1:05 AM
It is automatic that $J^2-S^2\geqslant0$
1:23 AM
how can a nonhermitian operator have a real expectation value?
the above expectation value can equivalently be read as something of the form $\langle U^\dagger S_+^2 U\rangle$; an identity was used to rewrite it in the above form
but, $(S_+^2)^\dagger = S_-^2 \neq S_+^2$.
hm I guess the condition is just that for a particular state $\psi$, $\langle \psi \lvert O^\dagger \lvert \psi \rangle = \langle \psi \lvert O \lvert \psi \rangle$, which is satisfiable by a nonhermitian operator
2:08 AM
@SillyGoose Coherent states are eigenstates of the annihilation operator, which is non-Hermitian. You can choose its eigenvalue to be real valued. i.e. you can be lucky~
H O N K ~
2:23 AM
i remember one time i was on the main site
and i asked a q and got a good answer so i was like "thanks!"
classic stack exchange XD
@naturallyInconsistent bah that is a reasonable point
2:47 AM
lol

2 hours later…
4:28 AM
This question involves fiction, but lemme double-check this: Suppose a magic violated conservation of energy or conservation of momentum. That would break all the physics, right?
4:39 AM
how will it do this violation? if it is only one-time, maybe it wont be so bad.
The kinds of magic in question include: 1. Applying a force remotely, 2. Letting an object explode and choose how the debris will fly, and 3. Letting objects stick together.
#1 breaks momentum conservation unless the some other object compensates the momentum. In any case, it breaks energy conservation.
#2 breaks energy conservation unless some other energy (say, heat) compensates the energy. In any case, it breaks 2nd law of thermodynamics.
#3 poses the dual problem of #2.
4:57 AM
@naturallyInconsistent i have more to my PI drama
remember when i was saying that my PI was trying to put random ppl as coauthors
well there was another guy who tried to do my project but failed. when i was in the midst of the project and hit a big roadblock i emailed him to ask if he hit this same roadblock/what the nature of his issue was and no response
then guess who i see my PI has squirmed into the acknowledgements -- we thank xyz person for discussions
THERE WERE NO DISCUSSIONS my pi just wants to give other ppl my work BAH
and then he says im too greedy with authorship XD
academia rips the life out of me
2
5:21 AM
an unexamined lifeless life is not worth living
@DannyuNDos no, you can conserve energy if the momentum is compensated. Instead, this violates locality, i.e. SR.
@Relativisticcucumber miao miao would be more annoyed with discussions that were obviously uni-directional, because technically they are not discussions at all. Acknowledgement is not authorship; you should inflate the acknowledgement list as long as you can lol
6:26 AM
@Relativisticcucumber while perhaps annoying, acknowledgements are not authorship - people can thank god and the whole world in there (and frequently do). Giving authorship to someone who didn't do anything would be a breach of academic honesty, acknowledging people who haven't done anything is at worst tacky
@DannyuNDos yes, magic systems that do not have conservation of energy/momentum built into them (e. g. by draining spellcasters of the energy equivalent to the effect they're causing) frequently allow for perpetua mobiles
@Mr.Feynman but I do speak Latin more than barely - I had 6 years of it in school! :P
6:40 AM
hi
it says different sizes of infinity led to the invention of smartphones
i didnt know this math had real world applications
anyone know about how this contrbuted to smartphones?
7:36 AM
Alice and Bob is old :)
7:51 AM
@naturallyInconsistent I guess then, the magic #1 cast by the wizard is channeled at the speed of light.
@DannyuNDos there is no way to get around the lack of locality. You cannot have momentum disappear at one place and reappear somewhere else and still have things work under SR. The only way you can have something like this, is if you have a new quantum field and interactions for that to be carried microlocally.
Oh... I guess I'll confiscate the said magic then.
I guess the wizard in question gotta be just a magical martial artist.
If change under general coordinate transformations is a global symmetry for theories in which metric is not the dynamical variable, why does it not imply that all theories are Lorentz invariant?
I know diffeomorphism invariance is a much discussed topic, but I don't know if this particular question has been raised previously and answered before
Again, the issue is not that I am insisting that you have too much realism and break all the magic. It is that if you want to make fiction work with some semblance of realism, you have to consider what it is you want to keep working and what you want to break. Clarity helps with consistency; maybe you want to ignore consistency, especially if it is a one-off story that you don't care about insulting your readers who care about consistency.
Don't read the first three words in my above question: "If change under"
8:05 AM
@naturallyInconsistent The problem is that the wizard in question is a physics teacher, specifically for Classical Mechanics. If her magics violate what she must teach, that's just absurd.
@naturallyInconsistent If the said quantum field can exist, I guess a QM teacher can do that while the CM teacher cannot do that.
Technically, it would work in classical physics too, except that in classical physics we don't have quantum matter particle creation and annihilation. You can still create photons "classically", and those can carry energy and momentum just fine.
So... In CM perspective, the quantum field is just a wave that propagates in every direction?
8:24 AM
no. In CM perspective there is no quantisation of a photon. The photon can be split apart to any desired fraction. This is acceptable when the number of photons made is so huge that this illusion is kept up.
@ManasDogra Yeah. This is ACM's one of the most favourite topics, and whenever asked too much he recommends reading Trautmann's articles on this. You can have a look
Time for me to learn QFT, I guess...
@DannyuNDos i did not understand ur question
Huh?
IIRC, my institute doesn't teach QFT to undergraduate students.
i mean the question about magic
8:28 AM
Magic doesn't exist IRL, so that's fine, I'd say.
what r u looking for, specifically?
@DannyuNDos that's what miao miao wants to remedy
@RyderRude A way for my character to not break physics, while still being able to cast the said magics.
ooh
can u give an example of the magic
Lemme write again: 1. Applying a force remotely, 2. Letting an object explode and choose how the debris will fly, and 3. Letting objects stick together.
8:31 AM
oh
the first can b done in newtons physics. so i think u r looking for it to be consistent with special relativity
Yeah, especially when there is a physics teacher for relativity theories.
one way cud b that the character lives in a sub-manifold of spacetime... so that spells travel locally thru shortcuts in the other dimensions
In any case, I'm thanking @naturallyInconsistent so much.
ooh but u want it to be instantaneous
Not necessarily.
in The Bridge, 4 hours ago, by Dannyu NDos
I mean, applying force remotely breaks the entire physics, but fire-breathing doesn't break chemistry at all. The difference is just hilarious.
8:38 AM
yeah..
@RyderRude That was a joke :-p
In any case, there are plenty of faster than light stuff out there, but interpreting them carefully it turns out that they are either unphysical or we are just using sloppy language
@Sanjana i meant the paper Brian Green talked about in the video
@Sanjana technically tachyons are perfectly fine if we ignore the causality constraints...
Lighthouse paradox is one of my favourites.
@RyderRude Oh that...
8:42 AM
yeah
it allows faster than light on the submanifold on which the character lives
@Sanjana it's really cool
@naturallyInconsistent Tachyons fall within the sloppy language case, because afaik, they can't be used for energy transport. So when people gets crazy about "wow. FTL is possible with tachyons", they have actually not "broken the law" anyway :3
one can also try this paradox using a long stick. then the paradox has a different resolution
it's just that sticks cannot be rigid
Yeah, under relativity, everything is elastic...
i feel ur problem is just about making shortcuts in spacetime
like some topology with lots of shortcuts
the spells go thru shortcuts
I don't require the magic #1 to be instantaneous tho. The lightspeed is fast enough.
8:47 AM
oh
then u can use neutrinos to evade everything in between
but neutrinos will probably also evade the target
But ofcourse there are ways to travel at speeds FTL without breaking causality. One of the early works of Susskind (with none other than Aharanov of Aharanov-Bohm effect fame) and Komar of Komar mass integral fame, clarifies this difference very succintly using basic field theory (knowledge of Green's function is enough tbh)
There's also that famous thing where light travels to infinity and back within a finite time in AdS space giving the illusion that velocity of light is greater than $c$, but in reality it's the spacetime which is continuously contracting and the local definition of velocity changing every moment giving this effect
And the classic Alcubierre_drive ofcourse... I got to know about a ton of FTL effects and subtleties from one of the books on Slereah's shelf.
what is the book
@Sanjana really cool
I am forgetting the name. Let me have a look at that picture
You will get a lot of interesting book names from here. I was particularly talking of the blue books on the left in the 2nd shelf from bottom
thanks
9:06 AM
It is a good way of knowing things instead of guessing
4
9:56 AM
@ACuriousMind @naturallyInconsistent i guess i am confused about what acknowledgements should be and why its in a paper? i cant trust my advisor on these things since i already had to fight him on the authorship :P so is it really that anything can go in acknowledgements? i think i am just bitter bc the exact guy he decided to acknowledge refused to engage in discussion about the project so i feel like its just a slap in the face to mention him at all :P not smth to fight but just annoying to me
he makes the claim that gift authorship is good to maintain connections + makes it easier to get a paper through review so i dont trust anything he says for that and other reasons
10:20 AM
Yes, authorship had better be correct. If he did not contribute at all, don't allow them into the authorship. Unless all authors are happy to add the extra person e.g. when Gamow asked Alpher to add Bethe to the famous paper. In acknowledgements, you get to also fight him for "thanking for discussions" when in fact there was no such discussion. However, nobody really cares more about such acknowledgements so you should acknowledge and thank as much help as you can.
If you used someone's help and did not even acknowledge them, and later it was found out that a crucial idea / suggestion / whatever is actually from this extra person, it can turn into a nasty dispute over originality and so on. If you took money for any part of any work in a paper and did not acknowledge it, and later it turns out that it influenced your paper writing, it can be legal action against you.
You can lose your credibility and/or credentials.
11:03 AM
Guys I've been solving goldstein's 2nd chapter problems..some of the problems seem really difficult,I've been stuck for quite some time on ch 2 problems..any advice on what I should do?
11:45 AM
@naturallyInconsistent In solving for the geodesics of a sphere ,if I choose r,$\theta$ and $\phi$ as my independent coordinates and pareametrize them w.r time,I'm getting some horrible mess as solutions when I solve EL equations,this stackexchange post math.stackexchange.com/a/836248/965696 ,takes $\theta$ as parameter and takes $\phi$ as as a function of $\theta$ and solves the problem..but what about those curves for which $\theta$ is a constant and $\phi$ is varied?
For these paths the method fails since..d$\theta$=0 and hence $frac{d\phi}{d\theta}=\infty$

2 hours later…
2:12 PM
@Arjun Oh, this problem is extremely horrible. Goldstein alluded that this is horrible unless you take $\vartheta=\frac\pi2$ as fixed. Later around the Hamilton-Jacobi Equation chapter, Goldstein will cover how much work it takes to reduce the $\vartheta$ and $\varphi$ parts together, to show that $\vartheta$ is just some complicated yet equivalently periodic function of $\varphi$, as you know must be true. I'd suggest skipping this problem because it is mathematically intractable.
And worse, that it is mathematically intractable, yet, when you work so hard to actually get it to work, it would just give you no useful insights.
2:57 PM
guys I have a question about yesterday's exercise
$$H = \frac{p^2}{2M} + \frac{k}{r}(\mathbf{J}^2-\mathbf{S}^2), k >0$$
the eigenstates are of the form $$|n;j,j_z; l,s\rangle, s = 3/2$$
from the first condition I was able to restrict to the subspace of eigenstates with $n = \{2,3\}$, which consists of 6 states in total
The previous restriction comes from the fact that it must be $j = 1/2$
the family of states I must focus on is the following, where the notation refers to $|l,l_z\rangle$: $$f(r)\sqrt{\frac{8\pi}{3}}|1,-1\rangle-\sqrt{\frac{16\pi}{9}}|1,0\rangle + \sqrt{\frac{8\pi }{9}}g(r)|1,-1\rangle + \frac{f}{3}\sqrt{8\pi}|1,1\rangle-\frac{2\sqrt{4\pi}}{3}g|1,0\rangle+\sqrt{\frac{8\pi}{3}}g|1,1\rangle$$
thus I can now restrict myself to the subspace with $l = 1$
now the problematic part: I must impose that $\langle \psi |J_z|\psi\rangle = +\hbar/2$
which means $j_z= +\hbar/2$
so the subspace contains the following states: $$\mathcal{E} = \left\{| 3; \frac{1}{2}, \frac{1}{2}; 1, \frac{3}{2} \rangle, | 2; \frac{1}{2}, \frac{1}{2}; 1, \frac{3}{2} \rangle\right\}$$
how do I go on knowing the almost exact form of $\psi$?
oh ok I must use C-G
lol
no wait, maybe I should consider $j_z = \pm 1/2$ and not only the positive one?
forgot to write $\psi =$ before the big expression :P
maybe I should've restricted to the subspace $\mathcal{E} = \left\{| 3; \frac{1}{2}, \pm\frac{1}{2}; 1, \frac{3}{2} \rangle, | 2; \frac{1}{2}, \pm\frac{1}{2}; 1, \frac{3}{2} \rangle\right\}$
I would've never imagined that an expectation value could put me in such a shambolic situation hahaha
Oh I get it now lol, I've just now realized that the psi function is a "spinorial function", that's why it's written a column vector lol
Please ignore the fact that it says spinorial., I meant it in the sense $$\chi = \begin{bmatrix} 3/2 \\ 1/2 \\ -1/2 \\ -3/2 \end{bmatrix}$$, I know it's not correct but that's my professors' terminology
Moral: remember to carefully read the exercise questions guys :P
anyways yeah, the subspace is indeed the one with only $j_z = \hbar/2$ since
4:13 PM
@Relativisticcucumber Honestly, acknowledgements are whatever - they don't really mean anything (except when you acknowledge funding) and it doesn't cost you anything to be maximally gracious here: Not mentioning someone might upset them, but mentioning someone doesn't do much except making them feel appreciated. The typical doctoral thesis tends to thank parents, spouses and pets in the acknowledgements that didn't contribute anything to the content of the thesis itself ;)
@Relativisticcucumber Different academic fields and subfields have different traditions for authorship (most prominently some fields care a lot about author order and others lack the concept almost entirely), so this might be politically true in your subfield, even if it's concerning. Not saying that's good, but...well.
4:27 PM
Just use the standard list of acknowledgements
Parents, advisors, friends, God, internet, computers, electricity
Remember to thank any demon through which you obtained supernatural insight
2
4:54 PM
lol
Hi guys
im having a problem with point 1) of this : Three blocks of masses m1 = 2 kg, m2 = 3.5 kg, m = 4.1 kg descend along a smooth inclined plane, with angle $\theta$ = 40°, under the action of the weight force and the constant force F indicated in the figure figure . It is known that the force tangential to the plane to which block m2 is subjected is F2 = 8.4 N. 1) Calculate the value of F.
In the solution It says that F should be 37.4 , but I don't understand where I went wrong
Could anyone help me?
5:12 PM
How does the last statement follow? Note that this might have nothing to do with AdS/CFT.
5:39 PM
@Sanjana In 4d, the conformal scalar field has a term $R/6\phi^2$ for $R$ the scalar curvature, see e.g. physics.stackexchange.com/a/706466/50583
@Pizza I might be wrong tho
@ACuriousMind But what if we don't consider curvature couplings like that? We can also simply choose minimal coupled theories, right? Also this problem is there for massless particles only, right?
@Sanjana the minimally coupled scalar field is not conformal in dimensions not 2
@ClaudioMenchinelli Thanks so much, I'll see it 👍
Btw I retract my 2nd statement in my last message
@ACuriousMind What? $\mathcal{L}=\frac{1}{2} \nabla^\mu \varphi \nabla_\mu \varphi$ does not describe a CFT?
5:45 PM
@Pizza np
@Sanjana nope; did you even look at the post I linked that explicitly states why?
@ACuriousMind Yes. It is known to me from Birrell and Davies... What I knew was that for massless theories, only for conformal coupling we get CFTs. But then I started thinking that $\mathcal{L}=\frac{1}{2} \partial^\mu \partial_\mu \varphi$ is ofcourse conformally invariant, completely forgetting the fact that we are in curved spacetime, and the Lagrangian density I wrote above is not conformally invariant
@ClaudioMenchinelli you are correct, but he likely wont understand why.
@ACuriousMind But why is this specific to 4D? This should be valid in other spacetime dimensions also, right?
maybe the specific setup you're reading about does not generate scalar fields there?
note that the excerpt you posted does not necessarily imply that in the other dimensions there are scalar fields but they don't need to be coupled to the curvature in this way, there just may not necessarily be scalar fields instead
5:51 PM
@Pizza The $F_2$ that you are given is the net force acting on just the 2nd block. It is not clear what it is you are attempting to do. The $F$ you are supposed to find is the force you have to additionally supply for the combined 3 blocks together so that they move together as one. Those are totally different things and you are not relating them together in any sensible manner.
I'm going to sneeppuuu though
or maybe the author simply only knew for certain in 4d and was too lazy to check for the general case because it's not really relevant to the topic at hand :P
@ACuriousMind Actually he checks things for general case in great details using branes and what not. He is Witten :)
so?
But the section on branes is big, and this argument is small: hence my interest in it
if this is a small statement irrelevant to the actual argument of the paper he wrote that sentence in like 5 seconds and never thought about it again
5:55 PM
@ACuriousMind So are you suggesting that this might be not much to think about?
yes
I believe that thinking even the smallest part of something by Witten must contain great insight in even the most throwaway line isn't really a great mindset to read things
Oh. sorry... But you know very well that I have this bad habit of giving importance to things which are not, whether it's Witten or not is immaterial. I am just like this.
but note that I also gave an alternative explanation - that there is something specific about the setup here that's different from the general question of conformally coupled scalar fields - I simply don't know enough about the context to tell
But ofcourse when you say it, I realise what's important and what's not soon enough.
@Sanjana I think the English teacher here might perhaps expect others to choose their words with much more care than most do ;)
2
6:00 PM
@ACuriousMind Lol... maybe...
@ACuriousMind Yeah. I could give you some context, but that would take quite a while.
I am going out now ... so later sometime. Btw it is the paper "Connectedness Of The Boundary In The AdS/CFT Correspondence"
it probably won't be worth it since I don't know a lot about AdS/CFT to begin with
But unlike many AdS/CFT papers it has cohomology stuff which might interest you. It deduces the fact that the CFT must be defined on a manifold on which $H_n (M, \mathbb{Z})=0$
@naturallyInconsistent but I found F, not F2
@Pizza I'm saying you are using F2 wrongly to find F, which is why you get something wrong.

2 hours later…
7:45 PM
@naturallyInconsistent Yeah, I had to go grocery shopping and since I was in a hurry, I couldn't give any ulterior explanations or check his work. Thanks for checking mine as well :P
@Sanjana Out of pure curiosity, could I ask what's your background in physics like? Reading Witten's papers is a level already unfatomable to me :P
Do not feel obligated to answer obv
8:21 PM
@ACuriousMind Hi. I know I shouldn't bother with question of Mechanics or anything else, however, there is one aspect regarding the usual physical situation that puzzles me. When a mass detaches from a rod pivoted at one point and to the end of which another mass is attached, the system rotates around the pivot and there is tension in the rod, and that tension exerts an outward force on the pivot, that is, the rod can feel the pivot being as if pulled outward. The tension exerts an inward force on the mass and it is that inward force that causes the remaining mass to move in a circle instea
But herein lies what I don't understand. In some books I have read that these two forces are due to the third principle of dynamics, the centripetal force is opposed by a "reactive centrifugal force" (to distinguish it from the "inertial" force) and the two offset each other, canceling each other out. In other books, it is said that these two forces do not obey the third principle of dynamics because they are exerted on the same object, not different objects.
Therefore, there should be a net force. What should be that net force responsible for a torque (which would be zero anyway, since the force is radial)?
9:10 PM
I have $$|\psi\rangle = \left(\frac{\sqrt{3}}{2}R_{21}(r) + \frac{e^{i\alpha}}{2}R_{31}(r) \right)\left\vert j = \frac{1}{2}, j_z = \frac{1}{2}, l = 1, s = 3/2 \right\rangle$$
how do I compute (I should maximize it but I'm sure the maximization is only linked to the arbitrary phase $\alpha$): $$\langle \psi |r|\psi\rangle$$
I'd like to use the expansion via hydrogen atom eigenfunctions $|r,\theta, \phi\rangle \Rightarrow \langle \r, \theta, \phi|n,l,m\rangle = R(r)Y_{l,m}(\theta,\phi)$ but I can't write the expansion properly
the spin part is autonomously well normalized: $$|\psi\rangle = |\psi_{space}\rangle|\psi_{spin}\rangle \longrightarrow \langle \psi_{space}|r|\psi_{space}\rangle \cdot 1$$
May I ask for all the passages to compute the last expectation value if possible :P

3 hours later…
11:56 PM
@ClaudioMenchinelli No formal background as such: not even a B.Sc. Just heard some physics lectures (bunking English literature classes, cz tbh it was easy to pass the exams :p) and discussions with friends from the physics circle, reading up stuff and ofcourse help from PSE guys.
Btw, number of papers written by Witten is huge. Some papers on AdS/CFT are particularly easy to read.
I mean the math is relatively easier. The conceptual aspects are deep indeed in most paper I have seen.