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0celouvsky

22:00

I'm thinking about applying the maximum principle on larger and larger balls, then finding a contradiction to it being $\ge 0$ somewhere.

ACuriousMind

@0celouvsky Sounds like something that could be true to me

0celouvsky

@ACuriousMind I'm certain it's true. Exhaust by balls. The maximum of $\mathcal U$ on each ball has to occur on the boundary. But $\mathcal U$ on the boundaries has to $\to 0$ as $r\to\infty$.

Actually I have $\mathcal U=O(r^{-1})$

I guess that means it can't be identically zero

@ACuriousMind So my function $V$ is supposed to denote the "gravitational potential" of the star...is it reasonable to assume it's a Morse function? My advisor says sure because Morse functions are generic.

But that doesn't strike me as physically legit

ACuriousMind

Why not?

0celouvsky

because if I solve some physics problem I'm not guaranteed to get a Morse function?

ACuriousMind

Well, no, but...it's pretty likely? How does a degenerate critical point look, actually? (that's an unrelated question, I just never wondered how one would recognize them aside from the technical condition)

I mean, the non-Morse functions are pretty special points in function space, but in a physical problem, you can usually vary a bunch of parameters smoothyl and therefore also the solution - if these solutions were all non-Morse then you'd have found a pretty awesome way of generating such functions, I'd say

And if the solution is non-Morse for one specific value of the parameters...well, who cares?

0celouvsky

22:17

@ACuriousMind constant functions have only degenerate critical points

The condition basically means they're isolated

ACuriousMind

Well, but degeneracy does not imply non-isolatedness, does it?

It's non-degeneracy that implies isolatedness, but you can have isolated degenerate points...

0celouvsky

No, and admittedly I don't know of an example that's not a nonisolated example.

I'm just saying saying your "average" non Morse function will probably be of that type.

@ACuriousMind x^3 :P

Balarka Sen

22:31

@ACuriousMind if a critical point is not a min/max or a saddle it's a filthy degenerate

Morse lemma says that

eg monkey saddles

ACuriousMind

Why would I want to ride a monkey?

Balarka Sen

'cuz it's avant garde?

Monkey saddle is more like a saddle for a monkey to sit on anyway

Skyler

I got a question for everyone. Would you compare currently believing in a hidden variable theory is about the physicist equivalent of believing creationism?

ACuriousMind

@Skyler No, because hidden variable theories, if done correctly, actually have the same predictive power etc. as the "mainstream" version of QM.

Skyler

@ACuriousMind but are they actually testable?

Quantum AMERICCINO

22:41

Hi everyone. Does anyone know good textbooks on Rashba physics?

ACuriousMind

They're just...clunky, wasteful, and their proponents tend to make claims more grandiose than are warranted by the actual theory, but they are still scientific theories just like the standard version of QM

Skyler

btw, are only non-local hidden variable theories possible or some local hidden variable flavors exist

that dont violate QM

ACuriousMind

@Skyler What do you mean by that? Any "good" hidden variable theory will exactly reproduce the results of standard QM

It might deviate from QM in areas not yet tested by experiment, but that then depends on the specific theory

Skyler

@ACuriousMind well, could it create results that differentiates it from a randomness based QM theory in some untested parameter?

ACuriousMind

I'm not sure I understand the question

Skyler

22:48

To differentiate relativity and previous conceptions about gravity we looked a Mercury during an eclipse. Could a hidden variable theory have some kind of experiment that a quantum model based on randomness would fail to describe.

ACuriousMind

Yes

Foundations of QM are a subtle issue, but at least some of the interpretations/theories claim to have predictions divergent from standard QM, alas, usually not for things we could feasibly test currently

Skyler

@ACuriousMind any examples come to mind?

ACuriousMind

No, I just know that they exist, sorry.

If you're interested in foundational issues, Emilio posted a pretty good talk recently (alas, it's several hours long, I can understand if you don't want to watch it and I don't remember if it gave specific examples of divergent predictions)

Apr 3 at 14:19, by Emilio Pisanty

Rob Spekkens - Foundations of quantum mechanics - QuICC Lecture 1

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Physics Meta

Q: how to find a missing post

Earlier this month I gave a very good answer to a question about the twin paradox. Yet now I can't find the question or answer, either in my page, which supposedly lists all my answers, or by searching for questions on the twin paradox. Where is it?