2:51 AM
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Specifically this question. Why doesn't my phone scroll if I put a ring flat on the screen? It's been closed as being too engineering-based, and the Feedback message gave options of other SEs it might fit in. I didn't realise that there was a separate Electrical Engineering SE (although I did cho...

2 hours later…
5:04 AM
(How) will the Lorentz transformation change if a boost was made to a frame where the medium was no longer the same medium as the previous one from which the boost was done?
I think this should be an inhomogeneous transformation so invariance of interval will not be preserved anymore, and the background is not Minkowskian anymore..
so it's not a "Lorentz transformation" anymore???

There is no such thing as a "medium."

5:27 AM
If you are thinking that I am talking of some aether medium, no i am not...
I am just saying that say light was travelling in vacuum and then after some point in space it is travelling through glass...we keep a lab frame in vacuum and transform it to some frame moving through the glass...now the question is whether lorentz transformations relate this two frames? I think not cz of the reasons mentioned above.

2 hours later…
7:39 AM
@ManasDogra the notion of "frame" does not include a notion of whether you are in a medium or not
The Lorentz transformations don't change when you have a medium, all that changes is that the "speed of light" $c$ no longer is the same speed as the actual speed of EM waves in that medium

So I thought initially but if we just look at the $ds^2=ds'^2$ This shouldn't be valid if speed of light are different on two sides of the equation.
It isn't as simple as we are in a single medium..One frame is in one medium and another one is in another one.

@ManasDogra the speed of light is not different on both sides

Yeah why so?

the "speed of light" that the Lorentz transformations/relativity care about is not intrinsically linked to the actual speed of EM waves
it's more "the speed of massless particles" or "the universal speed limit"
when light enters a medium, the particles one would associate to the excitations of the medium have mass, and so this speed is no longer the speed relativity cares about

So you are saying it is $c$-the cosmic speed limit on both sides?

7:44 AM
yes

Hello

But the invariance of the interval is based on homogeneity of space which is clearly broken due to presence of a medium..If suppose we divide the space through which the particle can move to two parts-one part is vacuum and the other part is not. Then the space isn't homogeneous anymore..

@ManasDogra "homogeneity of space" just means that the laws of physics are the same at every point in space

@ManasDogra Light in a medium is not light. It is a mixed state of light with the electrons in the medium.

they still are - the laws include the effect of a potential medium at every point in space

7:48 AM
So the speed that light travels through a medium is not "the speed of light".
The speed of light is always just c regardless of what media are present.
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Time dilation, increase in mass, Lorentz contraction calcs all involve velocity of light in vacuum. But in optical media light slows down. So what of relativity calcs in media? Do we ever need to adjust the speed of light?

that some points have a medium and some don't is not a sign that the laws of physics are not homogeneous - it's just a sign that the state of the world is not homogeneous, which was obvious to begin with since space isn't filled by some uniform goo, but by discrete planets and whatnot
(of course in the end it turns out that the inhomogeneous state does affect relativity - that's general relativity then, where the distribution of matter determines the metric, but that's not what you're doing here)

So if I ask whether the space I described is homogeneous or not, you are going to check(according to this definition) whether the "laws of physics" hold good or not..but that's what my original question was...whether lorentz transformation hold good in the case I described or not...

So this is just ASSERTING that lorentz transformations hold true--like this happens just agree to that..
This seems cyclic to me
@JohnRennie I can't even call that "speed of light in some medium"?

@ManasDogra I'm not sure what it means for Lorentz transformations to "hold good"
it is an experimental fact that special relativity as I just described it is an accurate model of our reality (ignoring gravity)

@ACuriousMind Yes..yes..that's what I was thinking..but apparently I was wrong..I don't see how..I thought that presence of some medium implies a change in the geometry and hence we can't use Lorentz transformations in this case anymore--we need GTR.

@ManasDogra You can call it whatever you want, but it's not the speed of light, it's the speed of a mixed state.

7:57 AM
@ManasDogra the thing is that the "slowdown of light" in a medium is not caused by geometry
it's caused by the light being different excitations

@ManasDogra The speed of light is a fundamental geometric property of the universe, but the speed of light in a medium is not.

(it always is, in fact, just to different degrees)
so whatever argument you want to make about "the speed of light in the medium" can't work simply because there is no unique speed of light in any given medium
and, differently: The "speed of light" would be a universal speed limit even if there was no light!

What's wrong in this simple logic?
Presence of medium(say glass)-->presence of matter-->need for GTR.

No observer will ever perceive anything travelling faster than $c$
Why would this change just because you put the observer in a medium that slows down EM waves?
Did you think relativity would just go away if there was no electromagnetism?
@ManasDogra It's correct, but it is correct only in the sense that all matter technically creates gravity, even a tiny test mass. Again, the slowdown of light in the medium is not a GR effect, it's a condensed matter effect (the "photons" are massive)

I think this problems stems from me learning derivation of Lorentz transformation from an old viewpoint..

8:04 AM
you're really just getting hung up on people calling the speed limit in relativity "the speed of light"

So from the modern viewpoint...Deriving Lorentz transformation using Einstein's 2nd postulate about light and all is not at all necessary?

if we would have called it "the speed of gluons" or "the massless speed", you wouldn't even wonder about this

OKAY...OKAY...NOW I GET IT
oh my god
ok ok ok ok ok...now now now i completely get it...hmm..nice..

@ManasDogra the 2nd postulate, when stated carefully, is about the speed of light in vacuum

so someday if something somehow moves faster than light, the c in lorentz transformation will get replaced by speed of this new thing right?

8:07 AM
@ManasDogra yes, but also no, in that there are effects of the speed limit other than setting the maximum
the speed limit enters in relativistic velocity addition - the addition is the more unlike normal addition the closer the velocities involved are to the speed limit
so if the speed limit was secretly higher than we thought, all our computations would be off
which is why we're reasonably certain the current speed limit is the correct one :P
i.e. a world in which the speed limit was higher would be unlike our current world in many aspects, not just in what the maximal speed is
plenty of atomic physics/molecular phyiscs/chemistry has relativistic effects that would be different if the value of $c$ was different (more precisely, if something like the fine-structure constant was different - it is not actually meaningful to talk about changes in dimensionful constants, see this answer by Emilio)

Thanks...I was hoping to ask a a question like "If the lorentz transformations really didn't hold for a medium change, what happens inside particle colliders where there are a lot of sensors and other stuff..", Now I understand that L.T. doesn't change just due to presence of a medium...so..that question is ill posed.

It's good that you recognized you should first make sure you understand how Lorentz transformations interact with media before asking that more specific question!
it's often more difficult to rewind such specific ill-posed questions to the exact point where some misunderstanding led the asker in the wrong direction

8:22 AM
Hmm.. As always Thanks @JohnRennie and @ACuriousMind.

:-)

9:19 AM
I remember that Ronald Mallett pretended that the speed of light in a medium was the same thing as the speed of light in GR
and therefore he could make the spacetime he wanted by simply slowing down light in a medium

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2 hours later…
11:09 AM
If a particle travels faster than light, it's time travel backwards ???

depends what you mean by that

11:25 AM
I was reading a book on general relativity it says, "if a body propogates through space with some speed, the slower its clock ticks. Faster the speed ; more slower the clock ticks. Its time is slowest when it travels at speed of light."

11:39 AM
that is the problem of relativity
"Time" can mean a few different things
Especially for tachyons, I can't really answer that question without a precise definition of it :p

11:58 AM
Padmanabhan gave the best lectures on general relativity that exist on youtube

@bolbteppa Really? Personally I was following these ones

They are heavily influenced by Landau as his book is also but he does things slightly differently and adds modern stuff

@bolbteppa Interesting havent read Landau was following dinverno and caroll

Maybe give his lectures a try after you get through them

Does he offer homeworks etc on his webpage?

12:04 PM
I'm not sure but I doubt it

He passed away :(

12:18 PM
Mysterious science

The language looks extremely legit
what language is that though

It's not a language, those are from the codex seraphinianus, a work of art where the writing is meaningless

Very aesthetic Feynman diagrams

@ACuriousMind Art ?!

I mean I hope it is art
If it's real I'm not sure I like it

12:28 PM
@Slereah lol
Every art conveys the idea of the artist
what this art is trying to convey

Do tell me the ideas conveyed here

@Slereah I dont know :P what it could be ?

It's mostly a surrealist book
Everything is kind of dreamlike or like a hallucination
Everything looks familiar but you can't quite tell what most things are or what's going on
sometimes you can sort of tell what's happening but other times you're not even sure as to what something is

for the writing at least the article has word from the author: "what he wanted his alphabet to convey was the sensation children feel with books they cannot yet understand, although they see that the writing makes sense for adults"

Mysterious

12:34 PM
@Slereah General relativity in a nutshell

that one is actually in the zoology section
while mysterious, the book is organized by themes that you can roughly get

@ACuriousMind Nice

This is the lifecycle of the blorgabloo
or whatever this is

@Slereah Microbiology should make sense
Idk why it is in Zoology

Well lifeforms in general
Except plants
that's the first chapter

12:36 PM
oohhhhhhh

I guess the book is basically what you'd get if you asked a neural network to make an educational book

@Slereah lol

It has rainbow parasites

weird

12:53 PM
@Slereah However, lets leave particles, suppose if I am sending a signal to a receiver which turns a light bulb on, Then will the light bulb starts glowing before I send the signal ?

Depends on the configuration, but yes, you can have such systems using tachyons
It's called the tachyonic anti-telephone, which is a very fun name
Also Tolman's paradox, in a less fun way

Interesting

@Slereah is that an early prototype of plumbus?

@glS It is the same kind of idea yeah
Surrealist stuff

Is that the rick thing ?

12:57 PM
It is in Rick and Morty, yes

It is also somewhat similar to the Fantastic Planet

@Slereah pretty cool pictures though

It is a fun book

@Slereah how do you even find all this weird stuff

1:05 PM
It was recommended to me after watching Xavier Renegade Angel
another thing for normal people to enjoy

Taking lectures to juniors takes a lot of patience

@Slereah wtf. Do you have that book by the way? it's the kind of things that would probably be pretty cool to actually have physically

I have ordered it

it goes at 500€ on amazon... I hope you didn't take that one

@Slereah what

1:09 PM

there's a calendar version that goes for 10 euros amazon.it/Codex-Seraphinianus-Calendario-Luigi-Serafini/dp/…

It is quite a watch

@Slereah is that a full series? now I want to know what is in the black door

I mean if you want plot resolutions I'm not sure this is a show for you

> Xavier features a style characterized by an elaborate and nonlinear plot following the humorous musings of an itinerant humanoid pseudo-shaman and spiritual seeker named Xavier. The show is known for its ubiquitous use of ideologically critical black comedy, surrealist and absurdist humor presented through a psychedelic and satirically New Age lens.
yeah, that didn't help
"Itinerant Humanoid Pseudo-Shaman" is a dope band name, though

1:12 PM
The cuddlecrumbs

it starts here it seems: youtu.be/5cFvwT6gHns
did you watch the whole thing?

I did
there is a very broad plot but it is not too important nor does it ever get really resolved

"coroner ruled it a simple case of death by mysterious fire" god this shows is filled with gems

That episode does have a line "I'm a survivor, we're a dying breed."
"Like most folks, I've always been different, but not like the others."

@Slereah was going to quote that as well
so many drugs were involved in doing this...

1:21 PM
it is very stream of consciousness

1:31 PM
Hello,

I'm a physics graduate student and I've decided to buy a macbook. I'm planning to specialize in lattice QCD (which is mostly done on python). Is M1 Macbook Air sufficient or do I need to go for Pro (because of the fan inside)?

@AjayMohan all your "serious" simulations should be run on your university's computers, not your personal one, no?
also, it would really surprise me if the lattice simulations themselves were done "mostly on python" - simulations usually use close-to-the-metal languages to take advantage of their hardware, i.e stuff like C, Fortran or whatever language your GPU understands if you're running stuff on GPUs

Depends on the scale you're doing it I guess
if you're doing a small lattice to test algorithms that's probably fine
If you're trying to simulate a proton that may be a bit much

I mean, sure, some of the toy stuff I did in my lattice computations course I ran on my own computer, but it was really small and really slow - and we wrote everything in C because that's what the lecturer's working group used on their cluster for their real work

Also I wouldn't advise a mac in general for programming

1:47 PM
@ACuriousMind They haven't given me a university computer yet but you're right, I also assume that I'll be doing all the serious work on the university computer.
@Slereah Why is that so?

It's terrible

I actually know several programmers who like working on a Mac :P

also in general most programming tools are written for linux
Mac is mostly a linux platform these days but it can still be annoying

OSX is "linuxoid" enough that most stuff works well enough

very fancy

1:50 PM
I mean, I wouldn't use a Mac personally either, I'm just saying there's a lot of personal taste involved and many people can work perfectly fine with them

@AjayMohan I have an M1 air and haven't ran into anything that makes me wish I went with the pro. I generally do any compute-heavy stuff externally and having something based on ARM can cause a few inconveniences
I say Mac is the best laptop choice :D

@Dan
All that can be done on linux, can be done on mac too right?

I wouldn't necessarily say everything and even less so with M1-based macs, but it's complicated
I suppose it depends on university and group, but we had linux machines we could connect to for long-running computations

I see

Though we also did a fair bit of X forwarding through SSH, which may not be doable on mac anymore
Scientific computing can get weird
Actually I take that back, it looks like XQuartz even supports apple silicon these days

2:04 PM
I see..

even I'm making my decision upon the contingency that my university provides a linux system to fall back on, in case things dont work with mac.
How much RAM did you purchase for your M1 air? 8 or 16 GB?

I went for the 16GB model
though it may be worth noting that I'm not really in heavy scientific computing these days
I did make it through university mostly with a macbook, though I always had linux machines as a failsafe

I see.. Thanks for your input. I'll consult some more before I make the decision.

Sure thing! I will agree with ACM that it's mostly a preference thing though
If you go the linux route, you may want to carefully consider the laptop you use...some can be a bit more of a pain than others in my experience, especially if things like discrete GPUs are in the picture

2:38 PM
In combinatorics, the twelvefold way is a systematic classification of 12 related enumerative problems concerning two finite sets, which include the classical problems of counting permutations, combinations, multisets, and partitions either of a set or of a number. The idea of the classification is credited to Gian-Carlo Rota, and the name was suggested by Joel Spencer. == Overview == Let N and X be finite sets. Let n = | N | {\displaystyle n=|N|} and x...
If you can just master these 12 you become a genius, I barely get one of them :\

2:56 PM
Anyone is working as a professor here ?
2

3:14 PM
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Consider a $d=0+1$ theory of fermions, i.e., fermionic QM: $$L=i\psi\partial_t\psi-V(\psi)$$ The Hamiltonian is just $H=V$. What is the definition of a symmetry here? I can construct transformations that commute with $V$ but not with the kinetic term, so they leave $H$ invariant but not $L$. Ar...

@ACuriousMind what do you think regarding the constrained Hamiltonian stuff and symmetries in this

@bolbteppa both your and Prahar's comment are correct and would constitute answers if fleshed out a bit

With the 4D Dirac Hamiltonian it ends up just reducing to the usual one, I'm not sure if one 'loses symmetries' there like the post is trying to say happens (I guess it's really free in this case....)

4:14 PM
Fock modules!
(Hilbert modules are apparently the rigged equivalent of C* algebras )

Ah that's interesting

4:38 PM
Alas, it is very much math notes

I'd guess the rigged approach is probably the best starting point if one wants to be even slightly formal, apparently (via random MO comments) there is no real canonical exposition using them

no, the standard formal approach is not to talk about rigged spaces at all
you don't need them if you're willing to restrain yourself from trying to talk about $\lvert x\rangle$

Right, that's probably the first mistake the formal approach makes :p

Rigged spaces are fine
just use 'em

4:53 PM
OH I'm daft. I just ate 2 prunes thinking they were some sort of sour plum. Off to the lavy ta ta
good thing I skipped my coffee

"The phrase “rigged Hilbert space” is a direct translation of the phrase “osnashchyonnoe Hilbertovo prostranstvo” from the original Russian. A more faithful translation would be “equipped Hilbert space.” Indeed, the rigged Hilbert space is just the Hilbert space equipped with distribution theory—in Quantum Mechanics, to rig a Hilbert space means simply to equip that Hilbert space with distribution theory. Thus, the RHS is not a replacement but an enlargement of the Hilbert space."
https://arxiv.org/pdf/quant-ph/0502053.pdf

That physics chapter in the Codex Seraphinius looks like they put a physics textbook page into a neural network
they look like they have powerful Feynman diagrams
The most powerful version of a $\phi^4$ theory
Vertex has started to emit light and the propagators are waving

5:15 PM
I just had this question dropped on me by a JEE student:
To get this field geometry there must be a line of magnetic charge up the centre of the diagram, and therefore a magnetic current through the loop.
It's an ... erm ... "interesting" question :-)

I knew JEE was advanced but I wasn't aware they had discovered monopoles!

To be fair this wasn't from the JEE exam. It was some random book used to teach physics for the JEE.

it's the secret nonsensical question to make sure the student is not applying rules blindly

You can do the calculation. If you consider the Lorentz force acting on the electrons in the ring you can find ∫E.d𝓁 round the ring. In effect you're adding an extra term to the Maxwell's equation for curl E.

1

The reason I would suggest that an askers knowledge of terminology should be taken into consideration is that if by research effort we mean looking something up on the internet before asking a question, then a person's knowledge of terminology can actually have a impact on what he/she/they can fi...

5:33 PM
Good evening, i have a small and a stupid question. If we have a constant potential in a given area and zero else where say V(r) is equal to $V_0$ if r < R and zero otherwise. Would the force be also according to $F = d/dr V(r)$ equal to $V_0$ ? i am not sure how to derive this
Sorry i know its stupid ... physics student cant derive but i am not sure how to do it! ( i do reliaze however that the force needs to be a constant!)

@MadSpaces your potential is a Heaviside function and the derivative is the delta function $V_0\delta(x - x_s)$, where $x_s$ is the location of the step
i.e. there is no force almost everywhere, and it's "infinitely strong" at the location of the step

I am trying to reliate this to a homework i got where we are considering the path of a mass going into the zone of a constant potential that is in form of a ball. i was not sure how the path of the particle would look inside the ball ( does it swirls? does it go on straight path? does it take a new path but in linear fashion? ETC ) since this is important to the answer, the drawing given by my professor shows that the object takes a new path but linear
How would i understand the effect of an infinite force here?

well, the easiest way is probably to not consider this in terms of force at all, but in terms of energy conservation
the particle hits the step with some kinetic energy $E_k$, and after the step it has kinetic energy $E_k - V_0$ left

The problem is i am not interested in a solution of energy because we need to derive something geometrically.... so the drawing is very very important.
So it is important to know the path of the particle in the potentialsarea

the only place where it changes its direction/velocity is at the step
after that it's a straight line again since there's no force there

5:42 PM
Oh...
Ahhhh
I see... haha.. yea yea you are right!
But generally speaking, like they drew that the particle went inside and got out on the other side.... why would it not for example just bounce off?
Do i need an infinite potential for that?

well, it bounces off when $V_0 > E_k$

Alright... i will see that. So basically as i u nderstood potentais of these form have no force or "an infinite" force at the point of impact
Right?

sure, that's just what differentiation gives you - don't forget that differentiation is local - it only sees the value of the function close to the point where you're differentiating
so in the region where the potential is constantly either 0 or $V_0$, you just have 0 force - the force can't "know" there's a step in the potential further away
the only place where this looks different from a globally constant potential is at the place where it actually changes, and so that's the only place where the derivative is non-zero and you have a force

Mathematically speaking, at the step..How can we even find F at the step? i am guessing this is not a conservative force and we can not use F = d \ dr V(r) ?

...if it weren't a conservative force, why are you talking about a potential?
one of the definitions of a conservative force is that it has a potential

5:48 PM
Oh yea you are right sorry, so at the step.. we have a conservative momentarly force right?

and mathematically, the derivative of the Heaviside function is a $\delta$-function

Ah i see... i did not work with delta functions but i know abit about them.. it makes sense now
many thanks !!

(but you might need a bit more advanced definitions of "derivative" and "function" for this to actually make sense :P)

Yea i know it is not "orthodox" Calculus and analysis. But i just asked out of interest, it is not part of my course

People say that the dirac function is $\infty$ at zero, but then what is $\delta/2$

5:55 PM
$\infty/2$, obviously
or $o$, for short

People used to say c = $\infty$ :P
that means $\infty$ = $\infty$
::runs::

6:19 PM
0

There is an existing discussion/request for a system to tag or otherwise indicate level of questions: Can we have a level-of-question tag please? Differentiate research-level questions? The idea is that people answering or searching could use this to filter questions. The indicator could for exam...

I guess it makes more sense to say that $\delta$ is $\infty$ on $[-1/2\infty, 1/2\infty]$

2 hours later…
8:45 PM
Good evening. Is there someone into chat for an help, please?

9:29 PM
For some reason I've completely blanked the casual section including general relativity considerations in the L&L Statistical Physics book, obviously $\frac{\partial S}{\partial E_0} = T \sqrt{g_{00}}$ is how we get temperature now...
Out of habit that was wrong, should be $\frac{\partial E_0}{\partial S} = T \sqrt{g_{00}}$