1:01 AM
h o n k ~
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@ACuriousMind Hi, in this answer there are equations written for independent systems of the original system. Is this answer wrong or is it a different physical situation from the one we considered? Thanks.
2

A man holds in his hands two equal masses with outstretched arms, standing on the center of a platform that rotates with a certain angular velocity. If you drop both of the masses without moving your arms, what happens to the angular velocity of the man and the angular velocity of the masses? I...

3 hours later…
3:41 AM
Five, to be exact.

4 hours later…
8:02 AM
@PM2Ring : That graph is a masterclass in data visualization.

2 hours later…
9:38 AM
@Qmechanic Thanks! I justed added another one, covering a bigger timespan, with a prettier palette. It also shows the Sun radius (the solid circle) & the mean distance (~827467 km). astronomy.stackexchange.com/a/44903/16685
I could cover the whole Horizons timespan (9999 BC to 9999 AD), but I think it would just be an artistic mess. :) A good graph has to display the patterns in the data, so it's counter-productive to make a graph that obscures the patterns with too much detail.
if two observables, or two hermitian operators $\hat{A},\hat{B}$ in general, commute with the Hamiltonian $\hat{H}$ but do not commute with each other, then does this automatically imply that there's gooing to be degeneracy in energy levels?
@PM2Ring I saw your answer and your polar plots, beautiful :P
@ClaudioMenchinelli yes, cf. e.g. this nice answer by knzhou phrasing this in terms of representations of symmetry groups
oh that's why it was presented to us as a black box
@ACuriousMind thanks, I'll look into it
10:07 AM
hi
I'm reading the wiki page on irreducible representations: so basically I got the gist of it, but I don't quite understand the initial definition of representation, since it seems quite abstract: what does the function actually do in simple terms? It takes an element from $G$ and maps it into what...? Basically what does $\rho : G \rightarrow GL(V)$ translates into?
the matrix representation helps quite a lot :P
also, I see the connection between the discussion of decomposable representations, in terms of matrix representation, is connected to how the CG coefficients are discussed in Cohen-Tannoudji. They are basically equivalent representations
I remember ACM talking to me about this :P
10:55 AM
@ACuriousMind Sorry to bother again. In the problem with which you helped me yesterday, we said that the total angular momentum is conserved about the pivot O, but we can said that the total angular momentum is conserved about any point on the same axis, right?
@ACuriousMind Do you know a proof of the fact that the total angular momentum is conserved about the pivot O, the total angular momentum is conserved about any point on the same axis?
11:19 AM
@Bml No, if you choose any other point there will be a torque from the pin at O that prevents the rod from moving - the "pinning force" only exerts no torque because it is right at O and torque is $F\times r$, where in that case $r=0$ is the distance of the force to O.
@ACuriousMind This seems to be in contradiction tò what @JohnRennie said me in a Chat Room. He said:
The AM is not conserved full stop. i.e. there is no with respect to the pivot.

If the AM is not conserved it is not conserved regardless of what point we use to calculate the AM.
And also:
If angular momentum is conserved when calculated about O then it is conserved when calculated about any point.
@ClaudioMenchinelli Thanks, Claudio.
Greg Egan recently tooted a cute thing about the inertia tensor. It includes an MPEG animated diagram. mathstodon.xyz/@gregeganSF/112569151647288169
To make the anim play on a touchscreen device, you need to do a long press. But it can be a bit fiddly...
12:01 PM
@ACuriousMind If a rod is hit by a material point and the rod is free to rotate around a constraint O, what happens as soon as the ball hits the rod? 1) some impulses are created, which, if a point other than O is considered as the pole, must be taken into account: therefore, the angular momentum is not conserved; 2) if the pole O is considered, the angular momentum is conserved since the forces between pivot and ball are applied in O. Is that true?
12:12 PM
why do u think our universe has light in it
qft doesnt answer why these fields
not only is there light, it's also extremely prevalent
such peculiar ingredients for our universe
12:27 PM
@ACuriousMind @ACuriousMind I would be grateful if you would answer me, I am in great difficulty with this concept. Thank you very much and sorry again.
12:42 PM
Is there a website where people can go to ask physics questions from knowledgeable people?
This one
actually, that's not true. I've tried multiple times, with each question getting closed by a mod and now I'm banned from posting
I've only ever tried to ask questions and learn physics here
I'm not sure I'm gonna side against the mods on that one :p
What was your question
In the recent paper "The Decoherent Arrow of Time and the Entanglement Past Hypothesis" by Al-Khalili and Chen, the authors propose that the early universe had very low entanglement entropy, which increases over time and gives rise to the decoherent arrow of time. Building on this hypothesis, I seek to understand how entanglement networks and energy densities influence the nature of spacetime, time dilation, and black hole interiors.

Causal Structure and Entanglement Networks
Hypothesis: Light cones define distinct causal regions in spacetime, creating unique entanglement networks defined
I've had numerous posts closed by them
and now I can't even post
this site isn't built for people to ask questions
or seek knowledge
I'm wondering where I can go to interact and learn with people who know physics
@Bml This is only true if there are no forces/torques. In this case, in the moment of separation there is a force from the pin that keeps the rod from moving off (remember our conversation about linear momentum from yesterday), and so angular momentum is only conserved with respect to the point where this force acts, since with respect to that point the torque is zero
@Bml you don't need to ping me multiple times, just don't expect anyone to always reply immediately
12:49 PM
it's really most astonishing when you consider that my posts are just questions
and that isn't allowed here
so, where can I go to talk to knowledgeable physicists?
I would really like to learn more and wish there were a venue for that
As I've also linked on your meta post, we have a list of other sites where questions that are off-topic here might be on-topic.
none of my attempted questions have been off topic
they're literally all about physics
@ACuriousMind OK, the force from the pin should be the centrifugal force that keeps the system in motion after the mass falls off, right? The force is radial, so F \times r = 0. Am I going wrong?
@Asklepian We will not re-litigate the closure of your questions here, since this hasn't been fruitful in the past. If you just want to complain about now being question-blocked, please do that somewhere else.
@Bml yes
@ACuriousMind I don't want to merely complain, nor relitigate previous closures. What I want to do, what I have ONLY attempted to do on this website, is ask questions. What I would like to do is simply post my question and have a response on it
12:57 PM
@Asklepian i cant see ur questions
@ACuriousMind Why had you written no? Perhaps I should have said "force exerted on the pivot" rather than "force exerted from the pivot"?
@RyderRude they closed them all
@RyderRude then banned me from asking further questions
@Bml I deleted the 'no' because it was wrong, don't worry about it :P
@Asklepian try asking here in the chat. i can maybe help u if the questions are not good
I literally have no idea how it is even possible to ask a question on this website, in the first place
12:59 PM
@ACuriousMind It is a centripetal or a centrifugal force?
@Asklepian no human explicitly banned you from anything, the question ban is automated, see physics.meta.stackexchange.com/a/10640/50583 and its links
@Bml what do you think the difference is?
@RyderRude In the recent paper "The Decoherent Arrow of Time and the Entanglement Past Hypothesis" by Al-Khalili and Chen, the authors propose that the early universe had very low entanglement entropy, which increases over time and gives rise to the decoherent arrow of time. Building on this hypothesis, I seek to understand how entanglement networks and energy densities influence the nature of spacetime, time dilation, and black hole interiors.

Causal Structure and Entanglement Networks
Hypothesis: Light cones define distinct causal regions in spacetime, creating unique entanglement networ
that was my most recent question
there is nothing I can do to get unbanned
And most of your questions - while some were closed by others - were deleted by yourself. They weren't even all closed, of your 12 deleted questions, 7 were not closed at the time of deletion. Please stop misrepresenting what's happening.
@ACuriousMind The latter is a fictitious force, the former is not. Since the force on the pivot is outwards i.e. in the direction of increasing r, it should be a centrifugal force, shouldn't it?
@Bml but we're not worrying about the force on the pivot, we're worrying about the force the pivot exerts on the rod
1:02 PM
@ACuriousMind So, if I undelete my questions, I'll be unbanned?
I'm not misrepresenting anything
I've dealt more with the quirks of this website and the ability to even get a question on the floor on here than I have actually engaging in any kind of discussion with those more knowledgeable
this site is simply inaccessible
@Asklepian since the ban is automatic, I cannot say that for sure, but deleted posts certainly make the ban worse
@ACuriousMind After the mass falls off, rod + remaining mass is not balanced. In order to prevent the system from moving, the pivot should exert a force on the rod, right? Is it directed in the direction of increasing r or of decreasing r?
@Asklepian it seems to be violating the "one question per post" rule
@Bml What do you think?
@RyderRude fine then... all my posts have been downvoted or closed without any discussion about the actual question. I just want to post my question(s) and have an actual discussion
that has been impossible on here
1:07 PM
@Bml I'm sorry, but I really don't think it's useful if I confirm every tiny step of this rather basic exercise with you - at this point I don't really know why we're talking about all these details
can anyone just tell me what to do to get an answer on this website?
@ACuriousMind The direction of decreasing r.
@Asklepian Adhere to our guidelines. Many of our users don't have any problems at all with this and never encounter the automated question block, but if you find these guidelines make the site inaccessible to you - well, no one is forcing you to use it. There really isn't anything more to this.
how do I get unbanned?
I have really tried to adhere to the guidelines
I don't care that most people don't have a problem with this
I am having a HUGE problem with this
how do I fix this?
@Asklepian are your questions not answered in the paper?
Just read the paper and if you have any specific questions then ask them on the main site
1:11 PM
@Asklepian see meta.stackexchange.com/a/86998/263383, of particular interest to you is "Are deleted posts taken into account too?"
@Asklepian questions about textbook physics are more likely to be answered here
@Obliv you're really not helping because they're complaining they're question-banned on the main site :P
stuff that is vague like "how does this align with our understanding of QM and GR?" is not good for questions on this site
@Obliv I have already attempted this and the question was closed
@ACuriousMind Yes, you're right, but I have a serious problem with a classical physical situation, a ball hitting a rod. If a ball hits a Rod which rotates around a constraint O, what happens to angular momentum?
1:12 PM
@Bml Where is the serious problem?
i find ur question open ended. it references a paper and asks about how it relates to our understanding of QM and GR @Asklepian
i mean the first question
maybe better for meta or physicsforums
@Obliv I can only really ask questions to the best of my knowledge and understanding, not someone else's
if you're just curious about peoples opinions
the point is that I would like to learn more
I'm not interested in opinions but in learning through discussion
1:14 PM
yeah, that's not what this site is for, really - it's a Q&A site for well-defined questions getting well-defined answers, not to have free-form discussions
this might just not be what you're looking for
This chat room is better for more open-ended questions asking for peoples opinions and such, but if you want to actually learn (and you're not already graduate level+) then reading textbooks and watching lectures is better than asking questions on PSE
but this site is a good supplement and your learning shouldn't be bottle-necked by you being banned here shrug
@ACuriousMind @Obliv I spent 4 hours 'defining' that question to the best of my ability and knowledge
@ACuriousMind 1) some impulses are created. The ball hits a rod at a certain distance from the axis of rotation (pin). If a point other than O is considered as the pole, is the angular momentum conserved about this point other than O, if we consider the system as rod + ball? (If the system is considered as the rod without ball, the angular momentum should change about this point)
it appears that you need a PhD in physics to even be allowed to ask questions on this site
otherwise, you won't know enough to 'define' your question well enough
@Asklepian you asked three different questions in one post, contradicting the very basic guideline that there should be one question per post
you don't need to know any physics that that means the question will be closed regardless of the effort put into it
1:17 PM
that's only a single post, there were others that were downvoted and closed
can u give any other question here?
the point is that I've done my level best to post thoughtful questions, merely seeking answers...and that is unacceptable here
If you're going to be asking questions about research level physics that sound vague, then you're not going to get good feedback of course. It really depends though, because open-ended-esque questions can be relevant
:65804979 well, now, the point is that I can't post anything
and I don't know how to fix it
and all I've done is try to ask questions
"How does the concept that light cones form distinct entanglement networks, where FTL travel disrupts the unique historical record, align with our understanding of general relativity and quantum mechanics?" you need to phrase this better. What are you actually asking here
1:19 PM
please provide any other question. maybe we can see some persistent mistakes
"Why would energy density lead to the decoherent loss of redundancy in entanglement networks? How is this loss of redundancy related to the slowing of the propagation of coherent information within the network, and how does this contribute to the time dilation and curvature observed in general relativity?" (probably) too many questions in one post
I would love to just post the first question (if I could) and try to focus in on some sort of answer
what I'm saying is that a light cone must form a closed entanglement network
No, this chat is not intended for users to circumvent the question ban
workshopping questions and asking advice is fine, but trying to get an answer here while you're question-blocked on the main site is not
@ACuriousMind how are you so perfectly focused on prohibiting me from engaging in any sort of discussion on this website?
"How is this loss of redundancy related to the slowing of the propagation of coherent information within the network, and how does this contribute to the time dilation and curvature observed in general relativity?". im not familiar with entanglement network. are u sure this question is meaningful?
1:24 PM
@RyderRude honestly, I don't know how to reply because of @ACuriousMind
@Asklepian It's my role here to uphold the rules of the site; this is one of them. It has nothing to do with you personally.
@Asklepian as in, why do u think there is supposed to be a contribution of "loss of redudancy" to "curvature of spacetime"?
@RyderRude @ACuriousMind has indicated that I cannot respond to this
I honestly don't know what I should do
I don't know why I'm banned
I don't know how to fix this
I don't know why I can't ask simple questions and have a discussion
@Asklepian u can respond to this. im just helping u diagnose if there r mistakes in the question
@RyderRude which of your questions should I respond to first?
1:27 PM
@Asklepian Surely this has been explained to you
the second last one
@Asklepian Should be in the rules on the site, or ask ACM and they will let you know
and the third last one
@Asklepian Your questions are not "simple" and you now cannot ask them here since you got banned on the main site shrug
@ACuriousMind I've written a response with my first problem. The second is: 2) if the ball hits the rod in the same way (at a certain distance from the pin on the axis of rotation), but we calculate the angular momentum with respect to the pin O, is the angular momentum conserved if we consider the system as ball+rod?
1:28 PM
@Asklepian You've said this multiple times now; I've explained to you that this site isn't really for discussion and I've linked various meta posts that explain how the question ban works, why it's happening to you and why your last question was closed. If you're not going to engage with any of these explanations, please stop complaining here.
What do I do to fix this?
@Bml Again: What do you think?
18 mins ago, by ACuriousMind
@Asklepian see https://meta.stackexchange.com/a/86998/263383, of particular interest to you is "Are deleted posts taken into account too?"
@Asklepian one problem is that ur question does not contain math... when u r asking about the contribution of redudnancy to curvature, it shud b mathematical
Nah, that has nothing to do with it @RyderRude
this question may be meaningless, but im not familiar with entanglement networks
1:31 PM
there are tons of highly upvoted qualitative questions on main, but probably rarer
yes, but idk how to interpret this one without math
@Asklepian u can try using equations to make these questions more precise
I would love to work on the question to make it better or more acceptable but I'm banned
and after what ACM said, I don't really want to respond to it here
I really just feel like everything I do becomes instantly hemmed in
@Asklepian You can still undelete and edit any of your questions, which you would know if you had read the post I keep linking.
You can still edit your questions, which is suggested by the link ACM gave you. Have you even read it?
I don't know how to edit them because I don't know what makes them bad in the first place
I literally can't have the discussion
this site won't let me
do you see how little room there is for beginners in this community?
1:35 PM
I explicitly said that workshopping questions is fine, just trying to get answers to them here isn't.
@RyderRude Yeah I've been on a foundations of math/philosophy excursion recently and just viewing physics peripherally, seems like a sisyphean task to interpret and or devise questions in physics meaningfully (even with math)
@ACuriousMind I think that in case 2) (angular momentum with respect to the pin O) the angular momentum is conserved with respect to O if we consider the system as rod+ball, because no external forces are acting, so no external torques are acting. Actually there must be an external force that the pivot exerts on the bar that stops it from translating, but is it applied to pivot so r=0. Right?
@Bml yes!
@Asklepian if u r a beginner, u r most likely formulating meaningless questions!!
these questions r extremely technical
@RyderRude no
Well
1:36 PM
I will attempt to explain myself
@Obliv beginners can formulate meaningful questions, but not about highly mathematical stuff aspects of research stuff
they can formulate questions about qualitative aspects of research stuff
Ok let me backtrack, @RyderRude I don't think any question is inherently meaningless since they attempt to express a feeling but maybe the ability to convey the feeling to others is limited by natural language (especially online)
@ACuriousMind But in case 1) (angular momentum with respect to a point other than the pin O) the angular momentum is too conserved with respect to this other point if we consider the system as rod+ball, because no external forces are acting, so no external torques are acting. In this case it would make no difference...
@Obliv yes... what i mean is that the question becomes too open ended and impossible to interpret by others
@Bml I'm not following - this is the same situation as before: The pivot exerts a force on the rod!
you said it yourself - so why are we back to claiming there are no forces/torques w.r.t. to other points?
1:40 PM
@ACuriousMind Yes, but we are calculating angular momentum with respect to a point other than the pivot around which the rod is rotating...
@RyderRude @Obliv all interaction results in entanglement, however miniscule. thus, the sequence of interactions of all particles in a system forms an entanglement network defined by a single, unique history
since light cones are prohibited from interaction with anything external, light cones form distinct, closed entanglement networks
let's just start there
idk how to interpret these without math... @Asklepian
@ACuriousMind Because you yourself said that "if angular momentum is conserved when calculated about O, then it is conserved when calculated about any point if there are no torques/external forces". However, here there is a force exerted by the pivot, but $r \neq 0$ because we are calculating angular momentum with respect to other point than O. I don't understand why angular momentum should be conserved.
@Asklepian r these statements from the paper?
@RyderRude those terms have a mathematical foundation in their theories don't they?
like QFT or something
1:44 PM
@Bml yes - so angular momentum with respect to any point other than O is not conserved!
everything you say is correct, you just seem to think it isn't :P
terms do, but im not sure if about the sentences... but maybe it's from the paper @Obliv
well yeah it's in reference to the paper
@RyderRude these arise (as far as I can tell) as a consequence of the paper, which basically claims a decoherent arrow of time, where entanglement in the early universe was low and grew over time
@Obliv e.g. i cud say that the moment a measurement device entangles with the system, multiple parallel histories are created in the entanglement. so idk what it means by unique history
@ACuriousMind Even if we consider rod+ball as a system?
1:46 PM
@Asklepian oh
@Asklepian i want to ask, r u casually into physics at the moment, or have u studied GR and QM?
@Asklepian So, here's the problems: "Entanglement network" is not a standard physics term, it is very specific to the paper, and most people will have no idea what you really mean by that. If you ask a question about a concept that's not commonplace, the onus is on you to explain the concept so that question becomes comprehensible. Additionally, "light cones" are not objects, they're just regions of spacetime, and it is unclear what "interacting" even means for them.
yeah I'm just an unmotivated undergraduate student on summer vacation so I can't really help you with research level physics, sorry. @Asklepian hope you reformulate your questions well enough to get unbanned
@Bml Yes
@ACuriousMind I'm a physician by training but very interested in physics. However, while I've been trained extensively in the sciences, I have not studied graduate or research level physics except informally
@ACuriousMind If we consider the rod as the system, obviously the angular momentum is conserved only when r = 0, i.e. with respect to O. But if we consider the system as rod+ball, I cannot say precisely whether the angular momentum is conserved or not. At first glance I would think that it does not conserve, reasoning about it I say no because there is no external force (the system is ball+rod).
1:48 PM
naturally, I do not know what is commonplace or not
@ACuriousMind Why? There are no external forces...
I have a deep interest in these topics, however, and was hoping to engage this community to learn more
@Bml Why are we going in circles? There is an external force, that of the pivot on the rod
@RyderRude I have studied QM and GR from a conceptual standpoint for several years but haven't had the time or opportunity to go back and learn the math
@Asklepian there lies the problem... u r asking about mathematical aspects of research stuff. others cant interpret it
1:52 PM
@ACuriousMind OK, so you and @JohnRennie disagree on the fact that the angular momentum is conserved or not with respect to other point than the pivot. He said that in a system rod+ball, if angular momentum is conserved about O, it is conserved about any point. You said that in a system rod+ball, if angular momentum is conserved about O, it is conserved about any point iff there are no external forces. This was the source of my confusion
@Asklepian Asking questions about random research papers will not be useful for that since you can't even be sure you understand what they're about. That you could formulate a meaningful question about a research paper without understanding the average content of a graduate course in physics is extremely unlikely. You need to engage with material written for your level to make useful progress in learning things.
It's like me trying to engage in literary discussion about the classics of a language I barely speak
2
@RyderRude math is overrated..Temba, his arms wide
I'm like half serious, it's literally just an extension of logic which already can be expressed in natural language without symbols
did you watch the vid
@Bml Did you make it clear to John that there is this pivot here? Because you confused me yesterday, too, by not making clear that the rod is pinned to a point.
Idk, the objects in math serve as a tool for physics but no one claims real life experiences are mathematical objects
1:57 PM
@ACuriousMind Yes, I believe so, but if you want to check, the room is open:

### Room for Bml and John Rennie

then let's start smaller. when two particles interact, this results in an 'observation', where certain properties of each particle become defined relative to one another. have I misunderstood anything?
@Obliv what resource r u using for this stuff
@Asklepian observation in QM isnt well understood yet.
some peoples' papers may try to define it that way
ok, let's explore that... maybe that's how I should rephrase my question
Rovelli's interpretation is like that
@RyderRude this, for now
2:10 PM
from my reading, wave function collapse is simply an entanglement event. particles with which a system has little entanglement will appear as wavelike probabilities, whereas highly entangled systems will appear more classical and defined.
@user85795 thanks
@Asklepian this seems to be some research about the measurement problem. it is def not accepted physics yet
@Asklepian Everything you've said is relative to an interpretation of quantum mechanics - there are various points at which something becomes a measurement (not "observation") and that differs between each interpretation, and some interpretations don't even have wave function collapse
2:12 PM
but decoherence is well accepted, which is similar to this @Asklepian
and "particles appear as wavelike probabilities" doesn't really mean anything - this is the problem: You can't talk about the finer points of quantum mechanics without an understanding of the actual mathematical formalism
and that you won't gain from a few answers on this site, but rather reading (at least) one full textbook on the subject
in an ideal world, I would go back to college and do a physics degree but, for now, this is all that's available to me
the next video is about QM
...which is why it's so important to me to be able to have these discussions and learn from them
learn from a textbook
2:17 PM
I have never learned from a textbook but through conversation
@Asklepian both recordings of lecture series and textbooks are available elsewhere on the 'net - if you really want to dive into interpretations of quantum mechanics and ask questions that make sense to actual physicists, that's where you need to go first
alternatively, you can adapt your understanding manually by reading the relevant sections instead of building up your math from the ground up which would take a long time
@ACuriousMind Have you had a look into the room?
the format of this site is good for single, answerable questions, but not for learning a subject from the bottom up without any other resources
@Asklepian time to start
2:18 PM
like: oh this is expressed formally as X mathematics and such
I can't ask a textbook questions
I need to discuss things
where should I go for that?
here
@Asklepian that's why when in the course of reading the textbook you get a question, you can come back here and ask about it - many of the questions we get are precisely of this nature, people asking how to interpret a specific section in a textbook or apparent contradictions with other material
talk to the textbook^
it seems like you want a deeper understanding of physics anyway, which is inherently mathematical/precise in its language. So you may as well read the technical aspects of the theories
2:21 PM
I wouldn't mind being introduced to these concepts through discussion but my attempts at that here have been prohibitive
and, I believe you need a solid understanding of linear algebra to attempt a quantitative understanding of QM
reading a textbook is a skill that will pay off in the long run
I mean...there's a reason people have to study for years to write research papers, right?
there is someone here who is a high school english teacher that is learning QM/QFT so I think it might be reasonable that anyone can if they have the willingness
if you could just short-cut to understanding advanced research in a few discussions, everyone would do that :P
lol
2:23 PM
no formal education is necessary, but an open and curious mind is essential
I'm not trying to shortcut; I'm trying to figure out where my understanding currently is after years of informal reading
try to formalize your reading material
informal reading is likely going to net you a lot of familiarity with the concepts introduced in textbooks but the mathematical formulation will provide you with a richer understanding @Asklepian
I went to medical school and did chemistry and even algebraic physics. so, I'm familiar with textbooks... but physics is largely conceptual. F=ma is, ultimately, about the underlying concept
or at the very least a tangential understanding that can be used with your informal one
2:25 PM
@Bml Yeah, I think @JohnRennie is incorrect but because of an understandable confusion around the notion of "conservation". In terms of symmetries - angular momentum is conserved if the system is rotationally symmetric, that's how we usually say it. But what's really going on is that angular momentum about a point is conserved if the system is symmetric under rotations around that point.
Now, when there's a pivot, the system is only symmetric under rotations around the pivot (since rotations around any other point move the pivot around) and so also only the angular momentum about the pivot is conserved, but not any other point.
@Asklepian I'm afraid I don't think that's true - yes, physics is "conceptual", but beyond the shallow presentation in most popular science materials, those concepts are often inextricably linked to the math. You can't just remove the math from the physics and somehow a "conceptual" shell remains that still makes sense.
For instance, a popular "concept" is that of wave-particle duality, and we get many questions on the site from people trying to apply what they think the concept means to all sort of situations, ending up confused or with contradictions. The problem is that the actual QM formalism has no notion of "wave-particle duality" in general that would apply to all quantum systems, and if you work out the proper mathematical descriptions of the situations in question, all the contradictions go away
Some physicists are really good at presenting an apparent "math-free" story of how something in physics works, and these are valuable, but the problem is often that you can't use those stories and apply them to something else because the stories are hand-crafted for the specific situations the physicist who wrote the explanation cared about (another popular "myth" is that of electricity as a fluid - great picture, really bad at applying to some advanced electronics setups)
@Asklepian algebraic physics is hand crafted for med students :-)
@asklepian One prominent type of question asked on this site and chatroom is clarifications in an existing theory/framework which should be clearly defined and interpreted (since it's based in a formal system). Since your questions are not of this nature, they are probably concerned with the philosophical side of physics, which is like 1000x harder in my opinion to navigate
@ACuriousMind spoken like a true mathematical physicist :P
Have fun with your incomplete formal systems, Hilbert
rides away in poorly engineered non-mathematically derived vehicle
@Obliv no, I don't think this is particularly a mathematical physics viewpoint - sure, most physicists do math haphazardly and non-rigorously in ways I don't really like, but they still do a lot of math - the whole reason there's all this non-rigorous math is because it's part of almost every physical argument
@Obliv they're hard because you're not just asking "how did we get here" from a set of postulates/axioms and rules of logic. You're asking "where do we go" and that's essentially math/philosophy, except you guide that question with observation (usually) or pre-existing physics/experiences
@ACuriousMind Sure, but the way asklepian is learning is more like natural philosophy which doesn't require any formal mathematics. Physics is derived/evolved from natural philosophy and that shell still exists imo
2:43 PM
I remember going to some science fair by the local university at some point before I studied physics - I had read a lot of pop-sci material on particles and quantum fields and I cornered some poor grad student who was there to answer the public's questions. He was really nice, but he didn't really "answer" any of the questions I had, and I left feeling as if I wasn't taken seriously.
Years later after I'd learned how particle physics, i.e. QFT, actually works, I understood what had happened - none of my questions had really made any sense because they didn't use the same framework of reasoning that actual physics uses and of which math is an integral (not the only!) part.
@Obliv I feel you're focusing on a false dichotomy here: Again, I'm not talking about "formal mathematics" in the sense a mathematician would understand it, I'm talking about the kind of physicist math that's an assumed part of every conversation between physicists
That physicists didn't always use to reason this way is irrelevant - things can evolve beyond what they originate from
is that what attracted you to string theory
and if you look at modern engagement by philosophers with physics - in particular QM interpretations, relativity, etc. - they usually are also careful to first demonstrate a technical understanding of the subject, and then talk in a more characteristically philosophical way about it (such as e.g. my beloved Causation as Folk Science by Norton)
again: there is no short-cut, if there was a way to learn all of the "conceptual" physics without the technical parts, many people would do something like that
@user85795 had to have been the big bang theory if i had to guess
(awaits being smited by mod powers)
@Acuriousmind You know too much history since you're likely an AI, so I won't contend with you the history of physics but I still think until we've arrived at the contemporary form of scientific theory we have today, we utilized intuition and informal arguments made in natural language. This obviously changed with relativity&QM but it's not like intuition has left us. Even mathematicians rely on "intuition" when working on problems.
I think up to QM/relativity, one can get the core ideas of the physical theory without even physicist maths. But, it's probably not an effective way to teach since eventually to progress you need math anyway
My sister took a qualitative intro physics course last year and I was baffled that it even existed. They went over newton's laws and even thermodynamic theory without (mostly any) math. I felt bad for her since she had so many questions that I couldn't really answer. Now she's doing applied mathematics which is kinda ironic.
@ACuriousMind I guess we're beating a dead horse here though.
@Asklepian also this question is a good demonstration of a question, like ACM asked that grad student, which can be hard to answer without a formal framework.
But they're not meaningless questions, it's just this site functions (like most modern scientific institutions) on a mathematical foundation
3:02 PM
built on textbooks
41 mins ago, by user 85795
reading a textbook is a skill that will pay off in the long run
@ACuriousMind Ah, OK. I have one last question, which I still don't understand: in the ball+rod system, the external force exerted by the pivot in which direction is it directed? If the rod is horizontally pivoted in O, is this external force directed upwards? That is, is it always perpendicular to the rod?
3:22 PM
does somebody happen to notice any kind of symmetry for this operator $$\hat{V} = A(x^2 + y^2)$$
It acts as a perturbation to the Hydrogen atom Hamiltonian and when considering the degenerate level $|2,l,m\rangle$ it happens to not quite completely remove the degeneracy
so I wondered if anybody could help find whether or not there's a hidden symmetry :P, in the spirit of my previous messages today
I already know that $[L_z,V] = 0 = [\Pi,V] = 0$
@Bml why does it matter?
@ACuriousMind Because I didn't I understand what kind of force it is. In the exercise on the falling mass it was a centripetal/centrifugal force, in the case of a ball hitting the rod what is it? Why?
well, for one, unless the pivot is in the rod's center of mass, it's still providing a centripetal force
@ClaudioMenchinelli A degeneracy always implies a symmetry - the symmetry operator(s) are the operators interchanging the degenerate states, so look carefully at your degenerate states and see if you notice nice operators that just interchange those among each other
@ACuriousMind What is the difference with the pivot located in the center of mass?
3:38 PM
@ACuriousMind The degeneracy arises from the fact that $Y_1^{m}, m = \pm 1$ give the same energy shift since you go on considering $|Y_{1}^{\pm m}|^2$ in the computation, therefore it is likely linked to the fact there's no $\phi$ dependence at the end
hence, the operator probably sends $\phi \mapsto -\phi$
@ClaudioMenchinelli yes, so it's rotations + reflections in the x-y plane
i.e. the symmetry group underlying this is the non-Abelian O(2)
@Bml you don't need a pivot to keep something in circular motion around its c.o.m.
the reason you need a pivot in the other cases is that, without a pivot, both total momenta are conserved, in particular also linear momentum. But something that rotates around a point that's not its c.o.m. has non-zero linear momentum for its c.o.m., so you need a centripetal force to keep that c.o.m. in circular motion. When point of rotation is in the c.o.m., the c.o.m. doesn't move at all, so no need for a pivot (or if you put one there, it doesn't need to exert any force)
@ACuriousMind So the force provided by the constraint on c.o.m is the constraint reaction of the c.o.m., right? And the centripetal force on a pivoted rod points in the direction of the length of the rod, right?
Interesting, I looked at the other professor's solution, since he usually explains these things as a non-mandatory part of the exam and the answer is... it's a reflection wrt the xz plane
and $[L_z, R_{xz}] \ne 0$, thus the degeneracy is not completely removed
I've noticed that the QM exams at my university are leaning more and more towards problems where you must identify the more evident symmetries of the system at hand but also some of the more hidden ones.
I like it
3:53 PM
@Bml What constraint? I don't know what a "constraint reaction" is.
But yes, of course the centripetal force on the rod points along the rod
I'm gonna go solving another exercise. See you guys, and thanks to ACM for the help as always.
cya
@ACuriousMind It is reaction by the hinge, by the pin...
@ACuriousMind The rod is constrained to maintain a fixed length (as a rigid body) and in order to enforce this constraint tension must develop internally which acts on the bead as centripetal force (due to Newton's 3rd law). So, centripetal force always points towards the axis of rotation. Yes?

1 hour later…
5:17 PM
I guess, for the (algebraic) physics that I have studied formally, as well as all the other mathematical representations I've learned that model reality in some way (medical numeracy, i.e. Absolute Risk Reduction, Number Needed to Treat, and other statistical measures) I've never encountered a situation in which understanding the math led to an understanding of a concept. Rather, by accurately understanding the concept, the math always just 'falls out' naturally and logically.
I guess some people are naturally wired so quantitatively that understanding the math leads to an understanding of the concept
that has just never happened for me
...and without going back to linear algebra and higher level calculus and THEN formally approaching higher level physics, I don't have any way to engage with these topics at my level of interest EXCEPT by thorough discussion at whatever my level of understanding is
I might not have a full, graduate student understanding of entanglement and superposition and relativity but I certainly have a more accurate understanding than most laypeople
I've been trained in the sciences and I have years of informal reading on higher level physics
so, I just need a place where I can discuss the concepts and be introduced to the math as appropriate
I'm just looking for a physics community that can teach me where I'm at
because I don't really have the option to go back to school and learn an entire physics curriculum

1 hour later…
6:27 PM
How to expand $r^{d-2}/(r^d-m)$ about $r = m^{1/d}$? Obviously it should be a Laurent series, whose coeffs I can in principle find doing the contour integrals as in the "definition" of Laurent series. But sometimes, taking some factor out, one can use standard binomial expansions to write down the Laurent series. I was wondering whether that sort of thing can be done here
I just need the 1st i.e. $1/r$ term btw
@SillyGoose Its a nice note. It has more background material on differential geometry than CS, which is absolutely helpful for beginners. As for the classical EOM derivation, everything was crystal clear. I also got to know about your question and QMechanic's answer on the main site.
I think your notation is more correct, because of the comments to QMechanic's answer on that post
6:50 PM
@Asklepian qm books have a chapter of the required linear algebra in the beginning. u need not use separate math books
7:04 PM
@Obliv i wud say qualitative and open-ended questions r fine... and r interpretable/non-interpretable 1/2-1/2 of the time
but it's hard for me to categorise the conditions that make these questions fall in the former half vs the latter category..
i can only tell after seeing the question. so it can be frustrating for people who want to know what exactly theyre doing wrong with their open ended question
one condition i can tell is that if one asks a qualitative question about the highly mathematical aspects, it can be non interpretable
7:45 PM
ok, I've made an attempt to clean up my questions using ChatGPT:

1.) Can you elaborate on how decoherence functions as the process by which an initially indeterminate quantum system becomes effectively determined through interactions with its environment? Specifically, how does this process encode information about the system's state into the environment, thus creating a unique local historical record of these interactions? Additionally, what are the quantitative measures, such as von Neumann entropy or entanglement entropy, that can be used to describe this transition from a quantum super
are these clear enough to post?
8:04 PM
@Asklepian The first sentence of your 1) is a complete question (and the topic of entire books on decoherence theory). The second sentence of 1) is unclear - why do you think it creates a "unique local historical record"? What does that even mean? The third sentence is again a complete topic in its own right. These aren't questions, these are prompts for dissertations and books.
2) is completely unclear - what does it mean to interpret something as "encoding a local network of quantum entanglements"? A light cone originating at a point/event describes the regions of spacetime that can causally affect that point (past lightcone) or be affected by that point (future lightcone). What is any of this supposed to have to do with entanglement?
3) unclear, and in addition likely to be closed as non-mainstream - "if FTL was possible" is not well-liked here, since neither classical relativity nor quantum mechanics really allow for it. The topic of how entanglement interacts with the limit of the speed of light is a frequent topic on the site, but questions that just assume that "superluminal travel were hypothetically possible" are not questions about mainstream physics, since both classical relativity and quantum physics forbid this.
Lastly: ChatGPT and other LLMs are bad at anything but the kind of physics questions that occurred repeatedly in their training data. Never trust them, and if you'd mention in your question that you used it, you're likely to receive downvotes just for that - many users don't really want to waste their time debunking the garbage these models generate (even if that's not how you used them - I'm explaining the reflex, not defending it)