@AntonFetisov yes?

Well it is an example of a bilateral symmetric system with a current.

@0celo7 which compactification scheme will u use

\o @JohnRennie

The electric field is zero, so symmetric. We make no claim about B, since we don't know B in our problem either.

Afternoon

@Slereah there are multiple?

what's on the menu for supper?

@AntonFetisov by bilaterally symmetric do you mean reflection symmetry in the plane of the circle?

Something started that current. If you reflected the apparatus that did that, it would cause a current in the opposite direction.

I mean reflection symmetry in the diametral orthogonal plane.

The current isn't symmetric, but that's what we're trying to do.

We have a system where the electric field is known to have such symmetry, and we're trying to prove/disprove that current is 0 by symmetry.

So here is an example where E is symmetric and J isn't.

But don't you have to do something to initiate the J?

@Slereah there are multiple?

I mean, I kinda agree that something started it, but symmetry doesn't know about history. The example shows that symmetry alone can't zero the current under these conditions.

@0celo7 Oh nvm, I was thinking of boundary construction

double send, nice

Which is related but not the same thing

In that sense in our problem "something" also can start it:after all, the bar is moving.

True. But if moving the sliding wire causes a current then it seems it's breaking symmetry.

Probably there is no current, but I don't see how to prove it without solving ME in detail.

Can you actually put your derivation into equations? Because I can't.

I will think about it more, and if I think I can put an coherent argument together I will get back to you

why is electromagnetism taking over the chat

computers run on it

So clear bias

computers run on magic you fool

black magic

I've read EM from a bundle perspective and it is magic

@bolbteppa since mathematical physics are math for theories like quantum theory and relativity if some1 wants to study about them as a mathematician what lvl o physics maturity he needs?

a phd

physicists don't actually use math

it's all a lie

@Slereah mb what Christo Doulou does isn't that bad

it's overkill but it might be rigorable

Did you finally get the trick

well, the trick is that he never writes down Straumann's nonsense expression

so it's still kind of shady

but that's how physics is

@AntonFetisov before I stew, can you let me know if you agree with the following? Without resorting to the weak interaction, there is no way to communicate the meaning of "left" or "right" unambiguously with only descriptions (no physical artifacts or diagrams).

@Slereah you're only guessing what's right, so there's bound to be nonsense

Yes.

Ok thanks

Is this question not about physics ? I think it is.

what do you think of feynmans 3 vollumes?

why would anyone actually read Feynman

@Ben I think it's easy to show by symmetry that under assumption of nonzero resistance there can be no current, since you can exclude E along wire by symmetry. But if wire is superconducting, then I doubt it's possible.

@Slereah Hmmmmmmmm

Let's say you prove that current is time-constant - ok, but that would mean that when the bar was infinitely close to the left rail, there was some looping current.

suppose I have an AF manifold

can I choose $g_{j0}=0$ in a neighborhood of $\infty$?

That's weird, but it's also possible, since macroscopically this current would be 0. This relies on some approximations, of course. We need to assume wire infinitely thin. But we did it anyway, and the problem doesn't explicitly exclude this case.

@Blue im a math undegrad and dont want to get in detail of everything i just want a general mapping of physics

so i thought about feynmans lectures

I imagine reading Feynman would be absolutely awful for anyone with an ounce of rigor in their bones.

try it

So there may be some current, but it's not caused by the motion of the wire?

\o @BalarkaSen

We can't exclude it.

Maybe there could also be some current caused by the motion, I don

don't know.

hm.. i thought in order to do the math you need to understand and have some intuition

I'm not sure what math would be used in Feynman besides basic algebra and calculus

just grabbing a book on applications of topology in physics i dont think will do the work :P

I guarantee Feynman didn't even know what a topology was

(nor did he care)

hahaha

@Blue It might very well be although I don't think it quite is. The fact remains, though, that it very much about physics. Specifically, physics notation. Notation about labelling multiples of the same variable, which is a very physics-y thing. At least, I think so.

@ManolisLyviakis Feynman's lectures are good and will give you some good physical inuition, but the sheer volume of it can be intimidating. Also you may need to have some physical intuition to start with.

@AntonFetisov thanks for humoring me, think I'm less bothered now

Humoring?

And is it really opinion based when most of the answers agree that subscripting is the agreed-upon notation ? It also seems like a hard question to phrase to Google and is also something not immediately obvious to beginners in Physics. As such, I think such a question would be useful in the future.

Yeah: putting up with questions

So what would you suggest as an introduction to physics to some1 with a good math background . interested in application of topology-group theory-diff geometry on physics

Oh. You're welcome. If you can rigorously prove that dj/dt = 0, write an answer. It would be interesting to see.

@0celo7 he does almost everything with basic algebra, at least in the first volume

yes i have a copy of it atm in lib and there is no math at all

though his topics are good

@ManolisLyviakis Quantum mechanics and QFT have quite a lot applications of groups, diffgem and topology. E.g. particles are irreducible representations of the Poincare group, and they live in sections of principal bundles.

But I don't know what could be a good introduction. You can try reading something like "Quantum mechanics for mathematicians".

ohh sounds good

so no need to read any classical physics

@Blue as you said "intuition" is his main focus.

ill eb forced on taking a course on electromagnetism this semester

so i can just tackle the subjects straight away?

quantum mechanics and general relativity? no need in learning inclined planes really good? :P

you have to remember, this is a noble prize winner teaching first year physics

@Blue ??

what are these formulations?

ok

@ManolisLyviakis this is adult physics en.wikipedia.org/wiki/Course_of_Theoretical_Physics

@JohnRennie, just carrying on from the comment...

Hi Steve

@bolbteppa haha is this for real 10 tomes?

...the ball is not moving horizontally relative to either in their own frames. Rather, it simply takes a different straight-line path. They can agree that the velocity is the same, if they choose to disagree about other variables.

Suppose you're holding the ball and at time $t=0$ you drop it. So at this moment the ball is stationary with respect to you. I am whizzing past in my car at velocity $v$ and I pass you and the ball at the same moment $t=0$.

Since I'm moving at velocity $v$ relative to you, you (and the ball) are moving at velocity $-v$ relative to me.

The two of us can't possibly agree that the velocity of the ball is the same.

But then you've already constrained the variables by assuming an absolute time frame ("at the same moment"). Btw I'm not too familiar with mathematical notation and I'm having to infer the meaning of your symbols.

@Blue so classical mechanics is the base of it all quantum theory and relativity what would you suggest then?

@Blue a book on classical mechanics with Lagrangian and some Hamiltonian formalism.

ok !

Shankar is good.

If you want to understand Noether’s theorem in GR you need more than Shankar...

to start

But why are the two different conventions adopted? The Newtonian model doesn't require an absolute time-frame to describe the ball moving - it's only because we can communicate faster than the ball (and see it in motion), that we are forced to accept that velocity varies between frames rather than the flow of time.

@Steve Newtonian mechanics is basically conservation of momentum, and that does require a universal time otherwise momentum wouldn't be conserved.

Special relativity extends Newtonian mechanics. The two are effectively the same at everyday velocities. Only when you get to velocities comparable to the speed of light is there a significant difference.

Special relativity still conserves momentum, but now it conserves four-momentum

If you say that both agree about the time, then what will happen when the ball is once thrown normally form top and obliquely projected upwards from the same height?

@JohnRennie what will be your thought experiment then?

@JohnRennie, accepted, but why is it assumed that the flow of time is "really" changing in SR? For example, when a redshift is observed, why do we reason that time has "really" slowed down for the source (as far as the receiver is concerned in his frame), rather than simply that it is taking longer to traverse the distance?

@NehalSamee If you throw the ball obliquely upwards then it's initial velocity will have both a horizontal component $v_x$ and a vertical component $v_y$. Yes?

...Since we don't reason that way in classical mechanics.

@Steve to really understand SR you need to understand that it is based on a symmetry called Lorentz covariance. It tends to be taught to undergraduates using rays of light in various improbably contraptions, but it's really the underlying symmetry that defines it.

@Steve So I'm not going to attempt to answer your question as it stands because any answer is going to be unsatisfactory. Once you start asking why questions about SR you can only really answer them by understanding the basis of the theory properly.

@JohnRennie Right...But I want to know how would you interprete the situation with a thought experiment and claim that the freely falling body falls quickly than the obliquely projected one...?

@JohnRennie, but I don't think it's the case that I'm misunderstanding that aspect of the theory. I'm quite sure that the maths add up. It's when the mathematical relations are translated into claims about the real world, that understanding seems to be vague.

@NehalSamee So suppose I throw the ball with vertical velocity $v_y$ and horizontal velocity $v_x$, and just as I throw it you come speeding past me with a horizontal velocity $v_x$ (i.e. same velocity as the ball).

It is the weekend

hurray

@NehalSamee Relative to you the ball still has a vertical velocity $v_y$, but now it's horizontal velocity is zero.

So you see the ball travel straight up, slow to a halt, then fall straight back down again.

While I see it move in a curve (actually a parabola).

@JohnRennie That's great!!!Thanks a lot...

@0celo7 Probably not?

@Steve I'm not sure what you mean by It's when the mathematical relations are translated into claims about the real world, that understanding seems to be vague.

Just pick a metric with $g_{j0} = 1/r^3$

I think it would be AF

@JohnRennie, what I mean is that when the maths is applied (maths being simply a tool to describe the physical world), there is a lack of clarity about what it means/how it is interpreted. As I pointed out with the ball-throwing analogy, it is not necessary to hold that time flows at a constant rate and velocity varies, in order for the Newtonian model still to work in its own terms - the assertion of a absolute time frame is a constraint that arises from outside the geometry.

@Slereah well I want to make a coordinate transformation of course

\o @ACuriousMind

@0celo7 Hard to come up with a proper counterexample because there aren't a lot of exact metrics that are AF and aren't rotationally symmetric

@Steve All physical theories are basically maths. Specifically they are mathematical models. We test them by comparing their predictions with experiment, and this is a no-bullshit test. If the predictions of the theory don't match experiment that theory is dead.

at least somewhat

Ahoi

@Steve Newtonian mechanics passed every test applied to it right up until we started looking at relativitic velocities.

@Steve you may argue that the assumption of absolute time was ... well ... just an assumption, but it worked. Newtonian mechanics worked perfectly for centuries and still continues to work perfectly outside particle colliders and GPS satellites.

@JohnRennie Newtonian mechanics doesn't apply to magnetic fields at any speed

@Slereah sssshhh :-)

@JohnRennie, but as I say, I'm not querying the predictive validity of the mathematics...

lol

@Steve then what are you querying?

@ACuriousMind so is your RAM faulty?

@JohnRennie apparently not, but we have no idea what caused the bluescreens :P

or is that classified info?

@ACuriousMind faulty CPU fan?

Perhaps? The laptop worked fine today, though

Unless the issue recurs I'm just going to forget about it ;)

...I'm querying which variables are held as constants (and, perhaps incidentally, what the actual meaning of those variables are understood to be - that is, what aspect of the physical world they describe). It might seem self-evident what the "speed of light" means, for example, but I'm not quite sure it is so simple.

...to take an example...

...If light is redshifted, then it seems perfectly reasonable to say it has slowed down - because, for example, a wave with twice the wavelength, must take longer to traverse the same distance as a wave of shorter wavelength.

@ACuriousMind some paper says that perturbative QFT doesn't converge because the sum doesn't contain instantons

Is that correct

@Steve Are we talking about the redshift due to the source moving away from us?

Or a gravitational redshift as seen in black holes etc.

@JohnRennie, yes, or us moving away from the source. With gravitational redshift, you can explain it in terms of space expanding - but I've done some reading that shows gravitational effects can be equivalently described in terms of the "refractive index" of space, where light speed varies.

@0celo7 I don't think the Kerr metric has zero $j0$ terms in any coordinates

And it's AF

Proof?

You can always do that locally

So why in a neighborhood of infinity?

If you can compctify then just do it in the compatified guy

Then uncompactify

@Steve The red shift due to an object moving away from us, or us away from the object, is very simply explained by the light having to travel farther as the separation increases. Why would you start arguing that it's because the light has slowed down?

Magic

The neighbourhood of infinity isn't very "locally"

It is in the compactified spacetime

Hm, true

The “unphysical spacetime”

@Slereah no, the traditional lore due to 't Hooft is that it doesn't converge because it cannot converge for negative couplings, so the radius of convergence is zero and the perturbation series merely asymptotic

@Steve Thats similar to a problem I discussed here..... wait lemme find it

@ACuriousMind There's something about the 0D case, tho

Where the non-perturbative case does converge

Please don’t be racist @skullpatrol

But not the perturbative case

Or should I call you Mrs. Trump

@0celo7 sorry

@Steve Do you mean something like this chat.stackexchange.com/transcript/message/42109740#42109740 ?

I don't know what it means for the non-perturbative approach to "converge" @Slereah

@ACuriousMind The path integral converges

@JohnRennie, but the light is not just travelling farther - each end of the wave is travelling different distances, and the actual whole wave is moving more slowly.

@0celo7 Wouldn't a neighbourhood of $i^+$ have infinite extent in the original spacetime

...That is, two "blue" waves can travel the same distance in the same time as it takes for a single "red" wave to travel.

@Slereah ah, but the issue in higher dimensions is not that the path integral doesn't converge, it's that it's ill defined

@Steve But you know the object has some non-zero velocity relative to you because you can observe it as it passes you. That is, at the moment when both of you are at the same point you can observe the object moves away from you.

@ACuriousMind It's define in 2D, yet I still think the 't Hooft argument applies, no?

@Slereah yes

Does it even matter if the path integral converges or not?

I guess it might be interesting to find the Riemann coordinates of $i^+$ for the Kerr metric

@Slereah Sure, but the argument is simply about a perturbation series around zero coupling, it doesn't apply to a non-perturbative method at all

Interesting? We disagree on the definition of that word, clearly.

@ACuriousMind Do you know what that paper was on about then?

@Slereah no

@PrathyushPoduval, I probably do mean something like that. I'm struggling to find the reference I wanted quickly though - I'll come back to you.

Something about the difference of terms between the non-perturbative and the perturbative result being non-analytic and corresponding to instantons or something

arxiv.org/abs/1201.2714

It was this paper

Instantonic contributions are simply invisible in the perturbation series because the term they contribute is non-analytic and Taylor expands to identically zero

@JohnRennie, I'm not quite sure how that applies to what I've said, can you elaborate?

(I'm on mobile and can't read the paper for you right now :P )

@ACuriousMind could one make some sense of QFT as the perturbation and instanton contribution together?

@ACuriousMind so are you a proselytizing (spelling?) vegan?

@Steve the light emitter passes me, and as it passes me I can measure its velocity $v$. I can be sure about this measurement because the object was right there next to me at the time. Now I calculate the redshift based on the speed of light being constant and the separation distance increasing at a rate $s=vt$. And ... I get the correct answer. So why would I start wondering if the speed of the light had changed?

@Slereah yes, the traditional way is to sum the perturbations around each instantonic vacuum over all instantons

@0celo7 what?

@ACuriousMind Does that converge?

or is that an open problem

@ACuriousMind why what?

@Slereah probably not, but I've never seen anyone arguing about that either way

@JohnRennie, because as you pass the object (if you're not on a collision course), blueshift changes to redshift. Why do you maintain that the velocity of light remains the same (whereas in the ball-throwing example, you held that the velocity varied)?

@ACuriousMind unfortunate

Why is QFT so bad

I mean, as long as you are still doing perturbations, 't Hooft's argument still applies, why should the instantons do anything about it?

@Steve blueshift does indeed change to redshift, and both are exactly described by assuming the speed of light is constant and the distance to the object changes at the constant rate of $v$ metres per second.

I probably don't know enough analysis to be sure!

In the ball throwing example the ball is being accelerated by gravity i.e. it's velocity is not constant.

@PrathyushPoduval, the theory I was looking to refer to was "polarizable vacuum" - I'm not endorsing or adopting it, but it appears to suggest that general relativity can be fully described otherwise than in terms of "curved space", but instead in terms of changes to the permittivity and permeability of space.

Ahahah

polarizable vacuum

@knzhou: the ball takes an infinite time to reach the event horizon.

You know who's a big proponent of PV?

Eric Davis

He thinks it explains flying saucers

@knzhou: at any finite time the ball can indeed ricochet off something and bounce back to you.

@JohnRennie, but you've missed the subtlety - the speed of light is not constant. It is faster for blue, slower for red.

@Slereah it's not about analysis - the argument is purely physical: if the radius of convergence was non-zero, there would be stable theories with negative coupling, which allows for infinite particle creation and is hence unphysical

@Steve and the interferometry measurements that say the speed of light (in vacuum) is constant?

@Slereah is that the insane Air Force guy?

@0celo7 yes

@ACuriousMind oh Jesus that’s an acceptable proof?

It is an acceptable physical argument.

@JohnRennie, but was the interferometer moving? Like I say - and I must be very clear on this - I'm not trying to propose alternative mathematical theory for relativity. I'm talking purely about the application and physical interpretation. To me, the very notion of redshifting (in the way both me and you understand it) is capable of being interpreted as change in the physical speed of light (and what remains constant is something else, which I can't quite differentiate in words)...

@ACuriousMind I don't know what that means. How do you know that some field theory doesn't have infinite particle creation?

@Steve you're free to propose any mathematical model you want to predict observations. Provided your model also agrees with experiment then it is equally valid.

@0celo7 I don't. We just think that shouldn't happen ( and I should add that the QFT perturbation series has indeed been shown to be asymptotic, so physical intuition worked correctly here)

@JohnRennie, but I'm not proposing an alternative mathematical model. I'm trying to formulate a coherent interpretation of the one we already have.

@Steve The mathematical model we have describes the redshift on the basis that the speed of the light is constant. If you're saying the speed of the light is not constant then your model is different.

Nonperturbative QFT feels like wizardry to me.

@Steve I suspect you're asking the question what really happens and that question has no answer in physics. We leave that question to philosophers, though physicists have been known to discuss it late at night in the bar :-)

But that's probably as much a statement about my understanding of QFT as about nonperturvative physics :P

No, I'm saying that the "speed of light" in the model is some sort of invariant that is differentiable from any physical thing it can be related to, such as a wave. Because as I say, with redshifting, it really does take longer for a long wave to traverse the same distance as a short wave, because it has a spatial extent (it's not a point).

is nonP QFT observable

Some of it is, I think.

@JohnRennie, why are physicists reluctant to discuss what physics actually means? Physicists must have their own physical philosophy, otherwise they would not be able to apply their knowledge to the physical world.

I think a lot of what we know about QCD is nonperturbative

Buuuut I'm definitely speaking beyond my own radius of understanding :P

@Steve that's 100% wrong. Physicists construct mathematical models and test them by crunching through the maths and comparing the predictions to experiment.

@JohnRennie Well, that is a philosophy technically :p

Instrumentalism and all that

It's certainly true that the successful mathematical models were generally based on intuition about the physical world, but maths is maths and there's no arguing with a mathematical calculation.

But how would they construct and interpret the experiment, without operating on some understanding about what physical things relate to which numbers? It's that subterranean understanding that I'm addressing.

@Steve The physical theory also has a "translation" between physical quantities and elements of the theory

@JohnRennie, but nobody is arguing with the maths. We're discussing what the maths means.

We're discussing what the maths means - so we're back to what really happens

@JohnRennie, and what you call "intuition" is perhaps equivalent to what is formally called "physical philosophy".

@Steve Intuition is disposable. What matters is the mathematical model.

@JohnRennie, but what is the use of a physics that doesn't attempt to describe "what really happens" - that's the whole point of physics, to predict something about what happens in reality.

If you arrived at a good model by pure luck that's fine.

@Steve if you want to know the analytical philosophy behind it

But if you dispose of your intuition, how do you know what it means, and how do you apply it, without any intuition as to how it is to be applied?

@Steve the whole point of physics is to correctly predict the results of observations.

A theory has an abstract formalism (that's the mathematical model) and rules of correspondence between the formalism and reality

The "model" is a fully interpreted system of propositions with logical structures isomorphic to the formalism

@JohnRennie, but what I'm asking is, how do you get any observations, or relate existing observations to the theory, without applying the physics with what you call intution?

@JohnRennie, why is it that you see discussion of those "intutions" as being somehow peripheral, disposable, or less worthy of discussion?