.

    It’s a history that gets short shrift in the pop-sci literature, in my opinion. Just not mind-blowing enough, I guess.

    https://royalsocietypublishing.org/doi/pdf/10.1098/rsta.2014.0248

  12. Peter Woit says:

    LMMI,
    To be clearer, the amplitudes stuff reformulates the problem of computing perturbative QCD amplitudes in a different way, which may be quite important. But, as far as I know, it doesn’t give an approach to understanding non-perturbative QCD, which is the big problem, one where we are lacking a good idea. Recall that these are amplitudes for scattering gluons and quarks, but the physical states are something very different.

    I’m quite a fan of the ideas about how to exploit conformal invariance using twistors being used here, but, again, the problem is that QCD is, non-perturbatively, not a conformally invariant theory. From the early work of Witten on the “twistor-string”, it was clear that this kind of duality with a string was a “weak-weak” duality, unlike AdS/CFT where the weakly coupled string is supposed to be dual to a strongly coupled gauge theory.

    I don’t want to encourage more discussion of amplitudes here though, because there actually was nothing substantive about the topic in this article, it was really about other more “metaphysical” issues.

  13. Pingback: Changing the Question | 4 gravitons

  14. Gil Kalai says:

    Hi Peter, this is an an interesting and funny post, and meeting François is always a joy.

    Let me make the obvious (at least for a mathematician) comment (perhaps Peter also agrees) that there need not be a contradiction between a belief that “the way to understand the fundamental nature of physical reality involves extremely complicated extensions of the Standard Model, with large numbers of parameters tuned to avoid conflict with observation” and the belief in “a mathematical question from which all the answers flow.” It is nice that the same scientist can make progress in both these points of view.

  15. Peter Woit says:

    Gil Kalai,
    The problem is that Nima1 hasn’t actually made any progress, quite the opposite. The only progress in the field of BSM physics over the past 20 years has come from experimentalists showing that the models studied by Nima1 and others, besides being ugly and not explaining anything, also disagree with experiment, to the extent they make any predictions at all.

    Nima2 on the other hand is a mathematical physicist, and has been involved in significant progress in mathematical physics.

    Yes, there’s nothing mathematically inconsistent with the idea that there are mathematically very deep and beautiful ideas at the foundations of physics, which then are completely masked by a complicated, ugly effective low energy limit and mechanism for producing complicated, ugly ground states. The only problem is that there is zero evidence for this. Instead, our best theories are highly constrained by deep mathematical ideas about symmetry, and these get translated directly into what we observe about the world.

  16. Bernhard says:

    Peter,

    I agree with you to some extent but in the end Nima1 has contributed a lot to make these results possible. Experimentalists can only shoot the theories/models that are there to be shot, and Nima was probably the most important theorist during this time providing well-defined models that led to new topologies that could otherwise have been missed. Experimentalists do know how to add a Lagrangian in Madgraph, but to come up with the Lagrangian itself you need a guy like Nima1.

    It is true, every time I was in the audience in schools or conferences with him as speaker I had roll my eyes over some of the over-the-top BS he likes to pull, but it does not change the fact that Nima1 has significantly contributed to the results that came from LHC Runs 1 and 2.

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