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Anonymous
1:00 PM
@ACuriousMind Physicists do not have time to solve UG level / competitive problems...that is the problem we face at Physics Se
 
Anonymous
No...there won't be any drainage
 
SE will not launch a new site where the group of experts is entirely a subset of an already existing site
 
@ACuriousMind, wait, I'm confused. There are two math sites. There are multiple sites who might say their expert is programmers. There are two sites that include astronomy in the scope.
 
(Again, the math.SE/MO split is very special and exists for convoluted historical reasons)
 
Anonymous
@ACuriousMind Do you know that most users of Math Overflow also have a Math SE account? Users overlap but aims dont
 
Anonymous
1:02 PM
@ACuriousMind This is a special case too
 
Anonymous
@ACuriousMind there are atleast 5 programming sites on SE
 
@heather math.SE/MO is historical, and MO wasn't launched by SE itself. The multiple programmers sites (I assume you mean the trilogy sites SO,SU,SF and Software Engineering are there because each of them has almost overwhelmingly large traffic. Trying to funnel all those questions through a single site would be disaster
 
Anonymous
All the users overlap with Stack overflow
 
Anonymous
@ACuriousMind what about the 5 programming sites
 
Anonymous
they all overlap in user base
 
Anonymous
1:03 PM
but the aims differ
 
Software Engineering (former programmers) has fought for years against being the site where "questions off-topic at SO" go to die live a happy life
@S007 What "five programming sites"?
I just discussed the trilogy and SoftEng
 
@ACuriousMind, there's still the astronomy overlap. User base overlap is all over the place.
And yes, I know you said there was fighting against astronomy, but it got passed.
 
Anonymous
computer science, theoretical computer science, computational science all overlap
 
Anonymous
with SO
 
Anonymous
but still they are different
 
Anonymous
1:05 PM
@ACuriousMind
 
yes, there is another user base overlap.
 
@heather A bit of overlap is fine. astronomy.SE successfully argued that the typical astronomer has a different workflow and different needs from the typical physicist, that is, most astronomers actually care very little about other physics, and most physicists don't have the slightest clue about astronomy
 
@ACuriousMind, I might also point out that there are multiple sites with Christianity as their main focus.
 
Anonymous
@ACuriousMind Similarly professional physicists do not care about UG level problem solving...that's the problem...do you get it ? Students and teachers at that level are more concerned about problem solving
 
I would just have to say that while there is a bit of user overlap in this case, the difference is enough to make it its own site.
 
1:07 PM
@S007 No, they don't. SO is about programming. cs.SE is about the academical field of computer science, tcs.SE is about the academic field of theoretical computer science, which is often closer to math than to computer science, and computational science is about numerical methods in all the sciences.
 
Anonymous
@ACuriousMind I am talking about the user base...the users overlap
 
data science and computational science have a bit of overlap too
 
Anonymous
but the aims are different
 
Anonymous
there is nothing like drain of users
 
Anonymous
we are giving more choice
 
1:08 PM
@S007 Not the "aims". The scope is different, they are about different topics
 
right
 
Anonymous
@ACuriousMind yep
 
"Physics exercises" is not a topic, it's a specific kind of question about physics.
That's the problem right there: Your topic is a full subset of the topic of physics.SE
 
Anonymous
Physics Problem Solving is a topic...like Brilliant.org is completely dedicated to problem solving
 
@ACuriousMind, our scope is different than physics.SE's scope. yes, we might have user base overlap but I don't think that prevents it from being a site. Then, I'd say that physics problem solving is definitely a topic - how to solve various problems in physics!
 
Anonymous
1:10 PM
Brilliant.org doesn't answer theoretical questions
 
Anonymous
but they excel in problem solving
 
Anonymous
that is the type of site we aim at
 
Anonymous
just our model is different
 
Anonymous
but our scope is same as brilliant.org
 
Anonymous
have a look at the site
 
Anonymous
1:11 PM
yes..just now
 
@ACuriousMind, the connection between physics and physics problem solving in my mind would be like the connection between computer science and theoretical computer science - more conceptual stuff is sent to physics and practical problems, involving calculations and how to solve problems, is sent to physics problem solving.
 
@heather So far, the distinction between physics.SE and your proposal is the kind of question allowed, but not the topic of the question. The topics of your questions would be classical mechanics, electrodynamics, quantum mechanics, etc., all of which are on-topic at physics.SE.
 
@ACuriousMind, the kind of question is just as important as the topic in difference, I think. My analogy with computer science and theoretical computer science would apply here, I believe.
@S007, did you email Robert?
 
Anonymous
yes i did
 
Anonymous
just now
 
1:13 PM
@ACuriousMind We knew the HUP stems from the noncommutativity of observables, but other than the scaling property of fourier transform (which result in the fourier transform of a narrow function to be spread out int fourier space), is there a more fundamental (math) reason why some noncommuting continuous observables (such as x vs p) are related by a fourier transform?
 
Anonymous
hope he replies
 
@S007, yes, I hope so as well
 
@heather Again, you need to look at the scope of the sites you're citing. tcs.SE is explicitly research level in its scope, so all undergraduate topics should, in prinicple, go to cs.SE. physics.SE has no such restriction (undergraduate level questions are perfectly fine).
 
@Secret Cauchy-Schwarz inequality
 
@ACuriousMind, our scope is explicitly problems!
 
Anonymous
1:14 PM
@ACuriousMind we are talking about different types of questions..and not topics ....see my example of brilliant.org
 
Anonymous
Brilliant.org doesn't answer theoretical questions
but they excel in problem solving
that is the type of site we aim at
just our model is different
but our scope is same as brilliant.org
have a look at the site
 
@Secret For x and p, it's Stone-von Neumann: x and p are basically multiplication and differentiation, and the Fourier transform does relate differentation and multplication with each other.
 
I see
 
@heather Okay, we have a word problem here: "Scope" means "range of topics the site will cover". A topic is, well, a subfield one can know something about (network architecture, physics, classical mechanics, linguistics, etc.). Within its scope, each site then typically disallows certain kinds of questions (recommendations, "What is best?"-type questions, homework questions).
But this latter process is something that happens after the site has been launched, this is what all the meta discussions on a new beta sites will typically revolve around.
In particular, SE does not consider these policies fixed, that is, part of the site's scope.
 
@ACuriousMind Umm. If you try to do HUP with Fourier transforms you run into problems with integrating by parts. Have you figured out a way around this?
 
1:19 PM
Why is it stated on my book that reflection and refraction are properties of waves while diffraction and interference are unique properties of waves?
 
In the case of MO and math.SE, or tcs.SE and cs.SE, tcs and MO are not different by "not allowing exercise questions", but by their scope being research-level mathematics/computer science in contrast to undergraduate level mathematics/computer science
@0celo7 I don't know what you mean. Showing the HUP for Gaussians is a perfectly standard exercise (also in signal processing etc.)
 
@DHMO I think you can explain reflection and refraction with a corpuscular theory of light
 
@ACuriousMind, why can the difference between physics and physics problem solving not be allowing exercises vs not? That seems like a rather dramatic difference, especially knowing the physics.SE attitude towards homework questions.
 
(but there's something that dispersion would be the other way around in this case? Vague memories)
 
@AndrasDeak what about diffraction and interference?
 
1:21 PM
@ACuriousMind Yes, and I did it in high school. But in general, you're not gonna make it work
 
@DHMO most certainly not:)
 
The real magic is just Cauchy-Schwarz.
 
@AndrasDeak light can't choose when to behave as a wave and when to behave as a particle right
I am told that they are both at every time
 
@DHMO light doesn't choose
the particle-wave duality in my opinion is about humans' weak grasp on reality
 
then what are the particles doing in diffraction?
 
1:22 PM
@DHMO what are the waves doing in absorption photoemission?
 
@AndrasDeak no idea
 
yup
 
???
 
My current favorite interpretation being a type of $\psi$-ontic and that quantum objects are linear neither particle nor wave objects
 
@S007, I just noticed this post.
 
1:24 PM
my point is that light is light, and depending on how you look at it it can behave as something that resembles stones that you can throw, or something that is like ripples on a pond (just to stick with notions we picked up during evolution)
 
alright
 
my rule of thumb is "light tends to propagate as waves and it tends to interact as particles", but I'm absolutely sure that the regulars here can give a much better and more complete description of the problem
there's also extensive literature on the subject that I'm unfamiliar with
I just find it hard to shut up, is all:)
 
http://chat.stackexchange.com/transcript/message/33198558#33198558
the same idea that a time dependent metric is just proper distance changing without anything physically stretching nor moving apart at all
 
@Secret okay?
 
@Secret now what is a proper distance?
 
1:27 PM
Btw, In experimental settings, I generally treat light as wavelike, until it start interacting like billard balls
@DHMO spacelike separation between two events as measured by an observer in their rest frame, or the separation between two comoving events, if I recall
 
@Secret alright
 
Most of the time, light interact like a wave when alone, unlike electrons
which is more fuzzy
 
"most of the time" $^{[\text{citation needed}]}$
 
But otherwise, I have not learn enough QED to said anything more about how light is described as a quantum object
 
1:43 PM
wth was that
 
:D
I'd say paranormal activity, but this is not that kind of room
 
no, I had a message typed into the chat box when I opened my laptop o.o
 
@EmilioPisanty, what site did you use to create your community adds?
 
@EmilioPisanty I wanted to tell you something apparently
 
@0celo7 which was?
 
1:44 PM
@0celo7 that sometimes happens to me, but my previous message stays in the editbox...
 
No clue!
 
not the case now, apparently
 
@heather what do you mean?
 
@EmilioPisanty, how did you create the community ads? I assume you didn't draw them and upload them ;)
 
@heather well, there's a lot of them
 
1:45 PM
@EmilioPisanty, what tools did you use to make them?
 
just about all of this year's crop was done on Inkscape
 
Inkscape...okay
 
see the comments below each ad for more info
where there's an inkscape source it's linked to in a comment
 
okay, thank you
 
@ACuriousMind Crap!
It ended up next to Sachs and Wu again :(
 
1:47 PM
Hawking Ellis...=)
 
the real GR book
@heather you've decided on this one, right?
 
@0celo7, indeed
And I'm hoping I get all the books on my list =P
 
My copy is well-worn
 
The name of A. Zee reminds me of the book by Alpher, Bethe and Gamow...
 
I should try to reread it one of these days, but 900 pages is a bit daunting
 
1:51 PM
(or was it just a paper?)
 
@AndrasDeak, just a paper
 
thanks
makes more sense that way, but when I heard about it long ago, it seemed to be a book:)
 
@heather so when are we reading Zee?
 
@0celo7, hmm, I don't know. Depends on whether or not I get it. If I don't, I do have an Amazon gift card, I think, so I might get it with that.
 
you need calc 3 first
 
2:00 PM
@0celo7, will Apostol I and II prepare me appropriately?
 
I don't know calculus books
 
I believe II is multivariable calculus
 
@JohnRennie Hi
 
@0celo7 Afternoon/morning
 
@JohnRennie, our proposal got closed as a duplicate. S007 emailed Robert.
 
2:06 PM
@JohnRennie It's 10
I should probably get some food...
Hopelessly stuck on analysis homework
 
what kind of analysis?
 
Functional, but not really functional
$$\left|\inf_{\delta>0}\sup_{y,z\in I_\delta(x)}{|f(y)-f(z)|}-\inf_{\eta>0}\sup_{w,v\in I_\eta(x)}{|g(w)-g(v)|}\right|.$$
I need that $\le 2\epsilon$ if $||f-g||\le\epsilon$ (sup norm)
 
okay:D thanks:)
OK, took me a while, but at least I parsed the question
 
Anonymous
@heather can you send a mail too ?
 
Anonymous
I still didnt get a reply
 
Anonymous
2:21 PM
I think some more people need to mail Robert
 
@S007, sure, yeah. One moment
 
Anonymous
rcartaino@stackexchange.com
 
Isn't that harrassment?
are you sure that's called-for?
 
Anonymous
Why? Robert just closed it without any good reason
 
Anonymous
Not expected from a Stack Exchange moderator
 
2:24 PM
@S007 that could probably be argued. But you're right that it should be discussed. And I'm sure he will respond in a timely manner. I suspect that additional e-mails won't speed up the process, but piss him off (and he'd be right)
 
Anonymous
No. I think if just one person mails him he might not take it seriously. We need to explain that why is the new site different
 
Many would argue that already one e-mail outside the network channels is inappropriate.
[citation needed]
 
@AndrasDeak, please believe me when I say I wrote it as politely as I could. "If you don't mind, I like to understand further why it was closed, so I can help to fix the proposal." was one line. I just want to establish that I'm not some crank.
 
Anonymous
that is his network email only
 
You're all free to do as you wish, I'm just urging caution based on my extensive experience with Stack Overflow:)
 
Anonymous
2:26 PM
:/
 
@AndrasDeak, I understand, and I have to thank you for your advice. =)
 
I'm explicitly unaware of the customs on other SE sites.
 
Hey, does anyone know the name of the font used on Area 51?
 
which part?
inspector says "arial" and "impact" so far
 
the fonts like in this
 
Anonymous
2:31 PM
I changed the site description to "Proposed Q&A site for problem solving techniques in Physics at the High School,Undergraduate or Graduate level."
 
Anonymous
Does that seem right?
 
@S007, add something in there about physics enthusiasts
otherwise, yes, I think that's a good move
 
Anonymous
I think the word "level" does the job... we are not concerned with who is posting the question
 
Yeah, that's true. Okay, that makes sense, and it is clearer now what the purpose of the site is, I think.
@S007, you know, I wonder if Robert misunderstood the purpose of the site. Because it could've just seemed like an exact copy of physics to him.
 
Anonymous
@heather Maybe, I hope he sees our email !
 
2:34 PM
@S007, he will. He's busy, it takes time.
I bet you tomorrow we'll have a response for sure.
 
Anonymous
Alright...thanks for so much effort you took! I hope our effort doesn't go in vain :-) Cya
 
Yep, see you around
 
bye
 
2:52 PM
If light is an EM wave then why isn't it affected by E-field and M-field (b-field)?
 
Why would it be?
Maxwell's equations are linear, so as long as those hold, you can superimpose EM fields without them knowing about each other.
 
@AndrasDeak I am a layman
 
then that's why -------------------------------------^ ;)
 
Could you phrase it so that I understand?
 
if field (E1,B1) solves Maxwell's equations (so it's physical), and (E2,B2) solves it, then (E1+E2,B1+B2) solves it
 
2:54 PM
that's very layman...
 
i.e. you can cross rays of light and they will pass through each other, they can't interact
side note: I don't think light sabers could work in any reasonable universe:P
 
What does it mean that light is oscillation in E-field and b-field?
 
Exactly that. That there are solutions to Maxwell's equations that are propagating waves made up of both E and B fields propagating together. As it happens, light is an example of such waves
so are radio waves and X-rays
 
can you not mention Maxwell's equations?
 
not really:D
 
2:57 PM
what does E field mean?
 
haha, yes
 
??
 
I hope the regulars can point you to some basic reading on electromagnetism:) I'm not familiar with sources for laymen. I also have to go to try and break my laptop, so see you later
 
how does any change of E-field matter if there is no charge?
 
@DHMO static (constant-in-time) E fields only affect charges, but time-dependent E fields are related to B fields and vice versa. That's exactly what Maxwell's equations are about.
 
3:00 PM
@AndrasDeak how does any change of B field matter if there is no charge?
 
@DHMO see the above -----------------------------------------------------------------^
 
I mean, how does light affect anything at all?
 
@DHMO that's a pretty rough question:)
generally, you see it interacting with electrons in various forms of matter
 
oh, so you do need a charge
 
@DHMO to detect it, yes. For light to exist, no
 
3:01 PM
@AndrasDeak sure
 
most of the universe is full of EM radiation, and no charge
 
now, when a magnetic field is induced, and a light passes through that field, what happens?
 
anyway, gotta go right now, good luck
9 mins ago, by Andras Deak
Maxwell's equations are linear, so as long as those hold, you can superimpose EM fields without them knowing about each other.
 
but wouldn't the superimposed fields look like the light shifted?
 
3:04 PM
what would it look like?
 
bye
 
3:32 PM
@DHMO normally, nothing should happen - the light passes through the area and in that area, there is a magnetic field
 
@S007, tell me what you think of this "first draft" of the community ad:
oh, wait, that should be 4 followers...whoops.
 
3:52 PM
@Sanya but what would the superimposed field look like?
 
@DHMO what do you mean?
 
@Sanya when the B-field superimposes with the B-field of the light
 
you take the magnetic field $\vec{B}$ and you add the light field $\vec{B}_{light}$
and this sum is the total field
 
uh, sure, but what would it look like?
 
@Sanya uh, proof? Why isn't there an interaction term
 
4:02 PM
@0celo7 proof -> Maxwell equations
why should there be an interaction term?
@DHMO I confess that I do not understand your question
 
two superimposed fields:
 
@Sanya proof of those?
 
Anonymous
@heather Please take part in the commenting with robert
 
Anonymous
@heather Will "mathematical physics" be a better name ?
 
Anonymous
I like the ad btw
 
4:16 PM
@0celo7 those are axiomatic
@DHMO I'm not going to draw you field lines, if that's what you mean :o
 
@Sanya alright
 
4:30 PM
http://chat.stackexchange.com/transcript/message/33200143#33200143
Actually, I might need to check whether this is a good way to motivate the lorentz force, cause the only place I found this pics is some random website that does physics assignments
 
user228700
@DHMO: \o
 
@Kaumudi hi
 
4:47 PM
When light enters a new medium, some of it is refracted and some of it is reflected
is it probabilistic?
 
Anonymous
5:00 PM
@heather I think Robert isn't gonna listen. Maybe we have to wait until Physics SE changes some of its policies. Anyway I respect his opinion.
 
5:12 PM
@S007, I don't know about mathematical physics - I'd keep it the way it is. I will comment now, I had to go do some stuff.
 
5:37 PM
What's up, everybody?
 
@DanielSank What should I do math-wise
 
@0celo7 Too broad
 
@DanielSank Should I learn about covering spaces and then read Wolf, or learn about Lp spaces and then read Li?
 
what maths have you done so far (list)?
 
don't you know both of those
 
5:43 PM
@0celo7 I don't know.
 
@MikeMiller Somewhat
@Secret addition, subtraction, multiplication, division
counting I guess
 
shouldn't be just that, given your diverse GR background.
 
@MikeMiller I should just work through Wolf. But he said "by a standard connectivity argument" in some covering space proof and I had no clue what he meant
So I figured I'd review covering spaces
 
But anyway, if you really have a lot of free time, (for the algebraic side) some group theory is a good thing, (for the analysis side) topology and Lp spaces
 
I don't know any topology, seems scary
 
5:46 PM
I can count to 10. Just learned it today.
 
don't do it here!
there are children
 
@Ocelo7 What ? You are learning about covering spaces ?
 
Munkres should be a good starting point. Munkres also beef you up enough in PHD set theory
 
@0celo7 He's presumably showing that some set is both open and closed and nonempty.
 
also covering space is a topological notion
 
5:47 PM
@MikeMiller Agreed, I'll take another look at it
 
It is very helpful though, e.g. it helps you to understand why spin behave the way it behaves
 
I think he was showing that a function is continuous on a clopen set that contained the basepoint or something
 
what was the theorem
 
Covering Homotopy.
 
I don't know what you mean. That there exists a lift of every homotopy of functions given that the original function has a lift?
 
5:50 PM
Yeah
I think it's called Covering Homotopy Thm in Hatcher
 
I don't know the names, just what they do. Your proposed proof sounds fine.
 
@S007 That question we discussed yesterday... is there an error in the part computing the distance between the ring elements?
 
@KyleKanos, I understand what you are trying to say. But then how would you suggest I ask the above question in this forum... This is the only forum that answers physics doubts to my knowledge (I am a high school student... and I believe you can see that from my question)... you may edit the question to your likings (no objections) but at least keep the material of the question similar.... also could you give me an answer to the above in comments??? — Abhishek Bakshi Apr 9 at 14:05
[Rant]=this is not a forum FFS
 
Lol, PSE forum confirmed
 
(NB crazy emotion because a few minutes ago that crazy annoying EM friend of mine have almost caused an unrelated user on a fb goup to think I am a sockpuppet of his due to his constant pings AND the pings in the wrong order)
 
6:07 PM
1,2,3,4,5,6,7,8,9,10,11
I make progress....
 
try count to $\omega_1$ >: D
 
Please. I counted to $\aleph_1$ while bored one day
 
No set theory, please
 
Actually, you cannot count to $\omega_1$, in fact, it is not mathematically allowed, lol
 
@Ocelo7 By the way, you seem to evade my question why your blog is called "Einstein and the Evidence". What does this "evidence" stand for ?
 
6:14 PM
Sorry, I cannot tell you.
There's some bad history there
It's not a topic we wish to bring up in here again
 
Oh come on...
 
No, it is too painful
 
......
It's okay.
 
that is all I will say
 
Well, everyone knows that he's an.....
 
6:23 PM
A very nice guy, yes
 
7:09 PM
0
Q: Is this what we intended for a resource recommendation?

tpg2114Let's ignore all the other things that I find wrong with this question for the moment: Is there a tool online that lets me convert acceleration-time graphs into velocity-time and position-time graphs? I was surprised to see the resource-recommendation appear on it, given that it's more of a sof...

 
Hi, everybody.
 
hey
 
@DanielSank, hello!
 
 
2 hours later…
9:16 PM
@S007, what do you think we should do to get the proposal reopened?
 
user218912
what are you doing?
 
@obe, see this proposal
worthy of reopening
 
user218912
I don't think so.
 
user218912
stackexchange isn't a homework help site, and that's what problem solving basically is.
 
user218912
and you can just ask it on physics se.
 
9:23 PM
@obe and get it closed
 
user218912
xD
 
and math SE is just problem solving
so the argument that SE doesn't work like that is bogus
the only thing I see is the closing moderator being ignorant of physics SE
 
thank you, @Sanya, my frustrations exactly
besides, @obe, it isn't a homework help site per se, it is more of a way for students and enthusiasts to get assistance with problems and how to solve them. We would expect work to be shown.
 
user218912
but like
 
user218912
you can just modify physics se to accept homework-like questions.
 
user218912
9:25 PM
no need for a new site
 
@obe will never happen; should not happen
 
user218912
why?
 
because it scares big parts of the community away and there will be an influx of questions that are not interesting for the audience
by the way, math has two SEs too
so ....
 
user218912
oh yeah I forgot about that
 
user218912
hmmm
 
9:28 PM
I don't see why math gets that but physics not
 
user218912
so how about we re-open theoretical physics se.
 
user218912
and take homework questions here
 
especially if the request comes overwhelmingly from the community
 
@obe, erm...theoretical physics would be like the worst place for homework
 
well, theoretical physics is not what physics SE is only about
at least in theory
 
user218912
9:29 PM
@heather I said in physics se.
 
but in general, why reactivating an old SE, migrating all the users to that one and then using an existing one
when you could just open a new one
 
user218912
that's not what I meant
 
then what do you mean?
 
user218912
re-open it as in make a new one based off the same logic as the one that got closed.
 
user218912
so physics se for higher level physics.
 
9:39 PM
yeah well, that's the intention already
isn't it?
 
user218912
I thought you wanted to create a physics homework se
 
yeah
 
rob
Hello, all.
 
well, homework ... maybe we shouldn't call it like that
maybe "physics for non-research level"
 
rob
I'm confused about the goal of the proposed "physics problem-solving" site. Would anyone help me clarify?
 
9:45 PM
@rob to me it would be a place where we could move all questions that at the moment get closed as homework
 
rob
@Sanya all of them?
 
@rob well ... all of them, I don't say they would all be allowed there
 
I assume the network-wide norm of "don't migrate crap" would apply;)
 
but that would have to be a community-driven policy-finding process
@AndrasDeak then why do the mathematicians always migrate crap here ... :|
 
you should ask them... why don't you have a version of this for users of math.SE?
maybe that would help
or is it on-topic crap?
 
9:48 PM
@AndrasDeak I was joking ;) there are crap questions that get migrated, but it's a rather small extent
 
Ah, I wouldn't know:)
 
but if it becomes overwhelming, that would be a very good idea :)
sorry
 
and mathematicians not giving a crap would fit in well with my picture of mathematicians:D
 
rob
Are there examples of questions that have been closed here that would be a good fit for the "problem-solving" site?
 
@rob hmm, those would also help a lot in pinning down the scope of the new site, great point
 
9:52 PM
@rob I think there are some linked in the area 51 proposal, but I can't provide you with any myself (as I am not officially a head behind that new site thing)
@AndrasDeak actually, most of them are very kind and caring people I have found
 
@Sanya if you have nice shoes
and I mean this :D
 
@AndrasDeak O_O"
XD
 
10:16 PM
Is the site's logo supposed to look like a paper ship?
 
10:57 PM
@AndrasDeak It's a Mexican hat.
Spontaneous symmetry breaking is a mode of realization of symmetry breaking in a physical system, where the underlying laws are invariant under a symmetry transformation, but the system as a whole changes under such transformations, in contrast to explicit symmetry breaking. It is a spontaneous process by which a system in a symmetrical state ends up in an asymmetrical state. It thus describes systems where the equations of motion or the Lagrangian obey certain symmetries, but the lowest-energy solutions do not exhibit that symmetry. Consider a symmetrical upward dome with a trough circling the...
 

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