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Forgive my non specialist questions here, but doesn’t special relativity predict that special relativity is preserved at all scales?

ekjhgkejhgk 10mo ago
No. Special relativity postulates that special relativity is preserved at all scales. It's an axiom. Comes from nowhere. It's assumed. This is what a theory is: assume XYZ is true, and see how much of the world you can explain. Why is XYZ? That theory doesn't explain it. Theoretical physics is: what is the smallest set of XYZ assumptions that can explain other theories. So if you can come up with a theory that's internally self-consistent that _predicts_ something which is postulated by another successful theory, that's a very convincing result.
- drdeca 10mo ago
  Pardon, but, huh? I very much thought that Lorentz invariance was built into the assumptions of string theory. Concluding from “A AND B” that “A”, while it does reach a conclusion that is distinct from the assumption, is not impressive. If string theory does not bake SR into its assumptions, wouldn’t that make the way it is formulated, not manifestly Lorentz invariant? Don’t physicists typically prefer that their theories be, not just Lorentz invariant, but ideally formulated in a way that is manifestly Lorentz invariant? Of course, not that it is a critical requirement, but it is very much something I thought string theory satisfied. Why wouldn’t it be? Like, just don’t combine coordinates in ways that aren’t automatically compatible with Lorentz invariance, right? If you formulate a theory in a way that is manifestly Lorentz invariant, claiming to have derived Lorentz invariance from it, seems to me a bit like saying you derived “A” from “A AND B”. If string theory isn’t manifestly Lorentz invariant, then, I have to ask: why not??
  - ekjhgkejhgk 10mo ago
    Lorentz invariance is built into some descriptions of some stringy theories. For example chapter 1 of the Polchinski, you have the 26-dimensional bosonic string which is constructed to be Lorentz invariance. Obviously in this case it's not a "prediction", but then again, it's just a toy-model. Our Universe doesn't have 26 dimensions and doesn't have only bosons.
    - drdeca 10mo ago
      Ok, so I looked into it a bit, and here’s my understanding: The Polyakov action is kinda by default manifestly Lorentz invariant, but in order to quantize it, one generally first picks the light cone gauge, where this gauge choice treats some of the coordinates differently, losing the manifest Lorentz invariance. The reason for making this gauge choice is in order to make unitarity clear (/sorta automatic). An alternative route keeps manifest Lorentz invariance, but proceeding this way, unitarity is not clear. And then, in the critical dimensions (26 or 10, as appropriate; We have fermions, so, presumably 10) it can be shown that a certain issue (chiral anomaly, I think it was) gets cancelled out, and therefore the two approaches agree. But, I guess, if one imposes the light cone gauge, if not in a space of dimensionality the critical dimension, the issue doesn’t cancel out and Lorentz invariance is violated? (Previously I was under the impression that when the dimensionality is wrong, things just diverged, and I’m not particularly confident about the “actually it implies violations of Lorentz invariance” thing I just read.)
      - ekjhgkejhgk 10mo ago
        > losing the manifest Lorentz invariance. You understand that this have nothing to do with actual Lorentz invariance, yes? It sounds like you don't really understand the meaning of those terms you're using. Do you understand what "manifest Lorentz invariance" means?
        drdeca 10mo ago
        Yes? It means the Lorentz invariance is automatic from the form of the expression, does it not?
        ekjhgkejhgk 10mo ago
        Yes. But when "Lorentz invariance isn't automatic from the form of the expression" it does NOT follow that you don't have Lorentz invariance.
        10mo ago
drdeca 10mo ago
It does, but a number of alternative theories of quantum gravity do not. So, if Lorentz invariance is shown to be violated, this would favor those over string theory.

ekjhgkejhgk 10mo ago

No. Special relativity postulates that special relativity is preserved at all scales. It's an axiom. Comes from nowhere. It's assumed. This is what a theory is: assume XYZ is true, and see how much of the world you can explain. Why is XYZ? That theory doesn't explain it. Theoretical physics is: what is the smallest set of XYZ assumptions that can explain other theories. So if you can come up with a theory that's internally self-consistent that _predicts_ something which is postulated by another successful theory, that's a very convincing result.

drdeca 10mo ago
Pardon, but, huh? I very much thought that Lorentz invariance was built into the assumptions of string theory. Concluding from “A AND B” that “A”, while it does reach a conclusion that is distinct from the assumption, is not impressive. If string theory does not bake SR into its assumptions, wouldn’t that make the way it is formulated, not manifestly Lorentz invariant? Don’t physicists typically prefer that their theories be, not just Lorentz invariant, but ideally formulated in a way that is manifestly Lorentz invariant? Of course, not that it is a critical requirement, but it is very much something I thought string theory satisfied. Why wouldn’t it be? Like, just don’t combine coordinates in ways that aren’t automatically compatible with Lorentz invariance, right? If you formulate a theory in a way that is manifestly Lorentz invariant, claiming to have derived Lorentz invariance from it, seems to me a bit like saying you derived “A” from “A AND B”. If string theory isn’t manifestly Lorentz invariant, then, I have to ask: why not??
- ekjhgkejhgk 10mo ago
  Lorentz invariance is built into some descriptions of some stringy theories. For example chapter 1 of the Polchinski, you have the 26-dimensional bosonic string which is constructed to be Lorentz invariance. Obviously in this case it's not a "prediction", but then again, it's just a toy-model. Our Universe doesn't have 26 dimensions and doesn't have only bosons.
  - drdeca 10mo ago
    Ok, so I looked into it a bit, and here’s my understanding: The Polyakov action is kinda by default manifestly Lorentz invariant, but in order to quantize it, one generally first picks the light cone gauge, where this gauge choice treats some of the coordinates differently, losing the manifest Lorentz invariance. The reason for making this gauge choice is in order to make unitarity clear (/sorta automatic). An alternative route keeps manifest Lorentz invariance, but proceeding this way, unitarity is not clear. And then, in the critical dimensions (26 or 10, as appropriate; We have fermions, so, presumably 10) it can be shown that a certain issue (chiral anomaly, I think it was) gets cancelled out, and therefore the two approaches agree. But, I guess, if one imposes the light cone gauge, if not in a space of dimensionality the critical dimension, the issue doesn’t cancel out and Lorentz invariance is violated? (Previously I was under the impression that when the dimensionality is wrong, things just diverged, and I’m not particularly confident about the “actually it implies violations of Lorentz invariance” thing I just read.)
    - ekjhgkejhgk 10mo ago
      > losing the manifest Lorentz invariance. You understand that this have nothing to do with actual Lorentz invariance, yes? It sounds like you don't really understand the meaning of those terms you're using. Do you understand what "manifest Lorentz invariance" means?
      - drdeca 10mo ago
        Yes? It means the Lorentz invariance is automatic from the form of the expression, does it not?
        ekjhgkejhgk 10mo ago
        Yes. But when "Lorentz invariance isn't automatic from the form of the expression" it does NOT follow that you don't have Lorentz invariance.
        10mo ago

drdeca 10mo ago

It does, but a number of alternative theories of quantum gravity do not. So, if Lorentz invariance is shown to be violated, this would favor those over string theory.