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When you say "do non-perturbative QFT in curved spacetime" you don't mean "make a risky prediction that could be falsified in non-curved spacetime", right? As I

When you say "do non-perturbative QFT in curved spacetime" you don't mean "make a risky prediction that could be falsified in non-curved spacetime", right? As I understand it the whole purpose of perturbation is to approximate QFT so that it can predict macro-scale things.

pdonis 6y ago
> When you say "do non-perturbative QFT in curved spacetime" you don't mean "make a risky prediction that could be falsified in non-curved spacetime", right? I don't understand what you mean. If I make a prediction in curved spacetime, it's a prediction about what will happen in curved spacetime, not what will happen in flat spacetime. So you can't falsify it by doing an experiment in flat spacetime. You have to do an experiment in curved spacetime. Non-perturbative QFT can certainly make falsifiable predictions about the results of experiments done in curved spacetime, just as it can do so about experiments done in flat spacetime. But the predictions won't be the same, because they are about different experiments under different conditions. > As I understand it the whole purpose of perturbation is to approximate QFT so that it can predict macro-scale things. I have no idea why you would think that. Perturbation theory is applicable to any QFT problem; its first major successes were predicting the Lamb shift and the shift in the magnetic moment of the electron due to quantum field effects. Neither of those are "macro-scale" things. The reason not to do perturbation theory, in cases where it is possible to find a non-perturbative (i.e., exact) solution, is that perturbation theory is inherently an approximation, and why would you settle for an approximation if you can compute the exact answer?
- guscost 6y ago
  > I don't understand what you mean. If I make a prediction in curved spacetime... Perhaps "make a risky prediction that could be falsified if spacetime was in fact not curved" is a better phrasing. Spacetime is spacetime. It's curved. > Perturbation theory is applicable to any QFT problem; its first major successes were predicting the Lamb shift and the shift in the magnetic moment of the electron due to quantum field effects. Oof, looks like I badly underestimated the extremes of scale that are involved here. It turns out you need to use perturbation theory to approximate the solution for something as complex as a single atom of hydrogen. I guess "macro" was an awful choice of word, but that means non-perturbative QFT is even less feasible than I thought for stuff at macro (to say nothing of relativistic) scales.
  - pdonis 6y ago
    > Perhaps "make a risky prediction that could be falsified if spacetime was in fact not curved" is a better phrasing. That doesn't seem to me to be any better. If spacetime is curved, and you make a prediction assuming curved spacetime, you can test that prediction in curved spacetime. The prediction isn't assuming flat spacetime to begin with, so what would it even mean to say it could be falsified if spacetime were not curved? > that means non-perturbative QFT is even less feasible than I thought for stuff at macro (to say nothing of relativistic) scales It means no such thing. Non-perturbative QFT is commonly used in condensed matter physics, which deals with objects of macroscopic size. In fact, IIRC it was condensed matter physicists who first developed non-perturbative QFT methods; the particle physicists adopted them later. As for "relativistic scales", you are aware that relativity has measurable effects even on atomic scales, right? Look up why gold has the color it does, for example. For that matter, our best current understanding of why nucleon masses are what they are has to take relativistic effects into account.
    - guscost 6y ago
      We're talking past each other, I'm just looking for any example of a QM theory predicting something that overlaps with GR, which doesn't rely on a kludge like the renormalization in Loop Quantum Gravity, and therefore hasn't hit a dead end (with LQG this is the "renormalization problem"). I don't think such an example exists - String Theory seems to be in even worse shape, but it does have a much bigger scope. From re-reading your earlier comments it sounds like you think that the final theory will not be built on QM/QFT/Standard Model foundations, and will be different enough that QM and GR will remain incompatible approximations forever. I should have addressed that idea before, and you might be right. Anyway, here we go: > The prediction isn't assuming flat spacetime to begin with, so what would it even mean to say it could be falsified if spacetime were not curved? That's how the whole process works, your theory makes a risky prediction (spacetime is curved, therefore we should see X) and then you go check. If spacetime is actually flat, you're gonna see Y instead! > Non-perturbative QFT is commonly used in condensed matter physics, which deals with objects of macroscopic size. In fact, IIRC it was condensed matter physicists who first developed non-perturbative QFT methods; the particle physicists adopted them later. Pretty cool, when was that? Do you need a fast computer to do that? But it's not relevant to the rest of this, unless this is a good example where GR also predicts something that those objects do (riskily, anything that simplifies to Newtonian dynamics doesn't count). > As for "relativistic scales", you are aware that relativity has measurable effects even on atomic scales, right? Look up why gold has the color it does, for example. For that matter, our best current understanding of why nucleon masses are what they are has to take relativistic effects into account. Yes, I've heard of Dirac. I think you're confusing special and general relativity, and/or I should have used "gravitational scales" instead.

pdonis 6y ago

> When you say "do non-perturbative QFT in curved spacetime" you don't mean "make a risky prediction that could be falsified in non-curved spacetime", right? I don't understand what you mean. If I make a prediction in curved spacetime, it's a prediction about what will happen in curved spacetime, not what will happen in flat spacetime. So you can't falsify it by doing an experiment in flat spacetime. You have to do an experiment in curved spacetime. Non-perturbative QFT can certainly make falsifiable predictions about the results of experiments done in curved spacetime, just as it can do so about experiments done in flat spacetime. But the predictions won't be the same, because they are about different experiments under different conditions. > As I understand it the whole purpose of perturbation is to approximate QFT so that it can predict macro-scale things. I have no idea why you would think that. Perturbation theory is applicable to any QFT problem; its first major successes were predicting the Lamb shift and the shift in the magnetic moment of the electron due to quantum field effects. Neither of those are "macro-scale" things. The reason not to do perturbation theory, in cases where it is possible to find a non-perturbative (i.e., exact) solution, is that perturbation theory is inherently an approximation, and why would you settle for an approximation if you can compute the exact answer?

guscost 6y ago
> I don't understand what you mean. If I make a prediction in curved spacetime... Perhaps "make a risky prediction that could be falsified if spacetime was in fact not curved" is a better phrasing. Spacetime is spacetime. It's curved. > Perturbation theory is applicable to any QFT problem; its first major successes were predicting the Lamb shift and the shift in the magnetic moment of the electron due to quantum field effects. Oof, looks like I badly underestimated the extremes of scale that are involved here. It turns out you need to use perturbation theory to approximate the solution for something as complex as a single atom of hydrogen. I guess "macro" was an awful choice of word, but that means non-perturbative QFT is even less feasible than I thought for stuff at macro (to say nothing of relativistic) scales.
- pdonis 6y ago
  > Perhaps "make a risky prediction that could be falsified if spacetime was in fact not curved" is a better phrasing. That doesn't seem to me to be any better. If spacetime is curved, and you make a prediction assuming curved spacetime, you can test that prediction in curved spacetime. The prediction isn't assuming flat spacetime to begin with, so what would it even mean to say it could be falsified if spacetime were not curved? > that means non-perturbative QFT is even less feasible than I thought for stuff at macro (to say nothing of relativistic) scales It means no such thing. Non-perturbative QFT is commonly used in condensed matter physics, which deals with objects of macroscopic size. In fact, IIRC it was condensed matter physicists who first developed non-perturbative QFT methods; the particle physicists adopted them later. As for "relativistic scales", you are aware that relativity has measurable effects even on atomic scales, right? Look up why gold has the color it does, for example. For that matter, our best current understanding of why nucleon masses are what they are has to take relativistic effects into account.
  - guscost 6y ago
    We're talking past each other, I'm just looking for any example of a QM theory predicting something that overlaps with GR, which doesn't rely on a kludge like the renormalization in Loop Quantum Gravity, and therefore hasn't hit a dead end (with LQG this is the "renormalization problem"). I don't think such an example exists - String Theory seems to be in even worse shape, but it does have a much bigger scope. From re-reading your earlier comments it sounds like you think that the final theory will not be built on QM/QFT/Standard Model foundations, and will be different enough that QM and GR will remain incompatible approximations forever. I should have addressed that idea before, and you might be right. Anyway, here we go: > The prediction isn't assuming flat spacetime to begin with, so what would it even mean to say it could be falsified if spacetime were not curved? That's how the whole process works, your theory makes a risky prediction (spacetime is curved, therefore we should see X) and then you go check. If spacetime is actually flat, you're gonna see Y instead! > Non-perturbative QFT is commonly used in condensed matter physics, which deals with objects of macroscopic size. In fact, IIRC it was condensed matter physicists who first developed non-perturbative QFT methods; the particle physicists adopted them later. Pretty cool, when was that? Do you need a fast computer to do that? But it's not relevant to the rest of this, unless this is a good example where GR also predicts something that those objects do (riskily, anything that simplifies to Newtonian dynamics doesn't count). > As for "relativistic scales", you are aware that relativity has measurable effects even on atomic scales, right? Look up why gold has the color it does, for example. For that matter, our best current understanding of why nucleon masses are what they are has to take relativistic effects into account. Yes, I've heard of Dirac. I think you're confusing special and general relativity, and/or I should have used "gravitational scales" instead.