@vzn I'm not sure it's fair to blame Gödel for breaking Hilbert's consistency program: the problem was there all along, and just waiting for someone to notice. Possible Hilbert would have gotten there eventually.
@dmckee undecidability is a ubiquitous phenomenon but maybe something in the way that Turing/ Godel introduced it verged on "overkill".... it was seen as something as a "stop sign/ point of no return" for a problem. nowadays approaches for at least some few )( undecidable problems/ areas are still studied/ researched....
maybe some few big surprises yet remain in the field/ area of automated thm proving...
@vzn thanks! I'll look at that when I get the time next! Which could be a week since my plan right now is to do lie theory for three hours, sprint to my dorm, sleep, go to class, study lie theory (GOTO 10)
A (very) minor advantage of teaching at a direction state university in a small town is that I've only been approached by one person with a revolutionary new theory in the two years I've been here.
I sometimes got more than that when I was a postdoc at a first rank state university.
@Icosahedron The second most reproduced of all of Sid Harris' cartoons I'd warrant. But I like some of his more obscure stuff better.
@0celo7 Engineers are a different breed ... they care about grades so their grades are something vaguely like a correlate with their learning speed. Or something.
Too many physics majors are slackers with real potential to treat GPA as predictive of ability in that population.
Or that'd be my take, anyway.
On another note, just minutes after braging about how little I've been bothered by crackpots I got two crackpot emails advertising three theories between them.
So someone with a closed question is trying to circumvent the closure by adding answers (as they come) into the body of the question...is there anything to do about that?
@KyleKanos Outlook in the browser---what the school insists I use for official coorespondence---doesn't have a "mark as spam" option. I've been assuming that "mark as junk" does the same thing, but I don't actually know that.
@0celo7 One of the theories was the the Higgs detections are all wrong because they are really detecting xenon nuclei.
@0celo7 He picked that particular nucleus because the mass is about right. But either the decay behavior or its energy loss (if this is decently measured, don't know) would rule it out.
@0celo7 yes, more or less - what I mean is that the hypothesis that the Higgs is spin-1 has been excluded at some large confidence level, and the hypothesis that it's spin-2 has been excluded at some lesser but still large confidence level, but the spin-0 hypothesis is still going strong
Take this question:
Dark matter clumping
This is an excellent question and the answer is not at all obvious. I assume it was downvoted just because it's a duplicate, but is this really appropriate? Downvoting can be used to make questions disappear from the home page, and also to deter people f...
Assuming inter-universal travel is possible, can a perfectly mathematically describable universe exist inside a multiverse?
If it could, would that mean that the multiverse is mathematically describable as well?
I must point out, that a perfectly mathematically describable universe should be pe...
Correct me if I'm wrong, but when speaking in terms of sets, the universe is defined as the set of which any other set is a subset. If I might extend that to cosmological terms, would not the universe be that in which all things, concepts, and abstractions exist? Therefore any other cosmos or "multiverse" could naturally be defined as existing within the universe. Or is that extension of a definition not valid?
It could be any other set is an element of the universe set. I might have been imprecise about that
@ACuriousJim The mathematical universe (collection of all sets) is not a set; If it was, you would have logical paradoxes like the Russell's antinomy. These type of collections are called proper classes and cannot be formalized in an axiomatic fashion like sets
@ACuriousJim Let's say that formalized mathematical logic cannot help in "proving" the validity of your point. In more relaxed philosophical terms, you may have a good line of reasoning... ;-)
@ACuriousJim I think that @DavidZ 's point is that in nowadays terminology, astrophysics means pertaining physics applied to astronomical objects; while stellar physics means the physics of stars
I'm no astrophysicist, but I believe nebulae, galactic structure, black hole accretion disks, planetary systems, etc. all fall under astrophysics but not stellar physics as it is normally defined
Does anyone know a representation theory (of Lie algebras) book that is rigorous yet physically oriented? I'm currently reading, and starting to dislike, Fuchs & Schweigert for not being rigorous enough (it doesn't even have clear definitions!)
@ACuriousJim Glad you approve ;) Also, writing it was a bit of a rollercoaster between feeling happy about covering stuff and feeling bad about treating stuff superficially
@Danu I hear that. But explaining more about how $T_{\mu\nu}$ represents the matter-energy content would have required much more space (not to mention the math concepts I know you're fond of). So I can't be unhappy that you chose not to write a full text
It seems someone wasn't happy with my appraisal a few months back of that paper that said there was no big bang if you use bohmian trajectories. Apparently their issue with what I said is that I'm not recognizing that bohmian trajectories are geodesics in bohmian mechanics.
When I replied that the paper still didn't show that bohmian mechanics was a valid tool to use, they claimed it was a perfectly valid and legitimate way to include quantum effects in GR and create a general theory of quantum gravitation
I would like to ask if questions about connections between different interpretations of physical theories can be posted(let me be exact: an example of a question like that is "What are the connections between Relational and Bohmian Quantum Mechanics?).
Thank you.
@KyleKanos Yeah, I pointed out that if the paper rests on the assumption that this is quantum gravity, then it is in far more trouble than I initially appraised
classical this, classical that, Bell is wrong this, realism that
A claim of the existence of the existence and correctness of a Bohmian theory of quantum gravity is something I wouldn't have thought he'd claim. But I was apparently wrong
Given the significant interest and work done into developing QG, claiming that the general theory of it would be something like this would be very controversial. It would require a great deal of elaboration and validation. None of which is provided in the short letter that was written. Essentially, it rests the bulk of the paper on the assumption that bohmian + GR = QG. That definitely needs to be shown more rigorously before this paper can be given the significant focus it is asking for. — ACuriousJim5 hours ago
The Dark Side says shaddap all of you! I have 498 helpful flags, have flagged two obvious off-topic questions a few minutes back. And you ridiculous people are wasting your time in chat instead of reviewing. :: Fuming ::
@TheDarkSide I don't think so. The question I recently posted an answer to wasn't being upvoted all too much, yet it went into the queue somehow. I think it may be something different.
Relatively recent question with at least 2 upvotes and above average rate of new views. Being frequently edited or answered or having highly voted answers helps too
Then a scaling factor is applied so only a few questions from any one site can make it to the HNQ list
@ACuriousMind There's an easy counterexample in $n=2$.
Consider the obvious determinant 1 anti-symmetric $2\times 2$ matrix. It commutes with all $2\times 2$ anti-symm matrices, yet is not a multiple of the identity.
@Danu Ah. That is the only counterexample though, I think. My argument breaks down there because $\mathrm{SO}(2) \cong \mathrm{U}(1)$ is abelian to begin with
@ACuriousMind What guarantees that this will not happen in any other dimensions?
Also, is there any hope of you recommending me a decent rigorous yet physics-application-oriented textbook on Lie groups/algebras and (most importantly) their representations?
@NeuroFuzzy We're just talking about representation theory! :D
@Danu Well, the better way to phrase this would probably be that $\mathbb{R}^2$ is not an irreducible rep of $\mathrm{U}(1)$, so Schur's lemma doesn't hold
In any case, the original statement I wanted to prove is that $x\mapsto -x^T$ for $x\in\mathfrak{sl}(n)$ does not arise as $A x A^{-1}$ for $A\in SL(n)$.
@Danu Here's why my argument fails: You can only use Schur's lemma in the form I want to use it if we are over an algebraically closed field, so for the real reps of $\mathrm{SO}(n)$, my argument fails completely
also I'm st00pid for asking this but why does every self-intertwiner over a finite-dim irred. $\mathfrak{g}$-module $V$ over an alg. closed field have an eigenvector? I feel it's related to polynomial algebra and the fundamental theorem but idkkkkk
@ACuriousJim Well, I guess frantic first-post reviewing has a big role to play there. Plus, I only have a total of 48 answers and 3 questions on this site. So, FPR and flagging is all I do here :)
Ah, and the self-intertwiner simply has an eigenvector because the roots of the characteristic polynomial are the eigenvalues of an endomorphism, and every non-constant polynomial has a root over an algebraically closed field
Take this question:
Dark matter clumping
This is an excellent question and the answer is not at all obvious. I assume it was downvoted just because it's a duplicate, but is this really appropriate? Downvoting can be used to make questions disappear from the home page, and also to deter people f...
Assuming inter-universal travel is possible, can a perfectly mathematically describable universe exist inside a multiverse?
If it could, would that mean that the multiverse is mathematically describable as well?
I must point out, that a perfectly mathematically describable universe should be pe...
I would like to ask if questions about connections between different interpretations of physical theories can be posted(let me be exact: an example of a question like that is "What are the connections between Relational and Bohmian Quantum Mechanics?).
Thank you.
