4 ms·

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

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.

seanhunter 2y ago
I'm not sure that's true. My quick searching around is that the first paper proposing strings as a possible description of space and time is Nambu, Nielssen and Susskind in 1969 whereas Langlands first stated his conjectures in his letter to Andre Weil in 1967[1] (ie before string theory had even really kicked off mathematically which didn't happen until Ed Witten got involved in the 1980s). In his letter, Langlands seems to motivate the conjectures entirely from abstract algebra and topology (although this is way above my mathematical pay grade at the moment so I'd be more than happy to accept I misunderstand). [1] https://publications.ias.edu/rpl/section/21 https://publications.ias.edu/rpl/section/21 and https://publications.ias.edu/sites/default/files/letter-to-weil-1967-01_rpl_1.pdf https://publications.ias.edu/sites/default/files/letter-to-w... in particular
bdjsiqoocwk 2y ago
String theory is still the only self consistent theory of quantum physics.... I'd say that's extremely successful.
- defrost 2y ago
  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.
  - bdjsiqoocwk 2y ago
    > 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.
    - jerf 2y ago
      "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.
      - bdjsiqoocwk 2y ago
        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.
        noone_important 2y ago
        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.
        bdjsiqoocwk 2y ago
        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.
  - moomin 2y ago
    Indeed. Ptolemaic models of planetary movement work fine if you add enough variables.
    - defrost 2y ago
      You win two additional epicycles for that comment kind peer.

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.

seanhunter 2y ago

I'm not sure that's true. My quick searching around is that the first paper proposing strings as a possible description of space and time is Nambu, Nielssen and Susskind in 1969 whereas Langlands first stated his conjectures in his letter to Andre Weil in 1967[1] (ie before string theory had even really kicked off mathematically which didn't happen until Ed Witten got involved in the 1980s). In his letter, Langlands seems to motivate the conjectures entirely from abstract algebra and topology (although this is way above my mathematical pay grade at the moment so I'd be more than happy to accept I misunderstand). [1] https://publications.ias.edu/rpl/section/21 https://publications.ias.edu/rpl/section/21 and https://publications.ias.edu/sites/default/files/letter-to-weil-1967-01_rpl_1.pdf https://publications.ias.edu/sites/default/files/letter-to-w... in particular

bdjsiqoocwk 2y ago

String theory is still the only self consistent theory of quantum physics.... I'd say that's extremely successful.

defrost 2y ago
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.
- bdjsiqoocwk 2y ago
  > 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.
  - jerf 2y ago
    "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.
    - bdjsiqoocwk 2y ago
      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.
      - noone_important 2y ago
        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.
        bdjsiqoocwk 2y ago
        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.
- moomin 2y ago
  Indeed. Ptolemaic models of planetary movement work fine if you add enough variables.
  - defrost 2y ago
    You win two additional epicycles for that comment kind peer.