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Monumental proof settles geometric Langlands conjecture

(www.quantamagazine.org)
203 points jandrewrogers | 5 comments | 26 Jul 24 17:14 UTC | HN request time: 0.204s | source
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slanderaan01 ◴[26 Jul 24 20:44 UTC] No.41082121[source]▶
I'm curious what applications there might be if any in number theory. If I recall, langlands had motivations from string theory concepts which ultimately wasn't as successful as hoped in physics.
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bdjsiqoocwk ◴[27 Jul 24 12:18 UTC] No.41086092[source]▶
String theory is still the only self consistent theory of quantum physics.... I'd say that's extremely successful.
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defrost ◴[27 Jul 24 12:26 UTC] No.41086137[source]▶
Not particularly, it's so open ended it describes an enormous landscape of possible universes and lacks any specific testable predictions for our universe.

Unless it's been firmed up a great deal in recent times.

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bdjsiqoocwk ◴[27 Jul 24 12:33 UTC] No.41086167[source]▶
> lacks any specific testable predictions for our universe.

Predicts that special relativity holds up at all scales (check, according to all evidence so far), predicts general relativity at low energy scales (check).

So it's false that it has no testable predictions. None of this happened "in recent times" though, it's been understood for a long time.

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jerf ◴[27 Jul 24 20:08 UTC] No.41088988[source]▶
"No testable predictions" is shorthand for "makes no testable prediction that don't match our other theories, making it impossible to distinguish between string theory and relativity+QM". We know the latter doesn't really work, but without the ability to distinguish, it isn't clear that string theory "works" either. It really needs a solid new testable prediction.
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1. bdjsiqoocwk ◴[27 Jul 24 21:43 UTC] No.41089538[source]▶
If you grant arbitrarily advanced technology then "testable predictions" absolutely do exist, most immediately on the cross sections of basically every particle. We can't perform such experiments now, but that's a problem with the technology, not with the theory.

Imagine if someone had said 30 years ago that the "higgs boson theory" is a failure because we couldn't then perform the experiments to detect it.

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2. noone_important ◴[28 Jul 24 08:53 UTC] No.41092040[source]▶
This comparison is not really fair. On the one hand you have the prediction of a scalar excitation with a lot of restrictions (cosmology and naturalness). On the other hand you have a giant framework that can predict or fit almost anything.

Don't get me wrong, I still regard string theory as a big success. It taught us a lot about mathematics and field theories in the last decades. However the predictive nature is basically non-existant so far.

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3. bdjsiqoocwk ◴[28 Jul 24 17:03 UTC] No.41094407[source]▶
Nonsense. It can't predict everyone, in particular it won't predict special relativity bring violated.

In addition you haven't addressed the main point here which is that when some people say "can predict" they mean "in principle it can predict" whereas other mean "can predict today with currently available technological means". Regarding the former: yes it can. I already gave the example of one such prediction, but here's another one: all particles niches have stringy modes in their spectra. Regarding the later: maybe, but thats a problem with our technology, not with the theory.

I feel this conservation is going in circles already.

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4. noone_important ◴[28 Jul 24 17:38 UTC] No.41094643{3}[source]▶
Just because they are not mainstream, you definitely can have lorentz violation in string theory [0]. Spontaneous symmetry breaking can lead to induced finsler geometries, which can basically have multiple light cones (when there was the "faster than light neutrinos" result on the table. Some people used finsler spacetime to explain them).

So you made your prediction only by choosing an axiom.

There is a reason that even some proponents of string theory call it the theory of anything.

[0] https://arxiv.org/abs/0708.2250

5. jerf ◴[29 Jul 24 13:48 UTC] No.41100416[source]▶
"If you grant arbitrarily advanced technology"

I don't, thus neatly resolving your issue.

Neither does anybody else. Testable means something like testable today or in the designable future and it always has.

As for the fact this may mean a true theory is not testable today even though some hypothetical technology in the hypothetical future wielded by hypothetical beings could hypothetically resolve the problem, well, welcome to the universe we live in. This is not special pleading applied only to string theory. It's evenly applied to everything. It's just that string theory gets hit by this particularly hard, although not uniquely so (to the best of my knowledge, loop quantum gravity is also rather short on testable predictions). The only utility of quadruply hypothetical advances is to science fiction authors. And I've greatly enjoyed many such stories. But it's important to distinguish between science fiction and what we can do in reality.