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by esperent
1170 days ago
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> most physicists would come down on the other side of the issue. What's your reason for saying this? I'm more on the mathematical side of things so I don't know that many physicists. But it's been my understanding that equations that are extremely difficult to solve, impossible to solve except numerically, or involve infinities that can't be explained, are a major pain point for physicists. I mean, that's the entire premise of this article. |
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- I'm a professional physicist and most people I know professionally think this way. People like symmetry, it helps clarify things, simplify things, provides powerful principles. If the cost is practical difficulties, well, that's just the cost of doing business; the physical understanding offered by simpler rules is beneficial. I know at least 2 people mentioned in the article would agree with that.
- I have no conceptual problem saying that the only solutions are numerical in nature if the principles are clear. Nobody promised physics should be easy. In fact some of the people mentioned in the article also have shown how their formal understanding might unlock better numerical methods!
- Some infinities are worse than others, and a modern effective field theory perspective makes me not worry about most examples.* With a Wilsonian understanding, renormalization is perfectly simple to understand. For theories which have perturbative UV fixed points you can formulate a lattice discretization which flows to that fixed point and you never encounter any infinity along the way.
Theories without a perturbative UV fixed point, well, that's where the trouble lies. Either there is no UV fixed point, in which case the theory is not valid for all energy scales and the troubling divergences point to an energy scale beyond which your theory is invalid. Or there IS a UV fixed point but it can only be found nonperturbatively.
Handed a QFT with no perturbative UV fixed point, how should you decide?
Well, one step back: should you, as a physicist, care?
For instance, why should we worry whether QED as a standalone theory is UV-complete? We know that in the real world electrodynamics mixes with the weak force at high energy. So whether QED as a standalone theory is UV-complete is a question that I'm not worried about. It is an interesting mathematical question, and that can only be answered with new techniques, such as resurgence. For standalone QED it's a question of pure mathematics, as far as anyone can tell. That's what these tools are good for, at the moment.
HOWEVER. I do admire the program of trying to show that more quantum field theories even exist mathematically, beyond the handful that we already know (which tend to have exotic properties). That seems important to me. But if it's false that's ALSO extremely interesting, it suggests that there are additional principles that we ought to understand.
* except for gravity, where the divergences are SO bad that even the EFT approach has problems.