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4:19 AM
@SirCumference yeah; none of us are denying that it is suboptimal to teach QM before Hamiltonian mechanics. It is definitely preferable. However, it is shown through multple generations worth of experience that quite many students can understand QM before Hamiltonian mechanics, and the pressures of curriculum scheduling forces us to do so.
@qwerty that's the same thing with physics. Even in mechanics you can do Newtonian all the way and cry, or you can do Lagrangian mechanics, or you can do Hamiltonian mechanics, or you can use Hamilton-Jacobi, or Poisson brackets, etc. Similarly, in quantum you can ignore SR and do Schrödinger, or use Dirac, and in any of those cases, try variational, or do WKB, or whatnot.
4:57 AM
@ACuriousMind The OP doesn't like your dupe target.
> Ps- it is not a same question as "do tachyons really move faster than speed of light". Rather I want to know the speed of tachyons from tachyon's and normal observers perspective please reopen this
But that's just the OP not understanding what your answer already wrote: that there is no such things as any tachyon's perspective.
5:16 AM
@naturallyInconsistent Ok. But I can't think of anything I can add to my answer that will satisfy the OP. And they already acknowledged that "maybe it can't be defined just like lights reference frame can't be defined".
There is nothing to add. The problem now lies with the OP. As long as the OP verbally says that he understands, yet continues to go on and do things as if he doesn't understand, your attempt to convince him will be a steep uphill climb.
There, I've made my contribution
Thanks. Much appreciated.
defo np, esp for ya
5:38 AM
Here's a cute quadratic identity I noticed a few days ago. I'm a little embarrassed that I hadn't seen it before. $a^2 + b^2 + c^2 + (a+b+c)^2 = (a+b)^2 + (b+c)^2 + (c+a)^2$
@naturallyInconsistent so what is your take on my question? I'm curious
@RyderRude thus, putting a 1 tonne load on a long bone will break the bone just like if we put a static load on the same bone that was broken at 2 tonne load. Is it correct
6:19 AM
@SnoopyKid there is not enough information to determine this
note that whether or not something will break does not depend on how much impulse u impart to it
e.g. if u transfer 1000kgms^-1 of impulse to an object by applying 0.1N force for 10000s, u will probably not break anything
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Hello Everyone...
 
1 hour later…
7:42 AM
Hello
i no longer believe that there is sufficient evidence that QM likely relates to consciousness. i would put my beliefs at 40-60 in favor of objective collapse
@think_meaning_builds wth so that's why it was down?
one of the reasons i favored consciousness interpretations got eliminated, but few others survive
> A copy of a user authentication database containing the email addresses and credentials of 31 million users has been provided to Have I Been Pwned.
that's really bad, I recently gave them my details too
7:50 AM
Attack a clearly non-profit organization, now that sounds "artificially intelligent."
remaining reasons to favor consciousness interpretations : 1. Consciousness is the only place where we observe a definite outcome. Therefore, it is reasonable to believe that Schrodinger eqn applies at all other times
2. Quantisation is applied in the time direction, the same direction that consciousness experiences (but this is circumstantial evidence. it is weak)
@think_meaning_builds yeap low move
if these remaining arguments are also eliminated, please let me know
8:07 AM
12
Q: Internet Archive suffered a DDOS attack and passwords may have been compromised

FuzzyBootsI know many people here rely on the Internet Archive to source books for quotes, but they have been undergoing a DDOS attack and password hashes may have been compromised. If you haven't reused the password used on that system, you'll just want to change it when they're back up, but I know a lot ...

8:27 AM
@SnoopyKid You need to know the momentum that is suddenly asked to be stopped, and also over how much time. If the load is moving, the force needed to prop it up will be a lot more than when it is just standing still. The bone will also flex when it is suddenly subjected to a load, and that flexing also matters. "suddenly appear" is just nowhere near good enough a question for there to be a solution at all.
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Why conserved quantities are important in physics? I know conserved quantities are those which do not change over time even the changes occurred in the system. Does it mean we can predict future? Or are there any other benefits of conserved quantities.
@qwerty It's unfortunate that they got attacked, but it's not a disaster.
Why is 1 important to arithmetic?
8:44 AM
because 1≠0
@123 Physics that can't predict things is pretty useless. And you can't predict things without some form of regularity.
also looking for something that stays constant helps make connections
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@PM2Ring Can you pls share few benefits and importance of conserved quantities?
@naturallyInconsistent 1 is an abstract idea in mathematics. But we can always relate this 1 to physical objects as a quantity. Also there are many benefits of having 1.
@123 im not asking. and your answer is not even anywhere near an answer
@think_meaning_builds you can definitely make a complete and coherent mathematical system with $0=1$; it is just that it is useless.
@123 Well, one of the most important examples is conservation of energy. Because we know energy is conserved, that helps us calculate how a system will behave, if we know what energy is entering & leaving the system. If we know that, and can calculate how potential energy changes with position, then we can easily find kinetic energy.
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8:55 AM
@PM2Ring : ) Thanks
@naturallyInconsistent In arithmetic we use 1 to utilize in mathematical operation. May be
look, how is anybody going to get something useful out of the answer that you are trying to give?
Do they actually know anything more after reading your answer than they already knew?
Emmy Noether realised that the law of conservation of energy is equivalent to saying that the laws of physics are invariant over time. If you do an experiment today, and do the same experiment tomorrow (under identical conditions), the result will be the same.
Conserve your energy for more practical questions :-)
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Thanks all of you.
Remember anyone can keep on asking "why?" forever.
9:06 AM
@think_meaning_builds that's the reason why I asked in the first place. There are always some people who keep thinking that they are making a lot of progress asking all the why questions, when in fact they are just moving around in circles and not understanding it.
It is not that there isn't a wise answer to those questions. They can be. But it is not asked and answered in the simple levels. It is only asked and answered as part of an incredibly deep inquiry.
@naturallyInconsistent It's also important to have strong foundations to build on. That can be difficult in self-learning. Interacting with a good teacher, and learning systematically is vital, especially in the early stages.
@PM2Ring Precisely! And this guy had been here for years and made absolutely no progress, and still going on these questions. ACM recently dug up a 3.5 year old question from the same guy on one single topic that clearly showed that "I understand" has no meaning.
@naturallyInconsistent I wouldn't say there's been no progress, but I do agree that the progress has been rather slow. Perhaps that's partly simply because of poorly developed physics intuition, but I get the impression that 123 never learned some of that vital core foundation stuff. And it's hard for us to see exactly what those gaps are.
@PM2Ring I am trained to consider two quantities that are within error bars of each other, to be essentially the same. There had been multiple suggestions of books over the many years; even an amateur reader ought to have progressed way past his position by now.
And he is a practising chemist. It is absolutely unacceptable
Also, it must be hard to teach yourself physics in a foreign language. I think 123 would make more progress if he did some more work on his skills in English.
9:19 AM
my personal impression that other the obvious language and culture/context barrier which I suspect is larger than many here are giving credit for
is that there is an element of not having enough exposure to asking questions with the correct vocabulary
@naturallyInconsistent No, he's a technician who works on equipment used in chemistry labs.
@qwerty I mildly disagree. For many of his questions, the rest of us put in the effort to rephrase them into a form that he would agree with, and yet there is no learning from the answers, nor the rephrasings. Which also aligns with the lack of learning from the phrasing in the good books that he said he read.
@PM2Ring He has a degree in it. Technician or not, he has had scientific training.
@PM2Ring This I fully agree.
I'm teaching students beyond the language barrier too. I know how to handle them, and how to get progress. It is just not happening with this one
Then you should know that patience is the most honorable trait of a good teacher, sir.
@think_meaning_builds After 3.5 years of having no progress? Do you have that kind of patience?
Only with myself.
9:30 AM
@naturallyInconsistent yes, I agree with the last part of that. which is partly why I decided not engage - the primary reason being the complete dissonance between both asking for help on the sort of issues he does and yet saying he's completely understood Newtonian mechanics. that being said, I think having the correct vocabulary might have helped eased a lot of the frustrations on everyone's parts
@think_meaning_builds Then don't you think it is a tad bit hypocritical to ask someone else to have that kind of patience when you yourself do not have it? Like, I'm already saying that I'm working with students across the language barrier. Those are underprivileged students. Not the worst, sure, but patience had already been demonstrated. It is a matter of knowing when to stop a futile attempt. Especially one that floods a public channel after 1000s of messages within a few hours, of interest to none else
@qwerty Oh, that definitely is the case; but after so many years and so little improvement in vocab, and only fixating on stuff like virtual displacement, that had already been pointed out to him before that such fixations are useless and totally skip-able, one's patience wears thin.
I'm just trying to put myself in someone else's shoes.
Is that so bad?
No, that is not bad. The issue is that the other side won't be putting themselves in your shoes. There is empathic behaviour, which should be encouraged, but then there is also indulgence, which is not.
This case has turned this chatroom into 12 angry men (2024).
i have just received a downvote...
and attempts to close my question as "opinion based"
9:37 AM
I think it's fine to just not engage. I think physics is for everyone, even if anyone else think they're going about it the wrong way - no need to actively comment that you think they won't progress in ten years or anything.
@think_meaning_builds yay that's great
this chat is strange
@RyderRude You've been told before not to accost other users for downvoting you. Stop it.
i know with certainty. My past three posts have received a single downvote. and no one is taking action
you can't know with certainty
2
9:44 AM
Give the system time to detect serial down voting, pal.
@RyderRude There is nothing to take action on. Users are free to downvote your posts. Stop complaining about it in this chat.
so much drama tonight :(
@think_meaning_builds not your fault!
9:49 AM
@think_meaning_builds also in agreement; definitely not your fault
in less contentious news, I'm currently writing the answer on uniqueness of Lagrangians for given e.o.m.s I promised @qwerty
yayyy!!!! :D
yayyy!
Anyway, im off to a buffet dinner miehehehehe
thanks ACM :) I hope it's been enjoyable writing/reading
there will be a birthday cake~
9:53 AM
@SineoftheTime In what way is it strange?
is it your birthday @naturallyInconsistent? ;)
no, but this month~
happy early birthday NI and enjoy the dinner
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10:15 AM
HBD NI
@PM2Ring I don't know man, every time I join there are people arguing :(
@SineoftheTime Oh. We often have very friendly discussions here in The h Bar. Sometimes there are arguments, but they never get too heated.
10:31 AM
@PM2Ring I like this chat, even if I'm rarely here
And this is kind of a special case. ACuriousMind is very patient, but even he has his limits. As a mod & room ownet he could simply ban user 123, but he hasn't done that. However, a few days ago he announced that he was no longer interested in answering 123's questions here because it seems like 123 is not benefitting from the countless chats he's had in this room.
Oct 5 at 9:37, by ACuriousMind
if you keep coming back here with the same questions and people keep telling you to read the same thing but apparently you retain none of it something is going wrong
Oct 7 at 11:40, by ACuriousMind
@123 I told you two days ago that I don't consider the way you're asking questions productive, as evidenced by your lack of progress to anything but basic Newtonian mechanics in four years. You are free to ignore my judgement, but you can't expect me to contribute any more answers to your questions if you do so.
@ACuriousMind great! I'll save it to read it carefully when I get the chance, I like it from a skim through.
I can understand why people are losing their patience with 123. OTOH, some of us don't want to totally discourage him. And nobody intends to hurt his feelings. So we were having a little discussion...
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@PM2Ring Pls don't tag my 2021 comment. Even sine of the time didn't joined this room at that year.
10:37 AM
I joined MathSE in 2022
@123 I'm only quoting recent comments.
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How can you say, i didn't learn anything new or no progress. I personally feel more confident and understanding NM.
I joined over 8 years ago. I don't post in this room every day, but I often read (or skim) the transcripts, so I have a fair idea of what goes on here.
I'm more present in the maths chatroom
1 hour ago, by PM 2Ring
@naturallyInconsistent I wouldn't say there's been no progress, but I do agree that the progress has been rather slow. Perhaps that's partly simply because of poorly developed physics intuition, but I get the impression that 123 never learned some of that vital core foundation stuff. And it's hard for us to see exactly what those gaps are.
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10:41 AM
Pls don't highlight me as a negative impression.
I am also user SE since 6 years. I am also serious in learning.
@123 I'm just trying to explain why people were arguing about you. I think you've made some progress. But I also understand why ACM has lost patience with you.
And as I said earlier, you would probably make faster progress in physics if you also did more work on your English.
Actually, your English is definitely better than it was a few years ago, but there is still room for improvement.
Feel free to come into the English Language & Usage chatroom and practice :-)

 English Language & Usage: Multi-Layer

Not for the faint of heart or those easily triggered by Englis...
10:56 AM
@think_meaning_builds You sure? EL&U is rather explicitly not for learners of English, that's why English Language Learners exists.
yes I am sure
the ELL room is a ghost town pal
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@PM2Ring : ) Yes i am trying hard and best. When i was not here. I always learn books
My problem is that i always try to understand underlying idea behind the topic. Not just read and accept that as a part of definition.
Why do you think you keep doing that?
123 you are able to figure that for yourself if you really read as widely as you claim
a big part of learning physics is learning how to figure things out for yourself, especially on the sorts of questions you ask
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It is always a tough task and mental effort to understand ideas behind every topic.
11:05 AM
yes but that is part of it
@123 I find the implication here that other people don't have the strange problems you're having because they don't try to understand the "underlying idea" insulting to all those physicists who have come to understand a lot of physics without being stuck on Newtonian mechanics for 5 years.
you seem to think you're special because you "want to understand" things; that's not special, except for the people posting blatant homework questions most of the people on this site are interested in deeper understanding
don't get me wrong: It's good to want to understand things, but don't act as if this is something that somehow makes you better than the other users here
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ACM i am learning LM since 4 years but this required to clear many questions. Also i am learning SR since many years.
There's nothing wrong with being stuck. You @123 have to learn to dig yourself out of the rabbit holes you've fallen into.
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ACM This was not my meaning. I have also learned physics in my school and in university. But didn't understand anything. Now i have time to understand the physics from books, internet and mentors like you.
@ACuriousMind No, i never have a thought like that. I am here just for learning.
@ACuriousMind I will say this may be in part cultural/socioeconomic; I know you mean for the site but consider rather that a lot of cultures place heavy emphasis on mainly rote learning even into university.
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11:14 AM
Now i have completed my education period. And i have a lot of time to fulfill my enthusiasm about physics. That's why i continue my journey with all users here. And i always try to learn.
Try to learn from your mistakes as well as your successes.
@qwerty Yes, it may make one special among the general population. It doesn't make one special among the kind of people who seek out this site and ask questions here, and the implication irks me.
It's making "I just want to understand more than everyone else" one's excuse for not having to re-evaluate one's dysfunctional learning habits
@think_meaning_builds your last two comments are wise words.
thnx pal :-)
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In my region every student learn every subject by rote. Even topper here just rote the topics without understanding. That's why i have a problem. We don't have good teachers here.
11:23 AM
These rote memorization "toppers" have been spoon fed, and they will, in the long run, remember nothing but the shape of the spoon.
that's a quote by E. M. Forster
worth remembering :-)
and perhaps worth attributing correctly if you're saying it almost verbatim, no?
as you wish
Edward Morgan Forster (1 January 1879 – 7 June 1970) was an English author. He is best known for his novels, particularly A Room with a View (1908), Howards End (1910) and A Passage to India (1924). He also wrote numerous short stories, essays, speeches and broadcasts, as well as a limited number of biographies and some pageant plays. He also co-authored the opera Billy Budd (1951). Many of his novels examine class differences and hypocrisy. His views as a humanist are at the heart of his work. Considered one of the most successful of the Edwardian era English novelists, he was nominated for the...
> he was nominated for the Nobel Prize in Literature in 22 separate years.[1][2]
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ACM Here student's only learn math and physics by just doing exercises and problems from pre written formulas, all other things are rote memorization. They just know how to computation from formulae.
11:38 AM
If you want to Understand mechanics try to read Mach
You'll find no end of nitpicking on classical mechanics
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Ernst Mach?
@123 Despite the education system in your country, some students manage to go beyond rote memorization, and become excellent scienists. But the pressure is huge, and only a small percentage reach the top.
@123 where are you from? If you don't mind sharing
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Pakistan
11:47 AM
:)
The Indian / Pakistani STEM education system is like a steep pyramid. The goal isn't actually to create a nation of scientists. For 1 scientist doing top research, there are maybe 10 science teachers, 100 engineers, and 1000 technicians.
@123 Have you visited the grave site of Abdus Salam, if you don't mind me asking?
Pyramid scheme
Salam was from an unpopular sect. He had a lot of detractors, and his gravestone was vandalised. :(
The government ordered the word "Muslim" removed from the gravestone.
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11:53 AM
@PM2Ring Yes you are right
> In 1964, Salam founded the International Centre for Theoretical Physics (ICTP), Trieste, in Italy
I had no idea
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@think_meaning_builds Nope. Never. I think he was in USA. Because he didn't studied here.
@Slereah Something like that. People put in the effort, in the hope that they'll ascend the pyramid to some extent, but the system only works if it only permits a few to get near the top & most people stay at the bottom, supporting all the weight.
@PM2Ring tbh science is like that the world over
Just do the honorable thing and move abroad to get a better job
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11:56 AM
@PM2Ring Yes this is the here. We as a nation don't accept people from sect which has serious issues.
@123 He was buried in Pakistan.
@qwerty Perhaps, but I think people's expectations in that regard are a bit more realistic in the Western world.
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@think_meaning_builds Ooh.. I don't have idea, even no one here discuss about him. Because of sect issues.
Right, and his work is not presented at schools.
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Yes...
11:59 AM
5 mins ago, by think_meaning_builds
The government ordered the word "Muslim" removed from the gravestone.
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Have you ever listen the name imran khan. The famous cricketer
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@think_meaning_builds I don't know about that
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I don't know the above comment is okay for this room.
@think_meaning_builds At which country you belong?
12:03 PM
Pakistan is a scary place. It can be dangerous if people think you're blasphemous. And it's worse now than what it was a few decades ago
> The epitaph on his tomb initially read "First Muslim Nobel Laureate". The Pakistani government removed "Muslim" and left only his name on the headstone.
Mohammad Abdus Salam (; pronounced [əbd̪ʊs səlaːm]; 29 January 1926 – 21 November 1996) was a Pakistani theoretical physicist. He shared the 1979 Nobel Prize in Physics with Sheldon Glashow and Steven Weinberg for his contribution to the electroweak unification theory. He was the first Pakistani and the first scientist from an Islamic country to receive a Nobel Prize and the second from an Islamic country to receive any Nobel Prize, after Anwar Sadat of Egypt. Salam was scientific advisor to the Ministry of Science and Technology in Pakistan from 1960 to 1974, a position from which he played a...
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@PM2Ring blasphemy is very very serious issue here. No one can blasphemy here about religion. Not even pakistan all muslim world are very serious about balsphemy about religion.
Otherwise Pakistan is very good place to live freely. Peoples are very nice here, they respect each other. Religion is serious topic in Muslim world.
No religion likes blasphemy. But there are variations in how people define it, who they class as blasphemers, and how they punish blasphemy.
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@think_meaning_builds Yes i know his contribution. When i was a student 10 years back, the previous physics books had his name. Now the books change , idk about new books
@PM2Ring It depends on the situation and type of blasphemy.
Does anyone know of a resource which treats condensed matter in more geometric/representation theoretic terms even?
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12:11 PM
Abdus Salam sect has serious blasphemy issues. Even in the Muslim world don't accept his as a Muslim. Their sect claimed they are muslims but muslim world rejects and separated them
@ACuriousMind btw, does this mean you concede that Harvey brown had a point about symmetries not "explaining" conservation laws?
@qwerty Discussing that in my answer explicitly would have been off-topic since the question wasn't about that, but I think it shows the topic is more complicated than either the "standard lore" that Brown disagrees with nor Brown himself realize
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@think_meaning_builds Ooh.. I didn't know that. May be he is in other city.
What is going on is this: There is a group $G$ of symmetries of the equations of motion, which, for any given Lagrangian $L$ has a subgroup $G_L$ of symmetries of the Lagrangian. This $G_L$ is, by Noether's theorem, associated with a number of symmetries equal to its dimension as a Lie group.
If there is an inequivalent admissible Lagrangian $L'$, then also $G_L \neq G_{L'}$ as subgroups of $G$, but I heavily suspect that $G_L\cong G_{L'}$ as Lie groups since their Lie algebras consist of the same conserved quantities.
Furthermore, the theorem by Morandi et al. says that $L$ and $L'$ are related by some $g\in G$, and so I also think we probably have $G_L = gG_{L'}g^{-1}$
that is, while the Noether symmetries $G_L$ and $G_{L'}$ are not the same (hence "depend on the choice of Lagrangian"), both the algebra of conserved quantities and the abstract Lie group of symmetries associated do not vary under a choice of Lagrangian; choosing different $L$ or $L'$ means choosing a different representation of the abstract group of symmetries on the space of $q$ and $\dot{q}$
and those different representations are always related by other, non-Noetherian symmetries of the equations of motion
12:21 PM
hang on, do you think this is appropriate for the main site? I think it's an interesting question so if you agree and want to copy an answer over I'll write a proper question tomorrow
@qwerty it might be, if you can formulate in a way that's less peer-review-y than "is Brown right?"
but also to write an actual answer along my lines above I'd want to look a bit more into whether this has been discussed as a follow-up to Morandi et al.
Is there a deep reason for the high frequency that the Laplace operator shows up
@ACuriousMind this is very interesting. the maths is just a smidge above my level (well it's what I'm trying to learn) and it's late here but I will I bookmark it for later
thanks for giving it your attention :)
12:42 PM
@ACuriousMind Yet another wonderful answer from knzhou. Most of the other answers on that page are great, too. But knzhou's really shines.
there's too much to learn and too little time
1:13 PM
One time I accidentally misread "Archimedes' screw" as "Archimedes stew"
And ever since I wonder
What would be in Archimedes' stew
I found some reference to an ancient cook of the same town, but alas his recipe book is lost
1:26 PM
@qwerty thank you
@123 thank you too
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: ) , have a party and remember us in your prayers. NI
2:04 PM
i can haz warm bedding yayyy
2:17 PM
In Griffiths "Introduction to QM", in the beginning it is said:
"Bell showed that it makes an observable difference if the particle had a precise(though unknown) position prior to the measurement".
Is this statement implying that in reality (whatever is meant with reality) the particle/quantum system has a definite position in space, but practically, because of our inability or call it whatever you want, we use probability to make claims about the location of it ?
I got a blackboard for my apartment >:D
it has been christened with its first words of physics
@imbAF no. It is trying to say that if the wavefunction was spread out as a wide wave, i.e. imprecise, then its behaviour is not the same thing as "precise positions actually, but human does not know".
What? I don't get it
the last part
@imbAF are you familiar with bell's inequality?
Look, Griffiths is saying that Bell showed that if the particle actually had a precise location somewhere, just that human does not know, i.e. classical probabilistic distribution due to ignorance, then it will have a different experimental outcome compared to a true quantum wave that is actually spread out, i.e. one that is quantum spread out, not just classical ignorance
2:28 PM
@SillyGoose I am not. But I doubt, and correct me if I am wrong, it has anything to do with his what-if scenario of knowing the precise position of a system, because he can't emulate that scenario
I dont like that way of putting things, though. We should just straight up be clear: Whatever uncertainty it is that we mean inside Heisenberg's uncertainty principle, it has nothing to do with "silly hoomans don't know" It is not ignorance. It is fundamental to Fourier analysis, and just a consequence of treating things as waves.
@imbAF griffiths is just stating (in a very strange way in my opinion) the fact that one (John Bell) can actually come up with a way to experimentally test if quantum mechanics is consistent with a local hidden variable theory.
but you should only start discussing this topic after you are familiar with quantum theory
I mean, it was in the first chapter or even page
heuristically, a local hidden variable theory assumes that states of a system always do have definite values of observables. Loophole free Bell tests (the work surrounding the 2022 nobel, i.e. good experimental tests of Bell inequalities) have suggested that quantum mechanics is inconsistent with being a local hidden variable theory.
2:31 PM
So I was wondering how was Bell able to prove such a thing, when in reality he only encounter one scenario, that of the system being spread as a wave
@SillyGoose So this theory, is valid only for the macro world, since qm is inconsistent with it ?
Or am I asking something stupid
Cuz this is out of my depth. But I am just wondering
@imbAF depends what you mean by this question. an active area of research is performing loophole free Bell tests for larger and larger systems.
Out of curiosity again, what's the general consensus regarding what's macro and micro world? Would the inconsistency of these local variables reveal where does one end and where the other starts?
@imbAF Well, that's unfortunate, but you should skip this for now. As long as you aren't familiar with quantum theory, you cannot vet the veracity of this statement. It will just confuse you. When you have the theory for it, you will understand the implications much easier.
Yeah, that's what I did
I way past that. Rn I am at the D.E
2:42 PM
yes griffiths begins the QM text with interpretations of QM XD
 
2 hours later…
4:38 PM
is there a name for differential equations which have multiple stationary states, but which stochastically transition between them?
@SillyGoose such as?
the example i was thinking of was when we have a spin-1/2 in a magnetic field. so i am wanting to know more about the abstracted situation where there is some "base differential equation $D$" which has certain steady state solutions. then we add an additional "transition term $T$" to get a diffeQ $D + T$ such that transitions between the steady states are observed in a tunable way by changing $T$.
so i guess deterministic transitions (not stochastic) are better to talk about
I mean that's just perturbation theory, no?
the $D$ is your base case, the $T$ is a perturbation
well the problem i am actually interested in is. observation: a toy model of particle decay is heuristically something like $\lvert p \rangle$ is the initial state and through some unitary evolution it turns into two identifiable states $\lvert d1 \rangle \otimes \lvert d2 \rangle$.
how can this idea be generalized to apply to non-particles (i.e. just arbitrary states)
in other words, given some evolution of a system, can you recognize transition patterns between certain types of states
4:54 PM
I mean that would just be something like $H_1 \otimes H_2 \otimes H_3$ where you start with a state in $H_1$ and the evolution turns it into a state in $H_2\otimes H_3$
I'm not sure what you're after here or what you mean by "recognize transition patterns"
5:05 PM
hm maybe ill try to specify my question more
5:42 PM
separately, what interested you all when you were learning physics in your undergraduate
 
2 hours later…
7:44 PM
(disclosure this is my own note, so there may be mistakes) I am trying to work out here a description of the bravais lattice business in terms of representation theoretic terms. I am wondering what sort of things break down in Lie theory once we go back to dealing with non-continuously parameterized groups (e.g. group of discrete translations).
@SillyGoose I don't understand the question: Lie theory is not possible at all for non-Lie groups - you have no Lie algebra.
i think i am confused. it seems like i can just write down a generator for discrete translations: $\hat{p}$ and that i still have access to an exponential map. Except instead of allowing $e^{-i \hat{p} x}$ for arbitrary $x \in \mathbb{R}$, we restrict to $e^{-i \hat{p} n \vec{a}}$ where $n \in \mathbb{Z}$.
8:01 PM
You can do that; effectively that works simply because you constructed it that way - the group of translations is a Lie group, and your discrete group here is a subgroup of that, so of course it has a presentation in terms of the generators of the full group with the coefficients of the generators restricted to some discrete subset of $\mathbb{R}^n$
but this is specific to you dealing with a subgroup of a Lie group, it's not some general thing that would work for arbitrary discrete groups
hm i see
@SillyGoose Also I don't understand what you hope to gain from talking about representations here: The situation is not that you start with some abstract discrete group and look for representations, the situation is that you have your space of state $L^2(\mathbb{R}^n)$ with the natural representation of the full translation group $\mathbb{R}^n$ on it, and an operator on $L^2(\mathbb{R}^n)$ is periodic if it is invariant under a discrete subgroup of translations.
There's no choice of representations or anything.
i see i think that makes sense
i am also wondering about something that seems strange. Let $H$ and $O$ be some operators. suppose $[H, nO] = 0$ for all $n \in \mathbb{Z}$. Seemingly, this implies that actually $[H, O] = 0$ in general.
So the statement that $H$ is invariant under discrete translations in direction $\vec{n}$ is the same as the statement that $H$ is invariant under arbitrary translations in direction $\vec{n}$. But I feel I am maybe misunderstanding
8:17 PM
@SillyGoose The statement that it is invariant under discrete translations is $[H,O^n] = 0$ for $O$ the translation by the primitive lattice vector, not $[H,nO] = 0$.
hm wait i am meaning to deal at the "algebra level" so looking at the generator $\vec{p} \cdot \vec{a}$
or are you saying that that is not a correct way to state the discrete translation invariance condition
I am saying that
hm i am not understanding what is going wrong in trying to make the statement at the algebra level
if the Hamiltonian is invariant under infinitesimal translations (i.e. the algebra) then it is invariant under all translations; that's the whole power of the correspondence between the Lie group and the Lie algebra
@SillyGoose there is no algebra
a discrete group does not have an algebra, the correspondence statements from Lie theory simply cannot apply
The correspondence between $[H,U(t)] = 0$ and $[H,T] = 0$ for $U(t) = \mathrm{e}^{\mathrm{i}Tt}$ relies crucially on $t$ being smooth and us being able to differentiate $[H,U(t)] = 0$ at $t=0$.
you do not have anything of the sort for discrete groups
 
1 hour later…
9:40 PM
hm I think I am confused because we are starting with a Lie algebra defined by $[x, p] = i$ and its Lie group. Okay on the Lie theory side we have $[H, p] = 0 \iff [H, (e^{ip})^t] = 0$ for all $t \in \mathbb{R}$. I don't see what is wrong with naively restricting this existing relation from this existing machinery to $t \in \mathbb{Z}$, which is a special case of the general result. I seem to be misunderstanding the starting point, perhaps.
@SillyGoose Counterpoint: I don't understand why you think you can restrict the r.h.s. to $t\in\mathbb{Z}$ and still have the $\iff$ hold
look at the proof of the $\Leftarrow$ and explain why you think it still holds if you restrict to $t\in\mathbb{Z}$.
hm I guess I see
10:20 PM
Gauge Fields, Knots and Gravity (Knots and Everything)
looks like a great book :P
the part about differential forms starts with the quote As a herald it's my duty to explain those forms of beauty
lol
@Claudio i've occasionally dipped into this book for about 9 years now and have yet to be able to read or comprehend most of it xD
I haven't read it but Baez is a good technical writer, the this week's finds series is still a great read
@ACuriousMind what I'm now thinking is: even if the groups of the two inequivalent Lagrangians are isomorphic to each other, so what? the fact remains that the symmetries are different...
i am reviewing some condensed matter content but i cant even find where the band index even comes from ?? so we did blochs theorem, which i think was fine. then we move to tight binding, and suddenly there are energy bands. conceptually what we did for tight binding is just enforce the idea that electrons are tightly bound to "their atom" and only suffer from nearest neighbor interactions. but somehow out of this calculation comes energy bands?
10:35 PM
@qwerty Why is it troubling that they are different?
what is actually the claim we're trying to investigate here?
It's not troubling; except for usually when we say x explains y. in a context like this, it would be a specific x explains a specific y. if it's the case that for a given y we see there's some x, i feel like i agree "correspondence" is more accurate/precise
10:52 PM
I mean...that's what Noether's theorem is: A correspondence
"explain" is not a relationship a theorem can establish :P
yes, well that was Brown's gripe :p
because textbooks frequently say "explain" - even in LL
I mean..."explain" is not a technical term
whether or not you think the correspondence established by Noether's theorem is an "explanation" strikes me as a pointless word game
as I said initially, I think the relevant aspect of what people mean by "explain" is that the relationship between symmetries and conserved quantities gives us a recipe to determine conserved quantities for Lagrangian systems without having to solve the equations of motion
and that's what we use conserved quantities most frequently for in classical mechanics: to reason about processes (like collisions) without actually having to solve the equations of motion
whether this means that symmetries "explain" conserved quantities strikes me as irrelevant in this context
@ACuriousMind maybe thats why he's in the dept of philosophy
@ACuriousMind yes: i think that's the helpful point here.
no, philosophy is not just word games (unless we mean in the sense of Wittgenstein, but that's not what I mean)
e.g. I frequently cite Norton's Causation as Folk Science as an example of good philosophy of physics, since it interrogates what we actually mean by "cause and effect" and whether this is reflected in the physical formalism
mhmmhm
11:01 PM
but it is true that philosophy is prone to this kind of word game, where people argue endlessly about whether or not an X is a Y without establishing definitions of X or Y that would make the discussion useful
at the top of my current physics to-do list is establish and understand definitions of the following: \begin{itemize}[label={--}]
\item Invariance
\item Covariance
\item Diffeomorphism
\begin{itemize}
\item Diffeomorphism Invariance
\end{itemize}
\item Gauge Transformation
\item Symmetry
\begin{itemize}
\item Global Symmetry
\begin{itemize}[label={--}]
\item Continuous
\item Discrete
\end{itemize}
\item Local Symmetry
\item Phenomenological Symmetry
\item Symmetry Group Principles
\begin{itemize}[label={--}]
I somehow made it through 5 lectures with these words thrown about without the definitions at the start
at least of all of them
oops, message was a bit long. sorry.
"diffeomorphism invariance" and "covariance" are some of the most misused words in physics, it's something of a running gag in this chat :P
yes, you mentioned last time I brought this up! but still, having something that's coherent and consistent for my purposes would be good. the other thing I can't stand is when physicists randomly say something is non-local and I know its different to what the mathematicians mean
but they don't define it, so...
the something usually being an equation
non-local has two common meanings: 1. Something that depends on more than one point, i.e. $f(x,y)$ instead of a "local" field $f(x)$. 2. Something non-causal in the context of relativity, e.g. an evolution equation for $f(x,t)$ that allows values of $f$ in space-like separated regions to influence each other
@qwerty Even a consistent version of these terms won't do you any good because plenty of resources will use them differently :P
What good is an internally consistent definition of "covariant" if no one else uses it that way?
I instead just prefer to avoid those terms as far as possible :P
@ACuriousMind that's ok: if I'm consistent and understand what I'm saying within my own notes, I should hopefully be able to navigate what everyone else means, right...??
11:12 PM
@qwerty sure, but why would you insist on using this horribly ambiguous terminology with yet another overloaded meaning instead of just avoiding it? :P
well, it seems unavoidable! how would you avoid it?
I've never found discussing whether something is "covariant" particularly relevant to the topic at hand; usually there are much clearer formulations of the specific property that is meant, like "is an element of the tangent space", "transforms in the ... representation", etc.
the only times I use the term "covariant" voluntarily is in fixed technical terms like "gauge covariant derivative" or "exterior covariant derivative" where what's relevant is understanding the phrase as a whole
ah. I suppose my hand-wavy understanding was always "transforms such that it has the same form"
so a generally covariant equation would mean something like under a general transformation, the equation looks the same
well, I don't like the notion of the "form" of an equation, either
but that was just an impression, not something strict
oh? what would you say?
11:17 PM
usually there is a much clearer mathematical formulation of these concepts in terms of a mathematical object simply being invariant
ooo.
please go on?
for instance, the Morandi et al. paper I cited in my recent answer doesn't define symmetries of the equations of motion in terms of "preserving their form" or any similarly vague notion, it translates the equations of motion into a vector field on the tangent bundle and then a symmetry is any other vector field that Lie-commutes with the field for the equation
(and Lie-commuting of two vector fields means that one vector field is invariant under the flow of the other)
what the correct formulation in terms of proper mathematical objects is depends on the context (e.g. transformations that "preserve the form of Hamilton's equations" are properly symplectomorphisms, leaving the symplectic form of phase space invariant) - that's the problem with these phrases, the exact technical content isn't always the same
how would you describe my blurry notion of "general covariance" in the context of GR?
I would describe that as a horrible can of worms
that's not very mathematical! ;P
11:23 PM
I've grappled with the nature of GR for years; my most recent understanding of the issue is here and it is not very accessible, I fear
see this earlier answer for a rant on why phrases like "diffeomorphism invariant" or "generally covariant" are not helpful
@ACuriousMind ;_; yeah i'm going to need that translated to even understand the basic gist
even your earlier answer is also a bit above me
well, that's exactly the problem: Physicists throw these vague phrases around and act as if they're perfectly clear, and actually you need years of work to unravel what they actually mean in any consistent or rigorous fashion :P
I was hoping it was like infinitesimals. you can use them perfectly safely without needing a rigorous definition
in the pure mathematician sense
In my opinion, the problem is mostly that physicists don't separate differential geometry in general from the physics of GR as a theory of gravity in particular - instead everything gets lumped together, and the difference between physics as not depending on coordinates and GR specifically being "diffeomorphism invariant" or "generally covariant" becomes deeply unclear.
This can extend to other realms, see also this answer of mine about coordinate invariance vs. Noether's theorem
@ACuriousMind i recall
the right of passage of hbar is to ask acm about diffeomorphism invariance
so someone should collect this data and send it to all the writers of these texts
students are really collectively not getting the memo xD
11:42 PM
I must've done something really bad in a past life to be cursed to debate diffeomorphism invariance for all eternity :P
11:52 PM
sorry for being so predictable lol

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