The h Bar

00:13

@Relativisticcucumber usually what you do is that you solve for a spherical shell, where you can easily see the electromagnetic shielding, and then let the radius of the shell tend to infinity

Relativisticcucumber

00:26

i am afraid

naturallyInconsistent

00:38

why?

123

05:20

Hello Everyone...

Ryder Rude

06:24

hi

do time reparametrisation invariant lagrangians have pretty much every trajectory as a solution

why aren't these Lagrangians trivial

Slereah

Why would they

Ryder Rude

@Slereah cuz reparametrising time transforms one trajectory to pretty much any other trajectory? is this not true?

Slereah

It transforms the parameters, not the image

Ryder Rude

image?

Slereah

Image (mathematics)

In mathematics, for a function f : X → Y {\displaystyle f:X\to Y} , the image of an input value x {\displaystyle x} is the single output value produced by f {\displaystyle f} when passed x {\displaystyle x} . The preimage of an output value y {\displaystyle y} is the set of input values that produce y {\d...

Ryder Rude

06:35

i am thinking that $f(t)$ gets sent to $f(g(t))$ for pretty much arbitrary $g$ as long as it's bijective

is this the wrong formulation

so $f(t)$ can get transformed to pretty much anything using a choice of $g$? @Slereah

@Slereah i am aware

physics.stackexchange.com/questions/778910/… this says it is the correct formulation

i guess it's not pretty much anything cuz it's differentiable and bijective

also, if we have internal degrees of freedom like in tensors, then the transformation cant act on those dof

is this what makes these Lagrangians non trivial

@Slereah also, i saw ur question. i am thinking that the first Lagrangian is not defined in the regime $\dot t=0$, so these two Lagrangians are not strictly equivalent

Slereah

That derivative is never zero, that would be a non-regular curve

Ryder Rude

oh

The EL eqns of ur two Lagrangians seem very different to me

but they match when we choose the $\tau =t$ parameter

ok i understand now. e.g. the SR Lagrangian is reparametrisation invariant, and while a ton of trajectories are solutions, they only differ in how we parametrise the straight line

non-straight lines are never solutions

so if the original Lagrangian is non trivial, making it reparametrisation invariant wouldn't make it trivial

so this is y u would call this a gauge theory. It trades a single physical solution for a family of redundant solutions

this also has profound consequences in QM, e.g. u r not supposed to path integrate all the redundant solutions, but a quotient, which makes it equivalent to the original theory's path integral

bolbteppa

07:16

You can re-write the non-relativistic Schrodinger Lagrangian in a time reparametrization invariant manner, it doesn't have every possible solution

Slereah

07:31

Current hunch is that the two Lagrangians are inequivalent but their quotients are, because apparently that is something that can occur in gauge theory

bolbteppa

They are equivalent it's just a constrained version of the usual one

Slereah

What is the constraint

(I mean the two different parametrized versions of the Lagrangian that I posted about btw, not the parametrized and unparametrized one)

bolbteppa

Reparametrization Invariant Free Particle Action

Slereah

I mean these :

1

Q: Lagrangian for a free particle with parametrized time

There are two seemingly contradictory Lagrangians for a free particle with a parametrized time. The first is the one given by Dirac in his lectures on quantum mechanics. Take the action of a free particle [1][2] : \begin{equation} S[x] = \int_{t_i}^{t_f} \left(\frac{m}{2} \dot{\vec{x}}(t) \cdot \...

Ryder Rude

@bolbteppa wow

@bolbteppa do u mean it doesn't have every possible solution of the Schrodinger eqn??

qwerty

07:40

hello~ . off topic: survived being a not-physicist for the day. gonna go home and think about symmetries :)

Ryder Rude

in string theory, how do we know the species of the particles that is incoming and outgoing, when the same string correponds to infinitely many particles

does the vertex operator have a specification for the particular string excitation that is incoming

e.g. if i see that a closed string is incoming, it could be any of the particles of the closed string

does the vertex operator specify what exactly is incoming

and intuitively, why is it that the vertex operator of the graviton excitation of the closed string has something that looks like the GR metric? Also, is this absent in the other excitations of the closed string

bolbteppa

07:56

@Slereah you can leave $E_0$ as a constant and then $E \dot{t}$ becomes a total time derivative, then it looks like the usual action in reparametrization invariant form

@RyderRude I was thinking of the thing in my link above, note the Schrodinger equation is the constraint, forget about the actual Schrodinger Lagrangian which adds complications

Slereah

@bolbteppa It is $\dot{t}$ though, not $\dot{t}^{-1}$

bolbteppa

Is that right, I'm looking at (8.14) and (8.15)

Throw away $E_0$ in both of them, or at least in (8.15) after imposing the $p_t$ eom

Slereah

Is that the same canonical Lagrangian as Dirac?

bolbteppa

Those two equations look like the usual thing, and they are coming directly from your orbit stuff

Slereah

Reassuring at least

Tho I should try to work out how the configuration space Lagrangians are equivalent from that mb

bolbteppa

08:03

Inserting $E = ...$ is inserting a consequence of the eom into the Lagrangian I think

This is a famous issue e.g. in solving Kepler iirc

7

A: Vertex operators in string theory

Under the state-operator mapping we have the following identification $$ |k;0,0 \rangle \longleftrightarrow :e^{ik.X(0, 0)}:$$ where $:e^{ik.X(0, 0)}:$ is the normally ordered closed string tachyon vertex operator and $ |k;0,0 \rangle $ is the closed string tachyon ground state. No...

Slereah

I guess I can try to just use their technique but only solve the constraint for $E$ and $v$ and leave $t$ alone

bolbteppa

What is the orbit approach useful for

Slereah

It is good to derive the Lagrangian for arbitrary kinematic groups

Easy to compute the Lagrangian of a free particle for a wacky group like Newton-Hooke or Aristotelian

Ryder Rude

08:38

@bolbteppa so the vertex operator indeed specifies the particle type

@Slereah cool

why does the vertex operator of closed string look like the GR metric? is this a big co incidence, or was this to be expected

also, how do we know the spin of a particular string state? Does it come from Noether theorem applied to the Conformal.field.theory

Ryder Rude

11:36

what would happen if we quantise the closed string without throwing away the states which are not rotationally symmetric

is this theory consistent

PM 2Ring

13:20

We need to sort out the inconsistency in our policy regarding GenAI. On the one hand we have physics.meta.stackexchange.com/q/14281/123208 which generally discourages questions and answers derived from GenAI interactions. But OTOH physics.stackexchange.com/help/gen-ai-policy says that such questions are ok as long as they clearly mention their sources.

Slereah

Well you know me, I go by old internet rules

PM 2Ring

It's not fair on OPs to DV & close their question purely on the grounds that they used GenAI when the Help page tells them that such questions are permitted.

Slereah

I say we make our own split group of stackexchange

PM 2Ring

Personally, I want to discourage GenAI based questions. And I definitely want to warn people against trusting anything a LLM tells them, without verifying it against actual trustable sources.

But if someone has a reasonable question, does it really matter that they "discussed" it with ChatGPT before they asked about it on Physics.SE?

@Slereah There's Codidact, which started in the wake of the Monica fiasco. But it doesn't exactly get a huge amount of traffic. codidact.org

Amit

@PM2Ring I think that "mention their sources" is just not enough. Like with any citation, anything generated by AI should be cited using the ">" markup directive. That way we can ensure a separation between human and AI text...

I think that the idea of "pasting AI is a form of plagiarism, so it was wrong even before the wide use of prompts" is a sensible one

it really is just plagiarism, even if the LLM itself can't tell you where he is plagiarizing from. It is basing its text on something a human wrote.

PM 2Ring

13:35

@Amit Here's a current question where the OP consulted ChatGPT. The question itself seems ok to me.

Slereah

amazon.com/Categories-Quantum-Theory-Introduction-Mathematics/…

PM 2Ring

0

Q: Is there an equation to estimate the energy required to compress a given amount of matter into a black hole?

It says it all in the title, really - is there an equation to estimate the energy required to compress a given amount of matter into a black hole? I asked ChatGPT, and have attached a screenshot of part of its response. Is this accurate, or has it hallucinated? When I plugged in a mass of 1000 kg...

black-holes mass-energy estimation

Slereah

neat looking book

Amit

@PM2Ring I'm not sure, because that may be a special case. This belongs to a specific subcategory of "Is the LLM right when it answered....", and these kind of questions are understandably vexing, it is not really in the interest of the community to point out all the ways in which LLMs get physics wrong, is it? :)

PM 2Ring

No, we aren't here to debug ChatGPT. And it's pointless, unless our feedback actually gets fed into ChatGPT.

Amit

13:41

If the OP here would go on to present his own calculation, compare it with the one made by ChatGPT, offer what he thinks is more correct and why, that could save such a question. But yeah, here he is just going for the "Is that right?" part.

Slereah

also not our job to do it for a for profit company

PM 2Ring

OTOH, the OP still has a reasonable question. We can answer that without worrying too much about what ChatGPT said.

Amit

@PM2Ring Agreed, an answer that just ignores the ChatGPT part can in fact save this question :)

PM 2Ring

@Amit Ok. I guess that would make it an off-topic "check my work" question.

Amit

> The only kind of "check my work" I think we should allow is the one where a derivation is presented, leading to a wrong result, and the question is "It seems as if step X is wrong? But it should be right because of Y, so why is this not the case?".

PM 2Ring

13:44

I don't know how to answer that question. I agree that gravitational binding energy (GBE) is important, but I don't know how to deal with it. The GBE is the energy you need to add to a system to unbind it. But that's not what ChatGPT is doing...

Amit

From here

PM 2Ring

@Amit Right. It's "check my concepts" rather than "check my arithmetic / algebra / calculus"

Amit

yep

even "check my concepts" can be problematic... as mentioned in this meta I linked to, if the answer may just be "You're right" it's not a good question. The OP needs to be pretty sure he's wrong :)

(or at least, at a complete loss conceptually as to why he may be "right")

Ryder Rude

14:40

@Amit i have asked questions like this and they got removed anyway

Amit

14:55

@RyderRude removed? :o I thought questions get deleted only on rather extreme circumstances

Ryder Rude

@Amit they also had negatives votes mainly because of naturallyinconsistent. there is a rule that such questions get deleted if they have no answers

Amit

oh yea that's like the offline deletion, "clean up" process, it's not what I thought you meant

Ryder Rude

yes. i have those questions in my "deleted questions" link now

no one is able to view them or comment

Amit

@RyderRude I think also the plural negative "votes" doesn't make sense here :P

Ryder Rude

@Amit i don't remember the exact count, but other people start thinking it's a bad question when it gets one downvote and they start downvoting too

Amit

15:01

yea, but then if a question goes a long time unanswered, it means people aren't really interested regardless of the votes isn't it?

Ryder Rude

the questions were really detailed. most people wouldn't have read them properly

Amit

@RyderRude mm idk, maybe. I didn't observe a lot of herd voting of the type you describe, but it may be right on occasion

Ryder Rude

@Amit i think its just a week

@Amit sometimes, yes. but it wasn't right in those cases because the questions were high effort

Amit

after a week of activity no one is likely to come across it really. the only chance is if you edit it to bump it up, or the automatic bump ups that happen every month(?)

Ryder Rude

i would've maybe started a bounty

Amit

15:03

@RyderRude If you think that's the case, maybe you should post that on the Meta

Ryder Rude

@Amit maybe

it was like a year ago tho

Amit

It's also weird if such questions don't even get comments, at least for people to explain why they don't find it interesting etc.

Ryder Rude

i did get comments...

Amit

Then you can sometimes edit, improve it etc.

Ryder Rude

one was simply called "non mainstream" :(

it wasn't non mainstream at all, and i couldn't edit anything to just make it more mainstrram

Amit

15:05

Well anyway, this stuff is always judged on a case by case basis... if there's a question you're still interested in, you can always try again, rephrase it differently or better than before, etc.

Ryder Rude

it was about some operators in QFT that i thought can work as position operators

it was just an operator definition

@Amit maybe..

but i put a lot of effort the first time

i feel discouraged... especially the other question, i spent a lot of time phrasing it right, so people could parse the idea

but that one just got called a "check my work" question

Amit

well you asked a lot of questions. I don't think you need to feel discouraged because most of them I see have net upvotes so apparently mostly you ask well received questions.

Ryder Rude

yeah... but mostly they're textbook questions

those two times i put some effort in making a new thing

and it wasn't like some "grand idea" theory, which throws known physics into the bin

both were basically just operator definitions in standard QFT

and it wasn't like i thought i had something significant. i just wanted to know what's wrong with the ideas

Amit

a "new thing" is always more dangerous territory because "personal research", even if it is only that to a very small degree, tends to become very open ended very quickly. see this on Meta for example...

Ryder Rude

maybe the questions weren't suited for PSE, yes

Amit

15:15

actually that may be more relevant. Although the other one to some degree, too

ACuriousMind

@RyderRude stop making up things, the lowest deletion time for non-closed questions is 30 days, cf. physics.stackexchange.com/help/auto-deleted-questions

Ryder Rude

@ACuriousMind oh

@Amit my questions weren't vague or open ended

i didn't say something vague like "what results can we expect if we research this idea"

the thing is, i had researched the idea and i had a concrete result. i just shared the result

but anyway, i will maybe try to post it again sometime in the future but i dont have the drive rn

Amit

> Note that if one comes across an issue while doing research, they are welcome to ask it as long as the question is working within the framework of modern mainstream physics. However, especially since discussion questions are not allowed here, discussing one's research usually leads to a question that is either open ended, broad, or non mainstream.

ACuriousMind

@RyderRude you also need to stop thinking one particular user is causing your questions to be rejected, your three most recent deleted questions were deleted because they were closed, and closure requires three votes or a moderator closure. In two of those three questions I left a comment (that was up voted multiple times) explaining why the questions were ill-defined as they were written and you did not edit them afterwards.

Ryder Rude

@ACuriousMind but i know exactly what happened with those questions. They went like 24 hours with zero votes and lots of views. Then suddenly, they get a downvote and everyone starts downvoting and it's closed in 30 minutes

the votes weren't independent at all

@ACuriousMind i tried to discuss it with you, but u refused to

u didn't let me address any criticism

ACuriousMind

15:27

By the standards of our site, there was consensus that they were unsuitable for this site, and your continued attempts to paint this as some kind of persecution are inappropriate. Please stop using this chat to air these imagined grievances against other users - by design, users can vote as they see fit.

Ryder Rude

I don't care much about it anymore. The topic of "check my work" questions came up, which is why i discussed it

the last thing my question was was "check my work"

and both of ur criticisms were address-able. neither criticism applied to that post

u did discuss the first question's criticism. But still, it was not "non mainstream" at all. It was an operator definition in standard QFT

and by "everyone starts downvoting" I mean two downvotes. they have two downvotes each rn

sorry they're both at +1-3=-2

Silly Goose

19:39

why do bispinor fields appear in our lagrangians as opposed to just spinor fields?

For the concrete case of spin-1/2, we refer to a left-handed spin-1/2 field as a field $\Phi: M \to V$ whose output $\Phi(x)$ transforms under the irreducible projective representation of the restricted lorentz group $\pi_{(\frac{1}{2}, 0)}$; analogously, right-handed spin-1/2 field transforms under $\pi_{(0, \frac{1}{2})}$

ACuriousMind

@SillyGoose because pure Weyl spinors are only consistent when they're massless (with the standard kinetic term)

Silly Goose

hm okay

separately, i am back to being confused about defining the in and out states

For one, in (11) how can we take the difference between vectors that live in two distinct Hilbert spaces (without invoking further machinery than what is stated)?

Secondly, even if we can compute this difference, how can we take the norm of it? What Hilbert space's norm is this?

Thirdly, how can we multiply $U_0 \Phi \in \mathcal{H}_0$ by an operator $U: \mathcal{H} \to \mathcal{H}$?

Unless there exists some isomorphism (or something) between $\mathcal{H}_0$ and $\mathcal{H}$ or unless one is contained in the other, these computations seem meaningless

ACuriousMind

20:19

@SillyGoose I mean, if you take the standard lore at its word, the interaction picture exists and there is a unitary map that relates free and interacting fields so that the eigenstates of the free field just span the space

if you want to be mathematically rigorous, you need to do Haag-Ruelle theory, for which see Reed & Simon vol. 3 :P

Slereah

Apparently this is how Galileo phrase his law of motion

> for so far as I know, no one has yet pointed out that the distances traversed, during equal intervals of time, by a body falling from rest, stand to one another in the same ratio as the odd numbers beginning with unity.

I guess the point is that the total distance travelled is $$d = \sum_{i = 0}^n (2n + 1) = (n+1)^2$$

@ACuriousMind You can spot where the secret assumption is in Peskin IIRC

At some point he just says that $\langle \Omega | 0 \rangle$ is something, because that makes sense dunnit

ACuriousMind

yes, exactly

Slereah

I mean just assuming that the inner product makes sense at all is already a mistake :p

but it was always a bit mysterious to me why that was true

outside of regular gut feeling

apparently there is a rigorous-ish version of the interaction picture : ncatlab.org/nlab/show/causal+perturbation+theory

Silly Goose

21:17

do people work on classical string theory?

ACuriousMind

do you mean guitars

Claudio

this is a perfect 23:17 question

hahaha

Silly Goose

Lol

ACuriousMind

I mean, the "classical" string theory is just either the strings of a guitar or the theory of throwing something like a wristband through a room, it's not terribly interesting

Slereah

People use classical string theory for cosmic strings

But that's a pretty niche application

ACuriousMind

21:23

that's just a very big guitar

Slereah

True

Claudio

How niche are we talking?

Slereah

Also I'm sure there's some string application to condensed matter physics

No matter what there's always an application in condensed matter physics

@Claudio fairly

Claudio

condensed matter physicists are probably shaking at the thought that they might have to learn string theory in order to make future developments

@Slereah I barely know what a Legendre Transform is, take it or leave it:P

Slereah

Is the guitar strut technically a brane?

Dbrane

ACuriousMind

21:31

@Slereah only if you play a D chord

Claudio

@ACuriousMind could I ask what was your preferred classical mech textbook?

@Slereah's too if possible

ACuriousMind

I don't think I've ever read enough of any single classical mechanics textbook to say :P

Claudio

whaaaat

I thought you'd say Arnold's

ACuriousMind

I learned mostly from my lectures and then reading scattered bits here and there whenever I stumbled on something interesting

Claudio

Hmm I see

Slereah

21:42

We basically had no textbooks at my uni

Just classes and poorly xeroxed material

Claudio

yep, same

the recommended textbook was the one by Fasano and Marmi hahaha

My professor was terrible

he used to write things on the blackboard with one hand, while the other was always holding Goldstein's book

ACuriousMind

the recommended reading for my classical mechanics course were books like Arnold, L&L, Jose/Saletan, Goldstein and indeed Fasano/Marmi, but I never read any cover to cover

but then again this was a first+second semester course that was taught by an extremely demanding (but excellent) lecturer who actually did Hamiltonian mechanics in terms of the symplectic form at the end of the second semester :P

Claudio

@ACuriousMind dang

much better than ours at least :P

ACuriousMind

the lecture notes (in German) for the second semester are here [pdf link]

Claudio

they look pretty advanced, they talk about tangent spaces, and such like Fasano-Marmi

but Fasano-Marmi is for graduate students

@ACuriousMind this is for a particular category of students (like purely theoritical) or is everybody required to follow this course?

ACuriousMind

21:55

yeah, I mean Hebecker wasn't a fan of dumbing things down though he was aware we didn't really have the math to do any of this properly - he was always very clear that there was a bunch of rigorous math missing, but he considered it his mission to show us as much of analytical mechanics as possible, given that there was no other mechanics course anywhere in the curriculum

@Claudio this was required for everyone in the first two semesters

Claudio

our department chose the opposite way hahaha

ACuriousMind

people either loved him or hated him :P

Claudio

I mean I totally understand why they would hate him

@ACuriousMind do you agree with his approach? Showing this much without the proper math background?

ACuriousMind

@Claudio I loved him and I think a lot of my love for theoretical physics is due to how much I learned in that first year - there was no pretension that any of this was complete, he was always very clear on what was missing and which math courses we'd have to take to fill in the gaps, but coming from school this was the first time I truly understood how vast the ocean of knowledge was I was about to learn

2

I understand that others were frustrated by this approach but I found it fascinating, it was exactly the contrast to the cookie-cutter way we learned things in school I needed

I took the "proper" math classes instead of "math for physicists" because he recommended to learn actual math over and over again and given that I ended up filling essentially all my electives with pure math I never regretted that, either

Claudio

he seems to have had a massive positive impact on your academic choices, good to know this

if only he could see how many gold/silver badges you received hahahah

ACuriousMind

22:06

And...I mean I don't know how I'd have felt if I hadn't been good at it, but he also always stressed that we should try to learn as much as possible as fast as possible - why not take graduate classes in your second year of undergrad? You can take QFT directly after QM, no need to wait! Learn general relativity directly after EM, what's stopping you? If you took it as an expectation it was soul-crushing, but I genuinely think he wanted to just be motivational and at least on me it worked fully

Claudio

yeah, I've also noticed that this approach leads to positive results, at least for the more proficient students

It might be too cumbersome for those who tend to struggle, but again no approach will ever satisfy everybody's needs

ACuriousMind

there's probably some people who quit because of him, to be honest; I don't want to pretend to be able to judge this tradeoff objectively

qwerty

@ACuriousMind hello! time appropriate greeting! how many other courses would be taken at the same time as one of these courses?

@ACuriousMind it seems like a very sink or swim situation - it strongly favours those who learn quickly?

ACuriousMind

@qwerty these are two 90 min lectures a week + one weekly exercise sheet and another 90 min session where the solutions to the exercises are discussed; a typical workload would be 4-5 of such courses + 1 or 2 other less time-demanding activities

Claudio

@ACuriousMind that's always sad to hear

ACuriousMind

22:16

@qwerty Yes, it probably does; again, I cannot really objectively judge this - I know I loved it, but I'm a very quick reader and have a good memory, and I know others hated it

Claudio

you were like an S-rank adventurer hahaha

qwerty

I was comparing course structures with physics undergrads from the usa on tumblr of all places back in the day... the consensus was that Aussie universities (or at least the ones I went to) covered a lot more breadth with a lot less depth (but possibly with with more repetition). I think I was a bit envious that they took few total courses than us at a time

ACuriousMind

I vividly remember people complaining the lectures were going too fast - he took that to heart and talked/wrote much slower after that feedback...for half an hour, then he had sped up to his usual frantic self :P

Claudio

they always do that hahahah

qwerty

I would not have been an ideal student. I made it through 20mins of those symmetry lectures stopping to pause and type and replay every few seconds last night... over about 2-3 hours

it's always interesting to see how how different courses and expectations everywhere

ACuriousMind

22:21

I mean realistically if you failed this course you could always retake it a year later where it would be held by a less ambitious lecturer; this takes some resilience but failing it wasn't the end of the world

Claudio

My eyes are bleeding, time to go to bed. Thanks for sharing these stories ACM

qwerty

bye Claudio!

Claudio

bye guys

ACuriousMind

@Claudio you're welcome - now I'm deeply afflicted by nostalgia for my student days :P

qwerty

22:33

awww

I'm glad you had so much a good time learning and you're now on Phys.se to pass on the batton

ACuriousMind

well...it wasn't all just learning but if there had been a straightforward way to just stay learning and teaching instead of doing research I probably would've stayed in academia

qwerty

@ACuriousMind we had about 8 courses min per semester because a lot of them were "half courses"

ACuriousMind

that doesn't sound so fun

qwerty

@ACuriousMind my friend did that straight out of his PhD, he's officially a lecturer but for first year teaching only. not really higher levels stuff

ACuriousMind

welp, would've had to do a PhD for that :P

qwerty

22:48

as far as I'm aware its permanent-ish

hahaha - you didn't complete one yourself?

ACuriousMind

no - bachelor, master and PhD are three distinct phases in Europe and I stopped after the master

qwerty

oh I see. masters in physics are fairly uncommon here - I'd say 1/50 people I knew got a masters instead of a PhD directly. we follow the British system

ACuriousMind

and it was the right decision because all of my close friends said I seemed like a weight had dropped off my soul when I had decided not to do a PhD

qwerty

oh actually two people I knew "mastered out" of their PhD. but that's separate to the one that signed up for a masters

ACuriousMind

nah, the normal progression is really BSc->MSc->PhD here and it's perfectly normal to stop after any of these

qwerty

22:52

that's fantastic. good on you for knowing yourself and standing up for doing what you wanted instead of following blind expectation

ACuriousMind

my parents did a very good job of raising me to do what I want, not what I should :)

qwerty

well I have to go to work now :') I'll be back tonight. the hbar has been really great to just hang out whilst I physics-as-a-hobby and it's in part to due to you as a mod so thanks

ACuriousMind

hope you have fun at/survive work, cya

qwerty

ciao all

Silly Goose

23:12

whenever i meet someone who went to heidelberg i think of you and your knowledge xD @ACuriousMind

i mean the university, not the geographic location

from an american perspective, i quite envy the european (at least heidelbergian) physics curriculum :P.

ACuriousMind

I mean I went to Heidelberg because together with Munich it had the best reputation for theoretical physics in Germany, this was decidedly not the average European experience

also my parents were very much of the opinion that I had to go and study somewhere where I couldn't just go home every weekend so that I learned to be independent so nearby universities were out of the question :P

Silly Goose

I tried to get away but I ended up very close XD

(for undergraduate)

Anyways, what is the reason for focussing so much on isometries of the Minkowski metric?

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