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> why do you need to [get rid of renormalization]? What does renormalization actually represent? Why does nature do that? Those rules seem kinda tacked-on afte

> why do you need to [get rid of renormalization]? What does renormalization actually represent? Why does nature do that? Those rules seem kinda tacked-on after the fact, to me... > There's nothing about the fundamentals of QFT that says it can only apply to point particles String Theory does not present a serious challenge to QFT or the Standard Model yet, but it is a massive set of additional ideas that are completely unnecessary for either one, and it is a paradigm in vigorous conflict with all of the other proposed completions to the Standard Model right now. If any of these completions ever wins conclusively, it will also "win" against the Standard Model, in the sense that the Standard Model will turn out to be a higher-level approximation of some truer lower-level theory, one which will never explain any of its fine-tuning, and therefore one which will fail. It's very similar to GR vs. Newtonian Dynamics, and I would argue that Newtonian Dynamics is in fact a failed paradigm, and it has been replaced by a better paradigm, no matter how useful it may remain.

guscost 6y ago
Oh, also: > There is plenty of work done in non-perturbative QFT, in which renormalization doesn't even arise at all. Yes, because that stuff doesn't even attempt to be compatible with GR. There is no conflict between the probably-incompatible paradigms of GR and non-perturbative QFT because their respective predictions have zero overlap.
- pdonis 6y ago
  > that stuff doesn't even attempt to be compatible with GR Sure it does. You can do non-perturbative QFT in curved spacetime.
  - guscost 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? 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.
pdonis 6y ago
> What does renormalization actually represent? Why does nature do that? We don't know whether nature "does that"; renormalization is a feature of our models of nature, but not all features of our models of nature are features of nature itself. That's true of any model. > I would argue that Newtonian Dynamics is in fact a failed paradigm You can argue that by defining "failed paradigm" in your preferred way, but you cannot argue that it is a failed paradigm in the sense that Aristotelian physics is a failed paradigm. So by using the term "failed paradigm" to describe both, you are ignoring a very important difference between the two. Similar remarks would apply to the Standard Model in the scenario where one of our candidates for a more fundamental theory has been confirmed and the SM is now just an approximation to that theory in an appropriate regime.
- guscost 6y ago
  > not all features of our models of nature are features of nature itself. Bingo! Therefore our models are each wrong in some way. Paradigm shifts happen when a new model (theory, paradigm, etc) that is "less wrong" conquers an older incompatible model that is "more wrong". That incompatibility is the defining characteristic, not the usefulness or the scope of the model. Of course I consider Newtonian Dynamics to be incompatible with GR, one uses a single frame of reference and the other uses infinite frames of reference.
  - pdonis 6y ago
    > our models are each wrong in some way Yes. > Paradigm shifts happen when a new model (theory, paradigm, etc) that is "less wrong" conquers an older incompatible model that is "more wrong". If you had left out the word "incompatible", I would have agreed with this as a description of what happens as science progresses, though I would still not like the term "paradigm shift" as a term for it. But you included "incompatible", and that makes a huge difference. By your definition, for example, no paradigm shift has happened in physics since Newtonian physics replaced Aristotelian physics, because "incompatible" requires that the old model not be usable as an approximation or special case of the new model. I realize you don't mean "incompatible" to mean that, since you say: > Of course I consider Newtonian Dynamics to be incompatible with GR And I disagree with that, for the reason I gave above (and have stated several times elsewhere in this discussion). The reason I consider that factor so important is the same reason Weinberg, in his review of Kuhn's book, took Kuhn to task for ignoring it: that ignoring it means ignoring how progress is made in science: by coming up with new models that still take advantage of all the true things we learned from the old model. As Weinberg says, if you have one of those T-shirts with Maxwell's Equations on it, you may have to worry about it going out of style, but not about its becoming false. But Maxwell's Equations are "wrong" and "incompatible" by your definition, since they're classical, not quantum, and classical electrodynamics is now replaced by quantum electrodynamics. So your definition basically agrees with Kuhn that no progress is ever made in science; all we can do is lurch from one paradigm to another, each incompatible with the last and throwing away all the knowledge we gained from the last. And in the transition from Aristotelian physics to Newtonian physics, that is what happened. Whatever true things Aristotelian physics had taught people, nobody has been taught since we got rid of it. The same is not true of Newtonian physics. And it will not be true of GR, QFT, or the Standard Model in some future time when we have found a new fundamental theory to which those are all approximations.

guscost 6y ago

Oh, also: > There is plenty of work done in non-perturbative QFT, in which renormalization doesn't even arise at all. Yes, because that stuff doesn't even attempt to be compatible with GR. There is no conflict between the probably-incompatible paradigms of GR and non-perturbative QFT because their respective predictions have zero overlap.

pdonis 6y ago
> that stuff doesn't even attempt to be compatible with GR Sure it does. You can do non-perturbative QFT in curved spacetime.
- guscost 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? 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.

pdonis 6y ago

> What does renormalization actually represent? Why does nature do that? We don't know whether nature "does that"; renormalization is a feature of our models of nature, but not all features of our models of nature are features of nature itself. That's true of any model. > I would argue that Newtonian Dynamics is in fact a failed paradigm You can argue that by defining "failed paradigm" in your preferred way, but you cannot argue that it is a failed paradigm in the sense that Aristotelian physics is a failed paradigm. So by using the term "failed paradigm" to describe both, you are ignoring a very important difference between the two. Similar remarks would apply to the Standard Model in the scenario where one of our candidates for a more fundamental theory has been confirmed and the SM is now just an approximation to that theory in an appropriate regime.

guscost 6y ago
> not all features of our models of nature are features of nature itself. Bingo! Therefore our models are each wrong in some way. Paradigm shifts happen when a new model (theory, paradigm, etc) that is "less wrong" conquers an older incompatible model that is "more wrong". That incompatibility is the defining characteristic, not the usefulness or the scope of the model. Of course I consider Newtonian Dynamics to be incompatible with GR, one uses a single frame of reference and the other uses infinite frames of reference.
- pdonis 6y ago
  > our models are each wrong in some way Yes. > Paradigm shifts happen when a new model (theory, paradigm, etc) that is "less wrong" conquers an older incompatible model that is "more wrong". If you had left out the word "incompatible", I would have agreed with this as a description of what happens as science progresses, though I would still not like the term "paradigm shift" as a term for it. But you included "incompatible", and that makes a huge difference. By your definition, for example, no paradigm shift has happened in physics since Newtonian physics replaced Aristotelian physics, because "incompatible" requires that the old model not be usable as an approximation or special case of the new model. I realize you don't mean "incompatible" to mean that, since you say: > Of course I consider Newtonian Dynamics to be incompatible with GR And I disagree with that, for the reason I gave above (and have stated several times elsewhere in this discussion). The reason I consider that factor so important is the same reason Weinberg, in his review of Kuhn's book, took Kuhn to task for ignoring it: that ignoring it means ignoring how progress is made in science: by coming up with new models that still take advantage of all the true things we learned from the old model. As Weinberg says, if you have one of those T-shirts with Maxwell's Equations on it, you may have to worry about it going out of style, but not about its becoming false. But Maxwell's Equations are "wrong" and "incompatible" by your definition, since they're classical, not quantum, and classical electrodynamics is now replaced by quantum electrodynamics. So your definition basically agrees with Kuhn that no progress is ever made in science; all we can do is lurch from one paradigm to another, each incompatible with the last and throwing away all the knowledge we gained from the last. And in the transition from Aristotelian physics to Newtonian physics, that is what happened. Whatever true things Aristotelian physics had taught people, nobody has been taught since we got rid of it. The same is not true of Newtonian physics. And it will not be true of GR, QFT, or the Standard Model in some future time when we have found a new fundamental theory to which those are all approximations.