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

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

@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

Why not?

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

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?

@ACuriousMind constant functions have only degenerate critical points

The condition basically means they're isolated

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

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

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

@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

Why would I want to ride a monkey?

'cuz it's avant garde?

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

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

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

@ACuriousMind but are they actually testable?

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

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

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

that dont violate QM

@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

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

I'm not sure I understand the question

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.

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

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)

@dmckee Ah, good to know :)