The h Bar - 2015-11-24 (page 2 of 2)

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2:01 PM

Actually, abut quantum mechanics, its maths can be formulated in terms of wavefunctions, state vectors, density matrices and C* algebra. But at the end of the day, what is the stuff that is responsible for the observed things like the interference patterns, entanglement and so and so. Do we have a concreate anwer on the possible nature of these things yet?, or that we only know that there's these phenomoen being

observed, and that the maths is our best model to describe how they interact and behave, but we still not sure what these things actually are?

@Secret What do you mean "what is the stuff that is responsible for the observed things"?

What is "responsible" for objects obeying Newton's laws in classical physics?

I'm not exactly sure what you're asking, but I think you're asking things that physics doesn't answer.

Like back in classical mechanics we can easily describe the various things we observed with particle model and kinetic theory, thus explaining pretty much everything in classical mechanics in terms of some kind of "basic building blocks"

Or in general rellativity where all you need is just spacetime, the constancy of speed of light for all reference frame and the stress energy tensor, and the notion of curvature, and then thigns can be described in a relatively straightforward way in terms of geometry

True, the building blocks I mentioned above for GR and classical mechanics are ultimatel just models, but they seemed to be discrete enough to pretty much derive everything qualitatively (which is how physical intuition is like)

But what is the analogue of this in quantum mechanics?

For example, the public have accept the notion of particles, spacetime curvature, and these are all shown in experiments via some easily observed outcomes (atomic force miscroscopy, gravitational lensing of starlgiht seen in solar eclipse etc.), but for quanutm mechanics, do we ever have any building block like concepts which all knwon quaumt phenomoen is based on and can be directly obseved?

@Secret Physics os not about finding "The Stuff". Physics is about describing and predicting the world correctly. The "basic building block" of quantum mechanics is that states can superpose. The correct way of mathematically modelling superposition is (infinite-dimensional) linear algebra.

@Secret Why does gravitational lensing convince you of GR, but the discrete spectral lines of atoms not convince you of QM?

QM is all around us, GR is quite far away and doesn't have a direct impact on our lives

But without quantum mechanics, there would not be enough fusion activity in the sun to warm the earth.

The very way matter is structured is only understood in QM

To say that GR and classical mechanics are easily demonstrated but QM is not is just ridiculous.

2:23 PM

I thought superposition is a wrong way to think about it because of our previous discussion saying how you cannot really see a state in superposition, but always end up measuring it to have some probability in some state?

I know, but what puzzles me is that we can measure gravitational lensing, which means we can see the spacetime curvature in some form

In classical mechanics, we have microscopes that can more or less see the billard ball like atoms and molecules that are buzzing around causing things like brownian motion and such and such

Whenever we try to measure a state, all we get is the probability it takes some values, but never as a superposition

We can see gravitational lensing, time dilation and length contraction, thus we can soemwhat see curvature

We can also see the particles jigging around with microscopes, which tell us how heat flwo form hot t cold, how there's brownisan motion, while pendulums swing etc.

Ths is why I think QM is a bit different from GR and classical mech because we only ever see the effect casued by the building block, but not the buidlign block itself (except its discrete nature, which is clearly demosntrated by atomic emission lines)

I think I will change my name again.

I don't like this colour.

@Secret Every state is the superposition of others, that is the content of e.g. the Stern-Gerlach experiment! A state of definite z-spin is the superposition of x-spin-up and x-spin-down, and a state of definite x-spin is the superposition of z-spin-up and z-spin-down

... I didn't know that, it seems I know less about stern gerlach than I thoguht

In that case, then I now agree that we do have cases we saw the superpositon of the states

@ACuriousMind Hmm, I am glad that at least I get the gist of quantum mech right (superposition of states), that will really help me in building the physical intuition on it when solving and interpreting harder problems

thanks for pointing out that we actually have seen experimentally a state when it is superposed

3:30 PM

@Danu I'm trying to calculate $\Gamma^r_{tt}$ for the Schwarzschild interior metric as described here:

2

A: How is gravity proportional to space-time curvature in the rubber-sheet analogy?

You have linked a YouTube video that shows the rubber sheet analogy for the curvature of spacetime. The trouble is that while the rubber sheet analogy is not a bad way for beginners to get a rough idea what is going on, it can be very ,misleading if you push it too far. In this case I suspect it ...

But I keep getting the value zero, which can't be correct.

$\Lambda$?

Who denotes the Christoffels with $\Lambda$?

oops, I meant $\Gamma$ - now I can't even remember my Greek letters :-)

Ah, okay :D

@JohnRennie I don't get zero.

I get...

something ugly:

$$\Gamma_{tt}^r= \frac{1}{2R^6}\big(2M^2r^3+Mr R^3(3\sqrt{1-2Mr^2/R^3}\sqrt{1-2M/R}-1)\big) $$

@Danu Can you have a look on swarchive.ratsauce.co.uk. I've put the notebook I'm using there as DanuGRSchwarzschildInterior.nb

Can you spot my deliberate mistake in the notebook?

3:40 PM

deliberate? :P

@Danu :-)

@JohnRennie I can't find it.

@Danu oops, try it now. My web server didn't have a MIME type configured for .nb

@JohnRennie Yes, I think you forgot to put spaces between the "M" and the "r"

Yup, that drastically changes the result

(this typo occurs twice)

Aaaaaaaaaaaah. Mathematica presumably thought I was defining a new constant called "Mr". Damn - the time I've wasted over such a simple mistake :-)

3:47 PM

Happens to the best of us ;)

Thanks! I'll go away and have a play. For no very good reason I'm trying to calculate the norm of the four-acceleration for a stationary observer inside a spherical body.

@JohnRennie "woohoo" ;)

4:00 PM

@Danu It works! The interior and exterior Christoffel symbols now match at $r = R$.

@JohnRennie Perfect

Hm...annav now is also a puppet of Daniel, only a matter of time till it gets you too, @JohnRennie!

physics.stackexchange.com/questions/220320/…

People don't seem to treat this seriously!

...is comment one-boxing removed?

4:22 PM

@ACuriousMind nah, it still works, I'm not sure why not in this instance

Perhaps the comment was too fresh and now the thing is deleted, anyway

Yeah, I didn't think there was such a thing as a comment being too fresh to onebox but it doesn't matter anyway

This is a test comment. — ACuriousMind 9 secs ago

Hm, not too fresh, it seems.

4:38 PM

I tend to interpret gravity in GR by using an improved version of the rubber sheet analogy, in that instead of considering the cloth visibly curves because of how it wraps aroudn an object, I tend to treat it as a flexible slilcone fabric, and then draw a grid on it, and (intrinsic) curvature is then shown itself as areas where the gridlines get squished closer together while the area of the fabric stays more or less the same)

I still think there are still cases that cannot be handled by this picture, however, but I am too occupied by my honours to compute the christoffel symbols to chec…

one way I can think of that it can break down in this conceptual picture of mine is that this analogy cannot demonstrate gravitational time dilation very well

since all you see in that picture is gridlines squishing closer together, even if you label one of these as time, it does not demonstrate the time relative to another inertial observer become longer

user image

5:01 PM

@Secret I have to say that I think the rubber sheet analogy has no value once you actually start learning GR.

6

@Secret At least draw perspectively :P

@JohnRennie Indeed, especially when you start calculating the schwarzchild solution, I don't think the rubber sheet can demonstrate how thigns look frozen at the event horizon for someone viewing at soem distance outside the black hole, and also that swapping between time and space coordiantes once the event horizon is passed

Well, the "improved" version is flat,, it's only the gridlines that look distorted to illustate it is being stretched by the energy momentum present at the centre of it (in the fabric, but not sitting on top of it)

But if you like:.. Here's

user image

Hopefully this looks perspective enough lol

With "perspectively" I meant such that one can tell which angles are right ones and which not, e.g. in the standard mathematical fashion of drawing the "third" axis at 45 degrees

Like this:

user image

Your drawings always look messy because there are no straight lines in them - one doesn't know where to look or how to orient oneself.

Ah I see what you did here, you used oblique projection while I tried to draw if as if I view it form my table at some weird birds eye angle

I'll keep this in mind to make myself clear in the future

user54412

@ACuriousMind What does one call that exactly? The techniques you learn in art class (one-point and two-point perspective) take some parallel lines in 3D and project them to converging lines in 2D, which is not quite what's happening here.

5:16 PM

Having mentioned about the schwartchild solution, I remember back in my GR course how I always have a question of: If things looks frozen and never reach the event horizon form the orbiting spacecraft's frame, then why we never saw frozen images from victims that fell into the black hole some time ago all piling up at the event horizon

and then my professor give us the answer after showing it with the gravitational redshift equation: The images don't stay forever, they get redshifted away until the phton wavelengths basically diverges and thus the energy becomes negligible

@ChrisWhite I...don't know what it is, you're right that it's not an n-point perspective because there are no points at infinity

But it is the way coordinate systems and mathy diagrams are often drawn

@ChrisWhite en.wikipedia.org/wiki/… It's n point perspective, of which 1 point to 3 points perspectives are most commonly used in engineering and art drawings

user54412

@TheDarkSide I have no idea where to find such scripts, since I'm not really interested myself. I just know people have used them to crawl this chat.

the messy diagram is an attempt to do a 2 point psepective

it fails obviously because I have not drew them in a rigorous way for a long time

Mine isn't an n-point perspective - parallel lines never intersect.

Ah, it's indeed oblique projection

5:19 PM

https://en.wikipedia.org/wiki/Parallel_projection
Yours is parallel projection
The advantage is that angles and legnths are not disroted
The disadvantage is that sometimes it is hard to see the depth clearly

I use paralle projection alot when drawing the projection of the tesseract and other 4D shapes

because it does not distort the distance relationships too much to give misleading results

but again, projecting 4D to 2D loses 2 dimensional worth of infromation, thus for more complicated 4D objects, such as a complex graph in $\mathbb{C}^2$, I just go back to maths unless I understood it well enough that I can "ant walk" on it with my pen

The main issue with representing GR in drawing is not the projection to 2D, it's that you project Lorentzian geometry to Riemannian geometry.

Because we always intuitively think of distance just as the actual Euclidean distance between points

user54412

@ACuriousMind My name has actually appeared in "deleted by..." messages. Why don't I get on the list? :(

Yes, that -1 signature of the time coordinate screws up all that intuition, as demonstrated by that null curve integraton question I asked you 2 months ago

https://upload.wikimedia.org/wikipedia/commons/thumb/5/5e/Orthogonality_and_rotation.svg/350px-Orthogonality_and_rotation.svg.png
I have once attempted to draw the full 4D version of these and I end up with...

@ChrisWhite Perhaps you didn't interact with the user? I think you have to leave a comment arguing with them to get on the list

@DavidZ: I've already raised one flag of this type, but I'd like to know in general: If I have reason to suspect there's a user sockpuppetering (with not-exactly-mainstream views), but I have not seen the sockpuppets interact, should I still raise a mod flag (since socks are allowed as long as they don't interact)?

user54412

5:42 PM

1

A: What question has the highest view count with still a zero score?

You can use the following cross-database query in SEDE if you can live with a dataset that is maximum a week old (refreshed in the weekend) -- start create url from dbname IF OBJECT_ID ( '#siteurl', 'P' ) IS NOT NULL DROP PROCEDURE #siteurl; GO create procedure #siteurl @dbname nvarchar(...

user54412

Turns out we have a question that does decently well even up against the other sites: 80k views

damn...preparing a seminar with written notes ends up taking an amount of time very close to writing a paper T_T

of course, to write a paper you have to produce some new results, but I ended up doing almost the same for this seminar

5:59 PM

@ACuriousMind sure, why not. When in doubt, choose to flag.

If the flag count ever becomes too high for us to handle, that may change, but I doubt that will become a problem.

And even if the sockpuppets are legit, it still helps for us to know about them.

user54412

The sinister plot revealed: ACM raises enough flags to overwhelm the mods, new elections are held to bolster their ranks, and the 95% become entrenched with even more power :p

@ChrisWhite You know too much.

@DavidZ Okay, just didn't want to annoy you with stuff that's not actionable

So, like, if DanielSank can get three more sockpuppets elected to mod positions he has a majority and can rule the site with an iron fist? lol :-P

user54412

@ACuriousMind Also, by my calculations, you'll surpass me in rep in 3 weeks.

@ACuriousMind oh, don't worry, it's not annoying. Even when we decline flags, we're not annoyed. The flag count is really not that high for us.

user54412

6:04 PM

There need to be more questions about galaxies orbiting each other. Or anything where I can post a Hubble image, really.

@ChrisWhite I'd help you out and ask one, but unfortunately I really don't know anything about astrophysics.

user image

...Made with powerpoint, to be checked with maths

Therefore, don't try to draw this thing without a computer software

@Secret ...is that supposed to visualize the well-known fact that the Lorentz transformations are just "hyperbolic rotations"?

Yes

and trying to visualise minkowski space in its entire 3D+1T glory (as a projection)

but as you can see, it is increadibly cluttered, thus not very useful except for very trivial stuff

which is one reason why we stick to the maths

user54412

6:19 PM

22 hours ago, by Slereah

user image

user54412

I feel there's a similarity here...

this thing reminds of a mushroom cloud

user54412

@ACuriousMind I found this search rather amusing

@ChrisWhite there are more amusing ones.

@ChrisWhite wat

6:28 PM

That conversation actually flows even if each of the posts are not necessayr close in time

actually that reminds me of something
Suppoer we have a video clip of a ball rolling downhill, is it possible to tell apart it from a single scene where the ball rolls downhill, and the case that the video is basically made by sticthing identical looking balls together such that the whole thing looks like as if a ball roll downhill

Is there simialr cases in phsyics given we have indistinguishable particles like frmions and bosons

Basically how do we know that two steps of a process are causally linked and not just look that way because of soething analogous to "putting multiple video fra…

user image

What is a discrete Fourier transform (really)?

nvm!

7:47 PM

@ACuriousMind: Do you know of a trick how to show that $Out(SL_2(C)) \cong \{1\}$ and $Out(SL_2(R)) \cong Z / 2Z$?

@Huy Nope, I don't know about outer automorphisms

2 hours later…

9:22 PM

@Qmechanic It's been 4 days, has anyone offered any arguments?

@ACuriousMind : Not much. Chris White & TanMath replied. What do you suggest?

I hear my name..

@Qmechanic Well...I'd suggesting unlocking it since there appear to be no disputes that need resolving then, and perhaps leave a message that if someone wants to vote to migrate this question, they should first discuss this here or on meta.

@AngusTheMan: No need to delete your answer if you feel OP can use it - I just doubt it

@ACuriousMind No having read your answer I feel you are correct in what you say, it seems a bit pointless to have two answers that pretty much go over the same thing right? Are you reading out of Abraham and Marsden ? :D I love that book!!

@ACuriousMind : OK, should I first clear the current close votes to give it a chance to survive, and then set it free? (Meaning: if people again vote to migrate, then accept that without further intervention.)

9:41 PM

@Qmechanic You mean the close votes, not downvotes, right? Hm, not sure about that - will it re-enter the review queue if you unlock it?

@ACuriousMind : 1. Ups: Corrected that. 2. Possibly. (Well, my plan was to clear close votes by closing the post after unlocking, and then reopen it. Then I think it would only enter review after a flag.)

@AngusTheMan No, haven't read that, I think I learned about the moment map from these notes when I researched something about BRST cohomology

@Qmechanic Ah, okay. Seems fine to me, what does the post owner @@AngusTheMan say?

10:19 PM

hey I got a question about snells law and optic fibers

how come no light is transmitted into the cladding if (n1/n2)sin(theta[i]) is greater than 1

lets say the incidental radiation is 45 degree angle

and the index of the core is 1 and 0.5 for the cladding

so 2*sin(pi/2) = 2*1=sin(theta[r])

theta[r] is an imaginary number so is that why?

10:38 PM

oops, replace 1 with 2 and 0.5 with 1 because n cant be less than 1

Greetings, minions.

@Qmechanic @ACuriousMind Thank you for the assistance with the question. I think we might as well let it loose and see what happens. If it migrates then I feel that people on the maths SE would want it to come back, perhaps it could find some equilibrium about the fluctuations haha.

@bolbteppa I have some (good) self-written documentation on the DFT.

Ok so the critical angle is the angle when we see light stop being refracted?

@ACuriousMind Cheers for the link, looks interesting! :)

10:43 PM

@AngusTheMan : Note that migration is final if it happens. (I won't intervene further.)

@ACuriousMind What are you all discussing?

1

Q: What are the implications of integrating the Poisson bracket?

Reading Ref. 1 I admit I am a little lost in some places. I was hoping that someone in this area could explain the basic premise of integrating the Lie bracket and further is it connected to nlab's Quantomorphism group? If this is so, can we 'derive' a quantum system by Lie integration of a Poi...

mathematical-physics differential-geometry hamiltonian-formalism poisson-brackets

also is there a critical angle only when light is going from a high refractive index to a low refractive index?

@ACuriousMind Ah. Yes, the meta resulting from that is an important issue.

@Qmechanic Oh I see, well in that case, I don't suppose having a question locked indefinitely will make the difference really, if people don't want that kind of question here then I suppose it's their forum. Do you think a better place would be to ask it on the physics/math overflow site?

10:47 PM

so if light is traveling from water to air, there are angles where the light just wont refract? Why is that? Not enough energy to break the barrier between the two mediums?

@AngusTheMan Well, the review was sitting at 2 close/2 leave open when it was locked, it's not evident whether people want that question here or not.

@ACuriousMind I'd say 2/2 means that we're in a superposition. Can't really say we do or do not want.

I personally think the two close review voters were overzealous, and I would have liked to know the motivation of the one who cast the first really.

@DanielSank Yep

@ACuriousMind It wasn't me, but I can definitely see grounds for closing. I mean, uh... it's a math question.

Ok, well I guess it's not.

As I said the other day, I expected down votes for lack or 'research' etc but .. close came as a surprise

10:49 PM

Actually, I'd VTC that as "unclear what you're asking".

...and it's not well written. It refers to resources without really stating the relevant material.

@DanielSank I wouldn't say that it is tooooo mathsy .. I am more interested in the implications of integrating that group for quantisation purposes.

could someone answer my question? :/ Or is this not the appropriate place to ask them?

@Nova The main site is for physics Q&A. That's the whole point.

@AngusTheMan What is "nlab"?

@DanielSank Its this site where I always find myself ending up! It has interesting pages on geometrical things etc

@AngusTheMan What is "nlab"?

@AngusTheMan Ok, I couldn't tell that from the question. Can you fix that?

10:53 PM

ncatlab.org/nlab/show/HomePage

yeah sure thing!

@DanielSank So what's the point of this chat?

@DanielSank : We can also make a compromise: I unlock it but close it as unclear what is asked. That way @AngusTheMan can edit the post, and people can vote to reopen?

@DanielSank That argument I can see. @AngusTheMan you should state the basic setting (cotangent bundle, Poisson bracket, classical observables) and then outline what you want to know (I suspect it's "physical meaning" of "Lie integrating" the bracket, and connection of that Lie integration to the "quantomorphism group". Did you stumble upon that reading this post?)

@Nova It's...a chat. Does it have to have a point?

@AngusTheMan More importantly, try to make all questions self-contained. If you refer to "nlab's xyz group", it's best to state precisely what that is right in the question. If a would-be answerer has to click a link and read a bunch of stuff that person is less likely to get to the point of producing an answer for you.

@Nova sock puppets.

Right, so I was hoping I could have a quick discussion with some brilliant physicists about concepts I am struggling with/curious about

10:56 PM

Well, that's what *I'd* do, but I'm not the mod around here.
..unless you believe that guy who says you're all under my control.

Hehe

@Nova Go for it, but we might tell you to just ask on the main site.

Also, no promises on the brilliant part.

@AngusTheMan : Unlocked & closed.

@Qmechanic dat mod power.

Oh, the first close voter was @Danu!

10:57 PM

@Qmechanic Which question is this?

@DanielSank brilliant relative to me (at least). Essentially, I was curious about why the critical angle exists when light is traveling from a medium with a high refractory index to a medium with a low index like water to air

@ACuriousMind That scoundrel!

@DanielSank @ACuriousMind @Qmechanic That sounds a fair plan. I will edit it over the next few days as I have some things at the minute! I appreciate the help with it etc!

@Nova Definitely ask that on the main site. It's a good question. I don't know the answer!

@DanielSank Probably just another one of your accounts :P

10:59 PM

maybe we should ask him why he didn't think it belonged here ?

@DanielSank no way! It's a good question? Ok, I'll ask on the main site.

@AngusTheMan I just pinged him up there, he will no doubt read the transcript in detail and deliver a statement ;)

@AngusTheMan Yeah @Danu, what's the deal?

@Nova I can't explain that better than pointing at Maxwell's equations. I'd be interested to understand it better.

@ACuriousMind I hope he stands up to the rigorous questioning :p

@ACuriousMind Again I have it upvoted so I guess I have been there before! I favourite a lot of questions based on the assumption I will come back to them and read!

@AngusTheMan Yes, Danu's dedication to the chat room is... well it's certainly unique.

@ChrisWhite Dude, that's Bespin!

11:12 PM

0

Q: Network science can be a branch of physics

I asked a question about some natural network and after about one hour the question came "On Hold", and there is something similar. But there is many physicist that work on this area(some thing like ecology network, biology network, finance network and models related to them). what is the differ...

user54412

@DanielSank You're right! Don't know how I missed that

Bespin?

@DanielSank Posted! :D

0

Q: Why does the "critical angle" exist?

I understand that when light moves from a medium with a high refractory index to a medium with a low refractory index (water to vacuum), that there exists a "critical angle" at which no more refraction occurs. 1.) What is happening conceptually(chemically, physically, thermodynamically, electrom...

user54412

@ACuriousMind well technically Cloud City

Ah

Well, the similarity is there

11:22 PM

@ChrisWhite Why you slimy, no good, double crossing swindler. You got a lotta guts comin' here, after what you pulled.

@Nova Edited! :D

Guys, seriously, please stop closing poorly written impossible-to-understand questions which might be off-topic as off topic.

user54412

Oh hey, Sports Illustrated did an article about Caltech.

Close them as "unclear what you're asking".

11:45 PM

@DanielSank re the critical angle question, I'm sure there's some kind of "destructive interference" phrasing of all of this but

I don't really want to stoop down to "imagine little moving wave sources" hehe

Maybe that would be useful though

@DanielSank For some reason, the unclear what you're asking close reason is not very popular. I've run across many "off-topic" votes for stuff that was just so confused that it was impossible to tell whether it's on-topic or not. It might have something to do with off-topic allowing you to write a snappy reason yourself...

There's no refracted state that satisfies conservation of energy, conservation of in-plane momentum, and the photon dispersion relation.

@elifino Of course. See my answer/DanielSank's comment.

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