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*inside*black holes), does it mean that now string theory can also get a Nobel prize? (If so, Witten and Schwarz would be most obvious candidates.)

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PAllen

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String theory remains, IMO, a theory framework yet to produce an actual theory. Thus Witten got a Fields medal rather than a Nobel for some of his work. A future scenario might be that that the string theory program evolves to some reasonably well formulated M theory, that gives rationale for some arbitrary features of the standard model, thus gaining more acceptance, while still being unable to make verifiable predictions (perhaps because there is no way to reach relevant experimental conditions for the foreseeable future). I still doubt a Nobel would be given without some more concrete achievement

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MathematicalPhysicist

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A little too late for Kaku's and Horgan's bet:insideblack holes), does it mean that now string theory can also get a Nobel prize? (If so, Witten and Schwarz would be most obvious candidates.)

https://blogs.scientificamerican.com/cross-check/string-theory-does-not-win-a-nobel-and-i-win-a-bet/

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Huh. Seems like an easy bet to me. Surprised Kaku took it. But maybe my perspective is distorted since that was before the LHC.A little too late for Kaku's and Horgan's bet:

https://blogs.scientificamerican.com/cross-check/string-theory-does-not-win-a-nobel-and-i-win-a-bet/

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Vanadium 50

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I don't think that's really what it is for. The citation is "Given that Penrose now got the Nobel prize for a theory that is almost impossible to verify experimentally in a near future (that is, for theorems that predict singularitiesinsideblack holes)

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PAllen

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Except, as noted by @PeterDonis, in the thread on this Nobel, Penrose didn’t actually show any such thing. His contributions were all singularity theorems, showing that singularities were not just a feature of BH with perfect symmetries. That is, he showed singularities were a robust feature of BH, not that BH were a robust feature of collapse.I doubt it. What has string theory ever done for me?

I don't think that's really what it is for. The citation is "or the discovery that black hole formation is a robust prediction of the general theory of relativity”The wordsingularityisn't even mentioned.

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MathematicalPhysicist

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I remember reading somewhere that Steven Weinberg had a nightmare before the commence of LHC, that it wouldn't find signs of SUSY.Huh. Seems like an easy bet to me. Surprised Kaku took it. But maybe my perspective is distorted since that was before the LHC.

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That's the citation, yes, but what Penrose has really done is proving singularity theorems. It looks as if the guys in the Nobel committee have not correctly understood what Penrose has really done.I don't think that's really what it is for. The citation is "or the discovery that black hole formation is a robust prediction of the general theory of relativity”The wordsingularityisn't even mentioned.

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George Jones

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I don't think that's really what it is for. The citation is "or the discovery that black hole formation is a robust prediction of the general theory of relativity”The wordsingularityisn't even mentioned.

In the document "Scientific Background on the Nobel Prize in Physics 2020" released by the Nobel folks, the word "singularity" occurs twenty-three times (including references).That's the citation, yes, but what Penrose has really done is proving singularity theorems. It looks as if the guys in the Nobel committee have not correctly understood what Penrose has really done.

https://www.nobelprize.org/prizes/physics/2020/advanced-information/

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ohwilleke

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More fair to say that the word "singularity" doesn't appear in the citation because it is a term which is less widely known among non-specialists than "black hole".In the document "Scientific Background on the Nobel Prize in Physics 2020" released by the Nobel folks, the word "singularity" occurs twenty-three times (including references).

https://www.nobelprize.org/prizes/physics/2020/advanced-information/

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You have to look at things in context, and not lose sight of the forest before the trees. Prior to Penrose' singularity theorem in his 1965 paper, the consensus of the discipline was diametrically opposite based mostly in a false proof by Lifshitz and Khalatnikov, not too mention a prior barrage by Einstein himself. In other words, not only was it generally seen that there was no need whatsoever for singularities in GR, but a false proof meant that searching for them was a hopeless idealistic endeavor; such false proofs are thematic in the history of physics (e.g. recall von Neumann's proof) and the only purpose they serve in the end is the obstruction of progress, but I digress.That's the citation, yes, but what Penrose has really done is proving singularity theorems. It looks as if the guys in the Nobel committee have not correctly understood what Penrose has really done.

Penrose' 1965 paper proved the first singularity theorems, but prior to this, namely in Penrose 1963, he had already put forward the concept of conformal infinity, which lead to the definition of asymptotic flatness, which again lead to the very idea of an event horizon. The singularity theorem, especially the latter Hawking-Penrose theorem, retroactively as a corollary directly legitimized these notions, directly leading to the standard theory of black holes we have today.

In other words, the theorems didn't arise out of the blue in a vacuum but were intimately linked to his own ideas which served as the original background motivation, which possibly weren't even fully and concretely verbalized prior by Penrose, let alone properly documented.

A simple historiography shows that it was of course completely aligned with Penrose' own personal motivation, which in true classical pure mathematics fashion cared nothing about the consensus of the field, but instead was just an attempt to make concrete his own vague ideas, for their own sake and to satisfy his own curiosity regardless of what the rest of the discipline wanted; this is classic Penrose.

What Penrose did required skill and creativity, but more importantly courage and boldness, namely to directly go against the grain and say based on your intuition that some generally accepted argument or proof is wrong and then follow your own path. Instead of wasting time by showing directly showing the Lifshitz-Khalatnikov argument was wrong, he instead mathematically constructed his own theorem by using new tools, and so demonstrating that the prior argument which represented the consensus of the field was completely irrelevant (again, recall the similarity with Bell's theorem and von Neumann's proof).

Looking at the 1965 paper in isolation, it might seem somewhat mysterious when viewed outside of context of Penrose's motivations. Somewhat regrettably, viewing such matters out of their original context seems to be the default modus operandi of most scientists when evaluating such matters, because of course 'context' needs to be wholly absent in any formally polished mathematical paper, which specifically goes out of its way to not take into consideration the actual historical progression of a discovery including all failed attempts, but instead just focuses on presenting the cleaned up ahistorical finished result, as if it was deductively arrived at in that manner.

To end, Grothendieck's description of the attitude which seems to be characteristic of such once in a generation stellar mathematicians which go against the grain seems especially apt in Penrose' case, so much so in fact that Grothendieck's immortal words could've been spoken by Penrose himself, were it not for the fact of Penrose being far too humble and polite as a consequence of him being the archetype of a distinguished English gentleman:

Grothendieck said:Since then I’ve had the chance in the world of mathematics that bid me welcome, to meet quite a number of people, both among my “elders” and among young people in my general age group who were more brilliant, much more ‘gifted’ than I was. I admired the facility with which they picked up, as if at play, new ideas, juggling them as if familiar with them from the cradle–while for myself I felt clumsy, even oafish, wandering painfully up an arduous track, like a dumb ox faced with an amorphous mountain of things I had to learn (so I was assured) things I felt incapable of understanding the essentials or following through to the end. Indeed, there was little about me that identified the kind of bright student who wins at prestigious competitions or assimilates almost by sleight of hand, the most forbidding subjects.

In fact, most of these comrades who I gauged to be more brilliant than I have gone on to become distinguished mathematicians. Still from the perspective or thirty or thirty five years, I can state that their imprint upon the mathematics of our time has not been very profound. They’ve done all things, often beautiful things in a context that was already set out before them, which they had no inclination to disturb. Without being aware of it, they’ve remained prisoners of those invisible and despotic circles which delimit the universe of a certain milieu in a given era. To have broken these bounds they would have to rediscover in themselves that capability which was their birthright, as it was mine: The capacity to be alone.

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Amrator

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The mathematical basis of AdS/CFT is actually completely independent of string theory, but instead is an almost completely general result from conformal geometry applied to SR i.e. this is quite a generic result in mathematical physics, which can be proven almost trivially in less than a single page:

I) Hyperbolic 3-space is a restriction of the time-like subsection of Minkowski space where the quadratic form is not merely positive but actually set to unity.

II) Then one has to recognize that the projectivization of a particular case of the special linear group - namely SL(2,##\mathbb{C}##) better known as the Mobius transformation - is the Möbius group PSL(2,##\mathbb{C}##), which is equal to the group of orientation-preserving isometries in hyperbolic 3-space.

III) If one identifies the unit ball in ##\mathbb{R}^3## with hyperbolic 3-space and realizes that the Riemann sphere can be seen as the conformal boundary of hyperbolic 3-space, it then directly follows that every transformation from the Möbius group corresponds to a Möbius transformation on the Riemann sphere. QED.

From a historically unsensitive strict formal viewpoint, this makes AdS/CFT practically completely a standard result in mathematics using only the theory of conformal manifolds and a bit of group theory. There are many mathematicians who could've discovered and probably have utilized this correspondence before Maldacena formally gave it a name.

However, within the historical context, it just so happens that the mathematical prerequisites and methods of string theory contains among others those mathematical fields as a subset, while Minkowski space, a canonical object from standard physics, is generically often taken as a starting point. Therefore it is not surprising it was formally discovered within the context of mathematical physics research in string theory.

The specifity of the mathematics of black holes in the context of GR however seems to have been much more of a specific prediction in the context of physics, than the fact that AdS/CFT has experimental analogues in condensed matter theory; as long as our universe is not AdS this prediction is pretty much falsified.

Whether or not those experimental analogues of AdS/CFT in condensed matter are worthy of the Nobel Prize is another question altogether; if they are, then there is a strong argument to make that Hawking and the team that discovered an experimental analogue of Hawking radiation utilizing sonic black holes back in 2014 should've gotten the Nobel Prize.

Lastly, any result being mathematically trivial or not, has no bearing on whether or not it is deserving of a Nobel Prize. What may seem to be trivial in one field can and therefore should be viewed as completely revolutionary in another, especially if this viewpoint is made without precedent contrary to an already dominant viewpoint within said field.

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PAllen

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https://physics.stackexchange.com/questions/505871/where-is-the-proof-of-ads-cft

https://inspirehep.net/literature/558113

and perhaps tangentially:

https://arxiv.org/abs/1808.07522

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I never claimed that AdS/CFT was proven, I instead claimed that the mathematical basis underlying AdS/CFT is proven and that AdS/CFT is just a particular applied model of that more general generically valid result which crosses a few branches of pure mathematics: the goal of mathematical physics is to examine such crossed branches, for historically they tend to naturally contain new physics. With respect to AdS/CFT however, it seems that it is essentially just a restricted case of pure mathematics instead of being a crossing branch containing new physics.

https://physics.stackexchange.com/questions/505871/where-is-the-proof-of-ads-cft

https://inspirehep.net/literature/558113

and perhaps tangentially:

https://arxiv.org/abs/1808.07522

Given the more general basis behind AdS/CFT within conformal geometry, which is already proven, I could care less about the status of AdS/CFT itself and I'm highly skeptical of it having any actual bearing on or relevance whatsoever to theoretical physics in the way that it was originally envisioned, i.e. at best its use in physics seems to be completely pedestrian, namely to say something about some experimental analogues in condensed matter theory, which is trivial because these are actually just "predictions" from geometry.

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On a bit more positive note, I fully agree with the answer given by Chiral Anomly in that thread. Even if AdS/CFT isn't true, it is useful indirectly because it makes us ask some concrete questions which perhaps we would otherwise have never thought to ask. This is completely aligned with Feynman's characterization of two (or more) different theories whose descriptions sound completely different and yet the theories are mathematically identical.

Feynman describes that although some theories may be mathematically identical, they are psychologically very different things because they both might give a man very different ideas: a simple naturally feeling change in the one theory may not be a simple naturally feeling change in the other theory. To paraphrase Feynman: '

Returning to the above link, Chiral Anomaly goes on to make a case that the utility of AdS/CFT as an example of 'experimental mathematics' and I more or less agree: crossing branches of pure mathematics in this manner and then trying to identify concrete mathematical structures which can serve as the basis of new or old theories in the sciences, physics in particular, is a very productive way of doing theoretical physics.

It is like a can of worms is opened, exposing us to whole new way of thinking. Worms are of course small, slippery, mobile, gross and fragile creatures that can be hard to grasp. Similarly, the correct idea is difficult to grasp as we are within mathematics literally grasping in the dark; even if we have already had the right idea in our hand we may just reflexively have let go because it didn't conform to our aesthetic standards, i.e. we find it too gross to appreciate its beauty. And having let go in the dark, the worm quickly escapes not to be found again.

In this analogy, a trained fisherman has developed an intuition of which worms appeal to which types of fish and knows where and when the fishes are likely to bite best. The fisherman knows which worm is most useful for the task of catching the biggest fish; because of this he isn't put off by the worms: he can appreciate each worms beauty as well as their utility. He gets up early, gets ready, prepares his boat and fishing rod, goes to the correct spot in the lake, hooks the worm and puts out his rod, solemnly waiting to haul the big fish.

Finally returning to physics, AdS/CFT would just be one of the worms from this can - i.e. pure mathematics structures that link conformal geometry and group theory - while the right worm for the job of catching the biggest fish - i.e. the unification QM and GR - is still unknown. If this 'right worm' happens to be in the same 'can' as AdS/CFT, we would only have to find it and grab it, instead of focusing too long on all the wrong worms . In my personal opinion, AdS/CFT is the wrong worm, while the Hopf fibration might be the right one.

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bobob

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Not that I can think of right off hand. The only claim I recall of such was some nuclear scattering sum rule that _could_ be derived with string theory techniques, but was a lot more complicated than just using generic scattering theory. I don't even recall what particular sum rule it was.Aren't string theory techniques also used in condensed matter physics and nuclear physics?

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Amrator

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https://en.wikipedia.org/wiki/AdS/CMT_correspondenceNot that I can think of right off hand. The only claim I recall of such was some nuclear scattering sum rule that _could_ be derived with string theory techniques, but was a lot more complicated than just using generic scattering theory. I don't even recall what particular sum rule it was.

https://en.wikipedia.org/wiki/AdS/QCD_correspondence

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Theoretical physicists and 3 letter combos, name a more iconic duo.

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Eh, physicists figured out room temperature superconductivity months ago, turns out all you have to do is lower the temperature of the room:

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bobob

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