Timeline for What justifies compactifying space and spacetime, in the context of instantons?
Current License: CC BY-SA 4.0
10 events
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| Jul 29, 2018 at 15:00 | history | tweeted | twitter.com/StackPhysics/status/1023584096184946689 | ||
| Jul 29, 2018 at 14:15 | answer | added | David Bar Moshe | timeline score: 2 | |
| Jul 29, 2018 at 11:46 | comment | added | ACuriousMind♦ | I disagree that one has to "physically justify" anything beyond "it matches experiment". Your string analogy is misleading because there's a clear ontology of the "theory of the string" in that it corresponds clearly to the physical string, but there is no such clear uncontroversial ontology for quantum mechanics in general. | |
| Jul 29, 2018 at 11:27 | comment | added | knzhou | @ACuriousMind I mean, I accept that instanton effects are real, and that you would get the wrong answer if you used $\mathbb{R}^4$, but one still has to physically justify taking $S^4$ over $\mathbb{R}^4$. For example, if you're solving for the harmonic frequencies of a string whose ends are attached to walls, you cannot just say "we postulate fixed boundary conditions, because otherwise the calculated frequencies would not match experiment". Instead, you justify those boundary conditions by saying the ends are physically held in place. | |
| Jul 29, 2018 at 11:23 | history | edited | knzhou | CC BY-SA 4.0 |
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| Jul 27, 2018 at 17:05 | comment | added | ACuriousMind♦ | I say at the end of the first section that non-trivial bundles, i.e. instantons, are necessary for their contributions to detectable effects like the axial anomaly. On $\mathbb{R}^4$, you don't get any instanton effects. | |
| Jul 27, 2018 at 17:03 | history | edited | Qmechanic♦ |
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| Jul 27, 2018 at 17:02 | comment | added | knzhou | @ACuriousMind Actually, that answer was one of the "mathematically rigorous sources" I was talking about! As far as I can tell, you pass immediately from $\mathbb{R}^4$ to $S^4$ and argue that if we didn't do that, the mathematics would be boring, since all bundles on $\mathbb{R}^4$ would be trivial. But that doesn't tell me why, physically, one should use $S^4$. Since the choice does have physical consequences, it should have a physical justification. | |
| Jul 27, 2018 at 16:59 | comment | added | ACuriousMind♦ | Large gauge transformations are a topic fraught with pitfalls, cf. physics.stackexchange.com/q/314384/50583, where my answer in passing also discusses an argument for compactified spacetime from instantons. | |
| Jul 27, 2018 at 16:49 | history | asked | knzhou | CC BY-SA 4.0 |