The h Bar - 2016-07-27 (page 1 of 2)

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12:01 AM

uh, the problem is, this is a taiwanese book, thus there is no english version

For english books, you can start here which provide you some introductory concepts on forms
https://en.wikipedia.org/wiki/Shape_and_form_(visual_arts)

My interest on art exists, but it is often obscured by the much stronger interest in science. Ever since I start developing curiosity to non science fields in 2015, my art interest also grows with it

What if the wavefunction is actually just superimposed states that a system can take, which only very weakly interacting entities like neutrinos can retain the original undisturbed form of a wavefunction,

whereas for other systems, (using the decoherence interpretation) they interact too strongly to the environment and thus end up becoming an entangled mess and hence lost all the superimposed properties when seen within a subsystem (us and the detector) of this statistically irreversible entangled state

(because the environment has a lot more degrees of freedom than the system itself)

12:25 AM

hi guys I'm having a discussion on IRC about the evolution of the universe. if we could go say 10 mins magically backward in time, would the universe evolve like it did before?

depends on if you believe in free will

my take on it is that no. because for me it's like having 2 identital systems and in QM, making measurements on identical systems yield different results

is it more complicated than that? I'm told this is not valid

I'd love to hear your opinions guys

12:52 AM

Depends on your interpretation of QM

1:04 AM

@Slereah you still up

The general concensus Slereah

if there is one

what would the answer be?

mb

@no_choice99 It's complicated

should I start a thread on the website about it?

Read up on the topic is probably a better time investment

ok

which area of QM in particular should I read about?

1:13 AM

Interpretation and measurement

thanks. sounds a bit scary though. more like philosophy

what do you know about dense flows on the torus

or flows in general

0celo7 you mean Slereah?

yes

unless you know something

I don't ^^

2:02 AM

Sci fi idea: A tensor valued momentum

(To be tested)

What does that even mean

(To be generalised to relativistic case later) Imagine $\frac{dx}{dt}$ not necessary parallel to the direction of momentum. Then you can have weird things like a silver bead rolling forward but whatever it collided with will experience a force pointing to the right, that is, it's momentum is 90 deg wrt its motion

So in an ordinary glancing collision of something moving with something at rest, you get the two objects bouncing off at an angle. But something with the above fictional properties in a glancing collision will behave like a head on collision of something moving to something at rest twisted at an angle

Therefore a tensor values momentum means the momentum of the object is a linear map of its velocity wrt some frame of reference (e.g another object)

So suppose we have two of these fictional beads, the momentum of A points to the right as seen from B. Conversely, momentum of B points to the left as seen from A

I suspect a lagrangian for these fictional beads might still be symmetric under translation, but in a weird way compared to ordinary momentum

Ordinary momentum will then be a special case of this tensorial momentum in that the factor that relate it and it the object's motion is just a scalar

3:01 AM

Oh. My. God. He didn't know that 18th century cannon used black powder, but he feels qualified to doubt that the gunners of the era knew how far they could shoot.

@dmckee ?

-2

Q: Skeptical of the "Cannon Shot Rule"

What I consider a highly suspect figure was imparted to me today in a lecture and it very immediately did not sit well with me. To wit, this cannon shot rule (see here for a reproduction of the following claim) states that nations could fire a cannonball approximately 3 nautical miles (!) from...

newtonian-mechanics classical-mechanics

And everyone he talked to doesn't believe it. But he presumably only talked to people as gobbstoppingly ignorant as he.

lol

2 hours later…

4:39 AM

0

Q: Universe spawned from the death of a hyper black hole?

Some Cosmologists have speculated that the Universe formed from the debris ejected when a four-dimensional star collapsed into a black hole a scenario that would help to explain why the cosmos seems to be so uniform in all directions. It is also difficult to explain how a violent Big Bang would ...

quantum-mechanics cosmology black-holes black-hole-thermodynamics

GR has got to be my least favorite part of physics.

I can reliably detect crackpottery in just about every other subfield. But I honestly couldn't tell for that post until the end. GR just uses so many loaded English words.

There's also this question which I'm 99% sure is complete nonsense. But I can't be totally sure because the Big Bang is involved!

Actually. @0celo7, you like GR, can you reliably tell real GR/cosmo research from fake?

Well not all arxivs are sensible stuff either, but currently it is too hard to test for a lot of cosmology models

user image

I can see what they are doing, but it might take reading the paper to understand why 4D stars they proposes must be made of universe forming material rather than e.g. 4D versions of hydrogen

Caption: My grossly simplified illustration of an ordinary supernova (left) and a 4D supernova (right) showing the ejected matter (hydrogen, helium and other stuffs in yellow, universe 3-brane in the shape of a 3-sphere in violet blue)

I am pretty sure after reading their arxivs, it is not an ordinary 3-sphere

o and then 3 years later there's this:

livescience.com/…

EDIT: Ok fine it is a spacetime version of a 3-sphere

EDIT2: The notion of star came from the interpretation of the variables in the metric calculated, thus its composition never went into consideration

6:10 AM

Some of the academic themed dreams of mine are weird, for example

"Remainder Theorem" in Dream 25/6/2016
$$\iint \eta \text{d}x+m\text{d}y = \iint \frac{h(x)}{g(x)}+r(x) =\iint \frac{\partial}{\partial}=\mathcal{E}\left(\frac{x^2}{x^2+y^2}\right)+\zeta\left(\frac{y^2}{x^2+y^2}\right)$$

The first bit looks like something from Green's Theorem, the second bit looks like remainder theorem save for the double integral, and the 3rd bit is I have no idea
The 4th bits seemed to suggest I must have been dealing with too many circle related problems in the previous day

@JohnRennie Good morning! :-)

Morning

1 hour later…

7:24 AM

@EmilioPisanty : ah, I see I'm the user with the most negative-score answers. Because "us experts" don't like it when I answer a question they can't, with robust references to back up what I say.

We don't see constructive or informative or critical comments, or another answer with even better references. We see 8 downvotes from the green-eyed goddess, and attempts at censorship instead.

@lucas : thanks. That's why I'm top of the list.

Hello everyone.

Hi!

@JohnDuffield I think public voting isn't suitable for justifying in science scope. (I personally think that public voting isn't suitable in any scope.) At least, if the reason behind the vote (up, down, etc.) is stated, it will be much valid, I think.

One thing else, he (Emilio) didn't refer to you, he was referring to a user with rep>10k and I said that sentence about him/her. Although, I respect you so much too as I said before in a comment for your answer.

7:45 AM

@lucas. I agree. Science is not a democracy, and IMHO anonymous voting just isn't working. Your recent question is a case in point. I got 6 downvotes for answering your question. Another poster, who you said insulted you, got 6 upvotes.

Sorry, I have to go. Bye.

Bye.

@CuriousOne: morning, we don't often see you in the chat room ...

@JohnRennie: Good morning to you, too. No, I am more trolling the public space, I am afraid... :-)

OTOH, since you are here... can you tell me what physics the information paradox is supposed to contain? I can't see it. There are really simple questions with physical content that I think are important, like lepton number conservation for black holes, but they aren't receiving nearly as much public attention.

The crux of the information paradox is that the wavefunction evolution must be non-unitary for any entangled system that spans the event horizon. But all of QM is founded upon the principle of unitary evolution.

It isn't a paradox of course - that's a pop science term.

I get the last part, what I don't get is how we are supposed to test this. My classical comparison is throwing a sugar cube and a sugar heart into two cups of coffee and asking a physicist to tell which was which after they are dissolved. That's just not a testable question. I am not even sure lepton number conservation on macroscopic black holes is, but that sounds at least borderline doable.

7:59 AM

Hey guys, planning on doing an experiment on coin frequency analysis for different surfaces. Any ideas on how to go about the exp?

@lifestooshort: see

301

Q: Can I compute the mass of a coin based on the sound of its fall?

Other day, I bumped my bookshelf and a coin fell down. This gave me an idea. Is it possible to compute the mass of a coin, based on the sound emitted when it falls? I think that there should be a way to do it. But how?

waves acoustics everyday-life home-experiment vibration

Hi @lifestooshort: Get a bunch of coins and a bunch of surfaces and then throw them a lot? :-)

What frequency are we talking about? Outcomes or sound? If it's outcomes, I would rather suggest to test the question if one can trick-throw dice.

@CuriousOne I agree that it's hard to see what the observable consequences are. Apart from the non-availability of any nearby black holes it's a long wait for our test black hole to evaporate.

Maybe the problem could be reduced to the high school level by minimalizing their degree of freedom (rails).

But it's a point of principle. If unitarity is violated anywhere that means we can no longer blindly assume it holds.

8:04 AM

Maybe it doesn't hold only in curved spacetime?

@CuriousOne Is your lepton conservation issue because you can throw in a lepton but the emitted radiation has net lepton number zero?

@peterh all spacetime is curved to some extent. Flat spacetime is one of those convenient approximations we physicists use.

@JohnRennie: On some level it sounds like a matter of beliefs. Do we believe that unitarity holds? I think so. It is probably testable on small quantum systems, though, so one should ask it independently of quantum gravity. I would love to see a precision tabletop unitarity experiment. That makes sense.

@JohnRennie I am simply skeptical of the no-hair theorem. I think it's mostly a consequence of what we stuff into GR. Since we don't really know how to package quantum numbers other than charge into it (or do we?), it's unlikely that the apparatus will churn out more hair than we have put it. Am I wrong about that?

@CuriousOne the no hair theorem is certainly true, but like any theorem it's only as good as the assumptions you fed into it. For example Hawking has recently proposed that there is a type of hair:

arxiv.org/abs/1601.00921

@JohnRennie By measuring the non-unitarity in the curvature of the Earth (or in a centrifuge) could serve as experimental data feeding the QG theories

@JohnRennie:Oh, wow... yes, that is exactly what I am talking about. Now that would make a lot of sense to me. Thank you so much for the reference!

8:10 AM

And in any case we expect quantum gravity to affect the calculation though no-one has any idea how this would work. The string theorists have an AdS/CFT description that they claim shows how information can get out, but I'd guess most of us regard this as interesting but speculative.

@JohnRennie calling the no-hair a "theorem" seems a bit far fetched to me

@yuggib hey, don't shout at me, I didn't name it :-)

@JohnRennie: What would be a rational name? It's really charge conservation, isn't it?

@CuriousOne it's an interesting idea, and if you're interested there is a Youtube presentation by Perry that explains it very nicely. But I would take it with a laaaaaarge pinch of salt.

05. Malcolm Perry - Black Hole Memory

@JohnRennie: I think you should know me better by now... :-) I will listen to Perry. I want to get, at least, an intuitive idea what they are talking about.

8:13 AM

@JohnRennie yeah, but when you say "a theorem is certainly true", you are referring to real theorems ;-P

the no-hair could be completely false as well

How do we measure non unitary, would it be something like a discontinuous change in probability distribution with time?

@JohnRennie: Let me ask this, then: if they threw an infinite amount of money at us to build an arbitrarily large telescope (cough!), what non-classical (i.e. post GR) physics could we possibly observe on a stellar size or galactic black hole? Do we have any suggestions from theory that are considered worth pursuing?

@Secret to actually measure it would be rather hard

@Secret: A very egregious case of unitarity violation would be the disappearance of mass from a macroscopic body. You may have heard that the kg prototype is shrinking. :-)

I don't know of any measurements we could make on a large black hole that would give us any insight into QM effects. The quantum effects are just too small.

8:21 AM

Aaaargh! That's what I thought.

Got to save a pretty penny for the Planck scale accelerator, then...

@JohnRennie What about vacuum polarization effects of merging black holes?

@peterh what about them?

[Thought experiment type question] We know black holes have entropy proportional to surface area of the event horizon. Suppose I have two unentangled photons and I threw one into a schwartzchild black hole. Will the entropy increase be the same as if I throw in one of a pair of entangled photons instead?

@JohnRennie Maybe they could be visible QG effects. Maybe they could be even viewed by telescopes.

@peterh not that I'm aware of

8:30 AM

@JohnRennie: How about event horizon tidal force noise for light passing very closely to the horizon? Any chance of detecting a modulation?

@Secret the problem is that any black hole we can do experiments on will not have a true horizon because true horizons take an infinite time to form. It will have only an apparent horizon. How that affects the calculations I don't know.

It may be detectable by watching the scintillation of a star that gets eclipsed by a black hole (OK... what are the chances of that...)

@CuriousOne horizon tidal force noise???

@JohnRennie In the recent LIGO event, 3 Solar masses where radiated away in some tenths of seconds. And there is some networked alarm system linking the large telescopes and the neutrino detectors, for the early checking of the supernovas. Maybe the LIGO (and the following GW detectors) could be also inserted into this network.

@peterh I just don't see why you think there would be any detectable effects from quantum gravity

8:35 AM

@JohnRennie: I thought Hawking radiation had an equivalent in the modulation of the tidal force near the event horizon, it's just very cold for the falling observer. One might hope that for light getting very close and moving almost tangentially there is an amplification effect?

@JohnRennie Merging black holes: big transient effects, complex curvature. Why do you think, there won't be any QG effect?

@CuriousOne I haven't heard of that, but that proves nothing :-) In any case the Hawking radiation from a large black hole is absurdly small. It's hard to believe there would be any detectable effects from it.

@peterh because the coupling constants are so small for QG. That makes it basically impossible to produce any measurable effects unless the curvature is really extreme i.e. a microscopic black hole.

@JohnRennie: I am also afraid that all of these effects are too small, even though, the temperature of a stellar black hole is not that small. 10nK or so, i.e. 1e-12eV ... if one could get that amplified by a relativistic effect and modulated on light, there might just be a measurable effect. If there is no amplification, then, I am afraid, we are done.

sciencenews.org/article/… If entanglement are really wormhole and space time is emergent from entanglement, then why we never see micro black holes form whenever something unentangle?

And in fact if micro black holes literally zip pass most things before settling down, then how can we actually tell they are black holes and not some fast moving ghostly particles?

@JohnRennie In the moment, and in the point, as the event horizons touch, at least the higher order time derivates of the metric seem to me extreme, because there is also a topological change.

Or not?

8:52 AM

@peterh: ooooh :-)

0

A: Can I use an electromagnet as a shark repellent?

On my opinion, the best solution of the shark problem is the dislocation. It means, you aren't ever on the same place at the same time, where there are sharks. Now what is important: you have an influence on your world line, but you have not on the world line of the sharks. To solve the shark ...

@peterh: The event horizons are not hard shells that touch and there is no simple quasi-static merging scenario that one could exploit. The actual phenomenon looks very complex, at least in the simulations. It doesn't sound like a precision experiment scenario. If the measured waveforms and the simulations won't match, then we got something. The LIGO folks will publish that, if they see it... who wouldn't want that Nobel? :-)

9:03 AM

@CuriousOne Yes, I know, and this is why I mentioned the topology change and the higher time-derivates. But it is only my layman intuition. I have also some Nobel-near ideas :-) for example manipulating the Higgs field through its W/Z coupling, which can be maybe done by nuclei with an asymmetric isospin/hypercharge distribution.

user116211

Hey @yuggib.

@MAFIA36790 \o

user116211

So, I'm reading mathematical theory from Bourbaki.

in the first book?

user116211

do you know what the point of introducing links in assemblies is?

user116211

9:05 AM

@yuggib yup.

@peterh: I am just not a strong believer in higher than second order effects. They are awfully hard to detect and measure with any precision.

it is related to the fact that they use Hilbert's $\tau$ symbol if I recall correctly

(and that is not standard as of now)

(Hilbert called the symbol $\varepsilon$)

@peterh: The Higgs, in my opinion, is overrated. We have learned exactly nothing, so far, from its existence. It was the safe bet. It was the boring man's solution. Nature didn't surprise us. Dark matter, dark energy, neutrino masses... those are surprises. The Higgs is just plain boredom.

user116211

@yuggib yeh, they used this symbol... ok, then I need to continue my reading.....

user116211

BTW, @yuggib, got the chance to apply either in BS-MS in Physics or BS-MS in Maths; what do you think which would be competent for studying mathematical physics in future?

9:13 AM

@MAFIA36790 that depends a lot on your institution's programs

user116211

@yuggib okay.

you can either go with theoretical physics and then shift towards mathematics, or if there is a program do directly mathematical physics in mathematics

user116211

@yuggib Well, not sure of the latter, but there are mathematical physicists in the applied maths dept.

@MAFIA36790 what do they do?

user116211

@yuggib I have to search a more; that's it I know till now; I would update you....

9:15 AM

@CuriousOne Yes, but finally the particle was found. Which is a strong argument, that maybe other resoults could be found, too. Although the particle decays fast, the field is permanent. But it is everywhere the same. But it shouldn't be so, as I understood there is a kinetic term in its Lagrange which effectively means, that its space-derivate has an energy density (it is maybe silly, this is what I could understood).

@CuriousOne Thus, if you can change it in many points in a given volume [for example, in a crystall], it will change everywhere in that volume.

user116211

@JohnRennie, did you see it?

user116211

Since my contribution is not valued and appreciated. This will be my last post here.

@MAFIA36790 I vote everything up if it looks professional, because 1) we need to encourage them 2) I find impractical that easily understable naive answers to naive questions are overvoted compared to their worth

@MAFIA36790 Probably not I am the only one doing this, your post was probably only not enough visible. This happens, even John Rennie has a lot of 0-voted posts.

@MAFIA36790 This post looks as if a programmer had bought some physics book in a university store :-)

user116211

9:31 AM

@peterh ;D

@peterh So, the only up-vote of my answer is certainly related to you ;-)

9:45 AM

@lucas No, it doesn't look professional. Non-prof posts are going on the common rules by me. Many OPs vote every answer up, even if it is not usable, only to rewarding the attention. Giving ups is cheap. I suspect it was upvoted by the OP.

@peterh Never mind! I was kidding! But I think that OP never votes my answers up. He/she doesn't tend to read my answers to his/her questions at all.

0

Q: Lag problems when writing answers

I've had a recurring problem when writing answers: a massive lag between typing and seeing the text appear. In got unbearable for this question, probably due to the enormous length of the answers and the many formulae. I am not sure if this is a problem with my system (I use Mac OS and Safari is...

@lucas You are @InformedA ? You have different nicks.

@lucas Sorry I understood it for @InformedA 's last post! Your answer, I didn't see.

10:11 AM

@lucas Now, that was me. .-)

@peterh Thanks! But I hope it was professional. I am afraid of you voted it up because of your kindness! :-)

@lucas No, it was really good, particularly compared to the question. I don't really find interesting/useful the "what is X really" questions, they are too phylosophic to me.

@peterh You made my day! :-)

@peterh they are - in my view - simply beyond the scope of physics because physics does not say "what things really are" (whatever that might mean in the first place)

user116211

11:12 AM

@peterh Well, I don't think at least my question has any philosophical implication or so; during that time, I faced difficulty in grasping the concept of entropy; in thermodynamics; the thing that is defined is entropy-change and not entropy; that was the main problem for me. Plus a sudden introduction of entropy is disorder didn't work much. Just to tell it is a thermodynamic potential was not enough for me then. so, was the necessity of the question for me then.

user116211

Nevertheless, it would be uninteresting for others, no doubt; but it was essential for me back then.

1:03 PM

@knzhou No

1:15 PM

If I have two qubit system $|\psi_1\rangle = (\alpha_1 0 +\beta_1 1)$

and $|\psi_2\rangle = (\alpha_2 |0\rangle +\beta_2 |1\rangle)$, will the density matrix of the two qubit system be $\rho = (\alpha_1\alpha_2 |00\rangle + \alpha_1\beta_2|01\rangle + \beta_1\alpha_2|10\rangle + \beta_1\beta_2|11\rangle)$

?

@ACuriousMind Do you know the Poincare Recurrence lemma?

Also, good morning

@0celo7 That depends on what you mean by "know"

Can you state it?

@AnuroopKuppam what you've written there is not a density matrix, it's a state. But it is indeed the correct state for the combined system

Hmm, I don't understand how to generalize it to flows

1:25 PM

@ACuriousMind sorry about that, will the density matrix be $\rho = (\alpha_1\alpha_2 |00\rangle \langle 00|+ \alpha_1\beta_2|01\rangle \langle 01|+ \beta_1\alpha_2|10\rangle \langle 10|+ \beta_1\beta_2|11\rangle \langle 11|)$

@0celo7 Given a Hamiltonian system with bounded orbits, every neighbourhood of a point has orbits that intersect it infinitely often.

@ACuriousMind If $g$ is a volume-preserving transformation of a bounded set $D$, then in any neighborhood $U$ of any point of $D$ there is a point $x\in U$ s.t. $g^nx\in U$ for some $n>0$.

@AnuroopKuppam No. What you wrote there first was the correct combined state $\lvert \psi \rangle$ - for the density matrix you have to form $\rho = \lvert \psi \rangle\langle \psi \rvert$.

Supposedly this generalizes immediately to the case when $g^t$ is a flow

But I don't see it, $n$ has to be integral.

I think my version already states it for a flow. I have no idea whether the two are equivalent.

1:29 PM

According to Arnold, they are.

He does not give a proof

Probably thinks it's obvious

The proof does not make sense unless $n$ is an integer

Or at least discrete.

@ACuriousMind considering the density matrix should be of the form $\rho = \sum{j} p_j|\psi_j\rangle \langle \psi_j|$, my $p_j$ are incorrect?

@AnuroopKuppam Yes. You can see that they are wrong because the density matrix needs to have trace 1, but $\alpha_1\alpha_2 + \alpha_1\beta_2 + \beta_1\alpha_2 + \beta_1\beta_2$ is not 1.

hmm, interesting let me work on it.

Also, you should see that you have no off-diagonal elements. Which you should generically expect.

aha, found some weird lecture notes that seem to prove it

1:37 PM

hi

I hope u guys have brainwaves as geniuses ........ — Vidura Sahasra 8 hours ago

...what?

aha

@ACuriousMind should I buy an actual rubber duck

(yes, I've tried using Reb but she asks too many questions)

@0celo7 I don't know, would you actually talk to such an inanimate object?

I've been known to just talk to myself, but that's not for everyone :P

Perhaps you should get a pet

@ACuriousMind I would whisper. Or does that make me crazier?

@ACuriousMind I did explain things to Einstein back in the day

@ACuriousMind Oh, I do that.

Whisper, once again

I've lately taken to pacing

Also browsing the meteorology books in the library.

@0celo7 Whispering to a rubber duck while scribbling down strange formulae? No, doesn't sound crazy at all to me

2

1:46 PM

I filled 9 pages trying to do problems last night

I fully solved 2

Completely stumped by one

Close to solving another

Haven't attempted the fifth

@ACuriousMind Honestly, I don't think you're the best judge of that.

Indeed, I might not be :)

@ACuriousMind I think I got it. Since $\alpha_1^2\alpha_2^2 + \alpha_1^2\beta_2^2 + \beta_1^2\alpha_2^2 + \beta_1^2\beta_2^2 = 1$.The probabilities in $\rho = \sum{j} p_j|\psi_j\rangle \langle \psi_j|$ are those.

...Your density matrix is written wrong. The sum $\sum_j p_j \lvert \psi_j\rangle\langle \psi_j\rvert$ only works when you are writing down the density matrix of a mixed state that has probability $p_j$ to be in $\lvert \psi_j\rangle$.

A general density matrix, however, is $\sum_{i,j} \rho_{ij}\lvert \psi_i\rangle\langle \psi_j\rvert$.

You have to take the state $\psi$ of you system and compute $\lvert \psi\rangle\langle\psi \rvert$, not guess the coefficients.

You've got the diagonal elements right in your attempt, but you haven't said anything about the off-diagonal elements

@0celo7 Another user agrees with your nickname ;)

2:12 PM

Are we supposed to be able to see that LaTeX as actual formulae?

@WilliamBulmer Look in the upper right corner of the chat room

@ACuriousMind Thanks

@ACuriousMind how did you find that

@0celo7 I saw a comment from that user on a question on RPG.SE

nerd

2:14 PM

Well, that was easy

user image

@ACuriousMind ...how do you actually get "dense" from that

@0celo7 I have a strong feeling of deja vu

@ACuriousMind me too

I didn't understand it properly the first time around.

I think now I'm able to

@ACuriousMind If you could at least give a hint, that would be great

They use the "a dense set intersects every open set" definition.

@0celo7 I'm not sure what you don't understand

I do not think that it "easily follows that"

2:22 PM

The $\delta$ statement is exactly what it means for $g^n x$ to be dense

Because I do not see it, after about an hour of staring at it.

@ACuriousMind Uh, what?

$x$ is fixed.

It just says that you can choose $n$ large enough so that $g^nx$ is within $\delta$ of $x$.

Am I missing something obvious?

@0celo7 Ah, see, that was what I needed to see where your problem is

@ACuriousMind ??

What did you think $x$ was

user116211

I'm voting to close this question as off-topic because it is based on a false assumption. — sammy gerbil 46 mins ago

user116211

It is not a correct reason to close a question, is it?

2:32 PM

@0celo7 Consider that the statement there says that $g^n$ is a rotation of angle less than $\delta$.

@ACuriousMind Ah, so we can compound $g$ to get an arbitrarily small rotation. Got it.

Hmm, that doesn't help with my actual problem.

I'll ask my prof

@0celo7 why would the integration constant that comes from the integration of $\int \frac{\dot{r}l^2}{r^3} - \frac{k\dot{r}}{r^2} dt$ be an initial energy?

$l$ is a constant

$r$ is radial displacement from the mass $M$ that this mass $m$ orbits

1

Q: Should one delete an example that could cause confusion but allready helped multiple users to better udnerstand the matter?

I made this rollback of an edit of Cort Ammon, where he removed an (in my eyes) good example that was a way to verify one has got him correctly in what he was saying. At least another user stated in a comment he was thinking so too. So I thought it would be a loss removing that example. But the...

oh i get it

that integral is actually the integral of acceleration through $dr$ if you re-arrange it

I don't think it's really an energy. It's more of a velocity since $m$ isn't considered in the equation

Calculate the deflection of light by the sun, applying what
you learned in the text to the case $\epsilon>0$

(he just said $\epsilon >0$ meant the mass was no longer bounded and shouldn't be called a planet) I don't see what he means

$\frac{1}{2}\dot{r}^2 + v(r) = \epsilon$ where $\epsilon$ is the integration constant I mentioned that is an initial velocity.

$v(r) = \frac{l^2}{2r^2} - \frac{GM}{r}$ where $l$ is some constant

3:11 PM

@ACuriousMind Bah. Maybe I should study legitimate symplectic topology, not this Russian BS.

This thing is unprovable

The proof does not exist.

you can try to prove it is unprovable

Maybe I need to read Jech and use forcing to prove that

with forcing you may prove it is unprovable

Do you know anything about Poincare recurrence @yuggib

youi know, it was introduced to prove the independence of GCH from ZFC

@0celo7 I only heard it mentioned in physics courses

and I don't care so much about classical system with finitely many degrees of freedom ;-P

infinite dimensional systems is where things become interesting

3:45 PM

user image

What is its name in English?

3:57 PM

@lucas It's a scale

@ACuriousMind Thanks a lot!

4:25 PM

Please help

5

Q: I'm used for mass

You might use me for mass I could tell you your mass I might even attack you I sound like a cross What am I? HINT:

4:53 PM

arxiv.org/abs/0803.2328

↑ so cool

user image

user image

Different shapes, same spectra. In the lab.

5:18 PM

I have a hunch. I understand that if $U^i$ is a vector flow of a vector field, $V^j$, then $\partial_i \left( U^i V^j\right )$ represents the "quantity" of U leaving a volume element. Then, does something like $\epsilon_{ijk}\partial^j\left(U^lV^k\right)$ fully account for how U "rotates" V? Sorry if my raising and lowering is off. I am still getting used to those concepts

I meant the "quantity" of V leaving a volume element

1 hour later…

6:33 PM

@EmilioPisanty That's awesome!

6:52 PM

@0celo7 Does that bother you at all?

user54412

@CuriousOne @JohnRennie I personally don't find any of the existing suggestions compelling, but there are many speculations on beyond-GR theories and their impacts on Sag A* and M87 observations due very soon with the Event Horizon Telescope.

user54412

@dmckee It's not just you. I do that every time.

@peterh The Higgs hasn't actually be seen, only its decay products have been seen, I am afraid. Whatever manipulation you attempt to do on the nuclear level doesn't do anything for the vacuum in-between. The field has a very short distance scale.

@ChrisWhite: That's basically my question: even if we have to go out on a limb, are there any possibly observable effects that could help us to differentiate different models? I don't quite see it, either, even standing on limbs, but that doesn't mean anything. I have zero experience with the theory and its possible extensions.

user54412

@CuriousOne Searching the literature for "Event Horizon Telescope" yields more such out-on-a-limb theory papers than papers describing the telescope itself.

user54412

7:08 PM

I don't really pay much attention to them, since I have a strong theoretical bias against tweaking numbers in a theory without observational evidence that they aren't right.

@ChrisWhite: I'll be darned, you are right. I've read some about the telescope itself, but I didn't look at the theory papers that reference it. No wonder I am so uninformed. :-)

user54412

Also, as my research involves the fluid dynamics of black hole accretion, it's my job to point out that what we see from these systems is incredibly complex, and most of the theorists tinkering with GR-esque lagrangians don't heed the emergent plasma physics and radiative processes that will dictate what we see in the data.

I do get you about theory building on the cheap, OTOH, let's give our theorists a little slack, nature is not exactly generous with showing her goods lately.

@ChrisWhite: So my point to, I think, peterh, that the accretion and merger processes are way to complex to hope to extract fundamental insights from them is shared by those who are working in the field? Are we basically talking about the equivalent of measuring the electron mass from the data from a fusion plasma experiment?

user54412

@CuriousOne I'm willing to bet measuring the electron mass from fusion stuff is easier ;)

user54412

Sag A* is a particularly crazy regime of plasma physics -- the mean free path between particles is of order the size of the black hole.

user54412

7:13 PM

That said, I'm particularly skeptical, even for a scientist. There are more optimistic people in the field.

@ChrisWhite: Skeptics are fine with me. I am not on the optimistic side myself. I like clean systems. If we can't find them that's a problem.

Is there any hope to find something unexpected on quiet stellar size black holes with e.g. lensing? The cross sections are too small, right?

user54412

@CuriousOne Yeah. Even with a literal alignment in the heavens to get high magnification, you can't go back and study microlensing events.

I was thinking about observing scintillation or something on stars behind the bh.

user54412

Well, I guess in principle. But often the only reason we know about stellar mass black holes is because their disks are emitting large amounts of light.

1

Q: How should we deal with incorrect comments?

On this site, there is a tendency for users to answer questions with terse comments. It's especially prevalent for low quality questions which are in danger of being closed. Recently, I've been noticing a lot of comments that are misleading or downright incorrect, especially on lower quality que...

7:18 PM

@ChrisWhite: I understand that just finding a quiet one will be hard.

user54412

It will be interesting to reevaluate things ~ next spring with EHT results. They'll include ALMA for the first time, and we'll actually be using the entire planet's diameter for interferometry.

@knzhou No, I'm not at the level where I can read research articles

I'm interested in the math

I am simply hoping that if one could actually observe a transit and get high enough SNR, that some non-classical effect could be observed, like tidal wave noise near the event horizon or something. I am aware how large the physical gain would have to be to magnify that...

user54412

My guess is that once that data comes out and they show something, they'll push for a space-based interferometer of order the Earth-Moon separation.

I cannot come close to completing the bibles in the field (Beem & Ehrlich, Hawking & Ellis, Choquet-Bruhat, etc.), I have no business reading articles

I might take another crack at Hawking & Ellis one of these days

7:21 PM

@ChrisWhite: We need space interferometers, at least in Lagrange points, better even out at Mars or further, wherever we can still get enough energy for operation without having to go nuclear.

@ChrisWhite You read Arnold, right?

user54412

@0celo7 Not religiously.

@ChrisWhite Do you remember anything about Poincare recurrence?

user54412

@0celo7 Nothing beyond what the wikipedia article says, I'm sure.

@0celo7: Poincare recurrence is theoretical nonsense. Nature doesn't do it, not even for the solar system.

Even Poincare could have known that.

7:24 PM

@CuriousOne Oh be quiet

@0celo7: Nothing against mathematical physics, but truthfully, it won't even happen in mathematical physics in a model of the solar system. Gravity will first slingshot something out before it repeats a configuration.

I'm not a physicist

user54412

^

@0celo7: The obvious problems with Poincare recurrence are the same for non-physicists. :-)

@CuriousOne But we care less about the problems.

@ChrisWhite What's that supposed to mean

7:27 PM

@0celo7: So you want to believe in a Christmas story version of it rather than understand what's really going on in physical systems (whether on the level of reality or mathematics)? Why?

I'm having a hard time connecting the thing Arnold actually proves to what he claims it shows.

user54412

Well all my textbooks are boxed away.

@CuriousOne Because I study mathematics, not physics. What could or could not happen over the time of a billion years is of little consequence to me.

I'm using it as a theorem in ergodic theory, not physics.

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I don't see how it follows that "Poincare's theorem can be strengthened, showing that almost every moving point returns repeatedly to the vicinity of its initial position."

user54412

We should start a betting pool though. Will Mercury be ejected before it's swallowed by the Sun?

Can I bet that I'll die long before either will happen?

7:31 PM

@0celo7: A billion years is waaaaay to short to be ergodic on the solar system. Either way you have to make unphysical assumptions to proceed.

@CuriousOne Billion, trillion. Hardly any difference for the purposes of this conversation.

You're supposed to somehow apply it to the phase flow of a system

@ChrisWhite

user54412

@0celo7 Probably something about continuity. Certainly given such an $x$ it will have an entire neighborhood that returns to $U$.

@0celo7: As a mathematician, shouldn't you rather be asking what the correct mathematical criteria are for a system to have a shot at being ergodic? Instead you are making a naive argument that it's just a timescale thing. It is not just a time scale thing. The potentials need to be of a special form, which 1/r is not!

@CuriousOne I'm applying this to vector fields on Riemann surfaces, not "potentials"

I don't know what you're talking about

@ChrisWhite ...hmm

certainly?

@0celo7: You still need a Hamiltonian dynamic, otherwise none of this applies. If your system doesn't obey energy conservation, then it has fixed point etc..

7:38 PM

What energy conservation?

If the system doesn't conserve energy (i.e. it's lossy), then it will not have constant phase space volumes but converge into minima. Chaotic attractors are even worse.

They definitely don't spread out nicely as statistical mechanics postulates.

My problem satisfies the constant volume hypothesis via Liouville's theorem

So you have a potential, then, and you are forcing the system to be in a constant total volume? Then you are automatically violating the third law of thermodynamics, which, for your purposes may be OK.

I don't see what thermodynamics has to do with vector fields on Riemann surfaces

I am talking about physics. That's all. At some point mathematical physics usually detaches from physics. Poincare recurrence is one of those points, that's all.

7:41 PM

I'm not talking about physics

I never was

OK. Fair. Would mathematics.se be better suited for your question. :-)

No

Don't get me wrong, but that's what we tell our OPs on the main site. :-)

This is not the main site

Anyway, I can tell that you are annoyed, so I will leave it at that. I didn't mean to annoy you, I just wanted to point out that Poincare recurrence is unphysical. It matters to us because there is an awful lot of misunderstanding about that out there.

7:43 PM

@ChrisWhite ok, suppose the neighborhood thing is true

but by Hausdorffness, this does not imply $x$ itself is in that neighborhood

no matter how small you make $D$, $x$ and the recurring point can have disjoint neighborhoods

Mathematically, isn't much of this covered by the KAM theorem? Am I mistaking things here?

I think it should be much more elementary

I'm just not seeing how the above quoted theorem implies how Poincare recurrence is used in physics

(which is how I need to apply it in math, incidentally)

Poincare recurrence isn't being used in physics. I already said that it's unphysical.

I'm not constrained by thermodynamics or 1/r or whatever

Physicists are. Physics has to deal with nature, not numbers and functions. Noise is not a theoretical annoyance. Neither is the third law. They are very hands on real.

Before you have Poincare, you have Lyapunov exponents, anyway, which destroy any hope of ever getting to Poincare practically, except in systems that are not ergodic.

2 hours later…

9:44 PM

Hi @dmckee

Did you see this message, by the way?

user54412

@Qmechanic Is resource-recommendation to be used for non-print resources?

user54412

I can see how software qualifies. Is that why you added the tag? Or would a pure apparatus-recommendation question also qualify?

user54412

(For this question it seems the whole software part is misleading -- they clearly need a device, since no computer program can solve the problem without input)

@ChrisWhite : Speaking in general, and not necessarily of the post at hand: Yes. Any kind of resource-recommendations: paper, electronic, etc.

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