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user116211
08:00
For it to be exact, we must have $$\frac{\partial B_1}{\partial q_2}= \frac{\partial B_2}{\partial q_1}\,.$$
Anyway, I would respond with this: if people are in favor of your proposal, why isn't it a highly voted answer to the Generalizing the homework policy post?
user116211
He then writes:
@DavidZ Ho boy. Because at the time that post appeared it was too complex for me to wrap my head around it, and now I doubt if anyone would read a new answer.
user116211
> The relation has to be reinterpreted in view of the fact that the coefficients $B_1$ and $B_2$ may depend implicitly on $q_3\,.$ We thus replace $(16.5)$ by $$\frac{\partial B_1}{\partial q_2} +\frac{\partial B_1}{\partial q_3}\cdot \frac{\partial q_3}{\partial q_2} = \frac{\partial B_2}{\partial q_1} +\frac{\partial B_2}{\partial q_3}\cdot \frac{\partial q_3}{\partial q_1}; \tag{16.6}$$
user116211
> the quantities $\partial q_3/\partial q_1$ and $\partial q_3/\partial q_2$ are given by $(16.4),$ and we get: $$\frac{\partial B_1}{\partial q_2} +\frac{\partial B_1}{\partial q_3}\cdot B_2 = \frac{\partial B_2}{\partial q_1} +\frac{\partial B_2}{\partial q_3}\cdot B_1. \tag{16.7}$$
user116211
08:03
I didn't get $(16.7)$.
@DanielSank and then there was also this one
@DavidZ Let me restate that. The meta post you just linked asks a lot of questions that I have no interest in trying to answer, because I don't even understand what the questions mean.
user116211
To get $\partial q_3/\partial q_1$ and $\partial q_3/\partial q_2$ $(16.4)$ was used which means \begin{align}\frac{\partial q_3}{\partial q_1} &= B_1 + B_2~\frac{\partial q_2}{\partial q_1}\\ \frac{\partial q_3}{\partial q_2} &= B_2 + B_1~\frac{\partial q_1}{\partial q_2}\,.\end{align}
@DavidZ ...and that one was waaaaaaay over my head.
I understand what that second meta post is asking even less than the first.
@DanielSank even with the abstract and important note? Because you can skip the rest of it
user116211
08:05
So, putting the values in $(16.5),$ we rather get $$\frac{\partial B_1}{\partial q_2} +\frac{\partial B_1}{\partial q_3}\cdot B_2 + \underbrace{B_1\cdot \frac{\partial B_1}{\partial q_3}\cdot \frac{\partial q_1}{\partial q_2}}_? = \frac{\partial B_2}{\partial q_1} +\frac{\partial B_2}{\partial q_3}\cdot B_1 + \underbrace{B_2\cdot \frac{\partial B_2}{\partial q_3}\cdot \frac{\partial q_2}{\partial q_1}}_?.$$
Well, the important note is orthogonal to the rest of the post (I think).
@DanielSank yeah, that was just supposed to be a clarification
user116211
Where are those extra terms? How did they disappear?
user116211
Hmm.
user116211
I don't think they turn to be zero ;/
user116211
08:07
As the author himself earlier wrote:
user116211
> If there is a finite relation between the variables $q_1,~ q_2, ~q_3$ on account of the given condition...
@DavidZ Anyway, to answer your question, I didn't respond to those meta posts because I didn't understand what they're asking. The argument given in my meta post about renaming the homework policy does not answer the questions posed in your meta posts.
This is a bit of a pattern: I want to just fix the close reason and help center to make them less wrong. You want to identify the principles by which we decide how to fix the close reason.
This is similar to the difference between of prescriptivist and descriptivist linguistics.
You want to have principles, and from them derive the written policy. I want to just write the policy.
user128101
@JohnRennie, I am baffled, is a free neutron a concrete object or not, and when it decays are a proton and an electron concrete massive objects or not? How is the electron created if not by a pair prodiction? as I said before a link will do, I do not want to waste more of your time.
@DanielSank Sure it would. I.e. "...what are better ways to characterize our actual reasons for closing questions where we currently use the 'homework-like' close reason?" (my question) -> "Calculation requests and requests to have your work checked" (your answer)
I don't think I can articulate why I feel this way. It's not a manifestation of a deeply held world view or philosophy. I just think that in this case my way is more effective (i.e. possible).
user128101
08:11
@JohnRennie, since I have the honour of chatting with you, can you explain your sarcastic comment here ( physics.stackexchange.com/questions/277565/…), which cost me 10 downvotes? You know that binding energy is 99% of a proton's mass, you really missed the rationale of my post? My hypothesis considered
user128101
two extremes a) was that: ".. if 1 mass (unit) occupies 1 space (unit) whereas 10^n energy can occupy 1 space). when we speculate on the electron's size (units of space) we might also refer to the effective mass of the proton, therefore the size of an e might be a mere 18 time less than a proton b) considering binding energy occupies same space we get 1/1836 = 4.5*10^-17
@user104372 I'm not sure what you mean by a concrete object but yes most of us would consider a free neutron to be a distinct and well characterised object. The same applies to the proton, electron and neutrino produced when it decays.
@DavidZ Oh, I forgot to type the rest of what I was thinking. I also kind of felt like since I already described my take on the problems with the homework policy and gave an explicit solution in my own meta post (which came before yours), I didn't understand why I should re-type it all in your posts.
I linked to my post all over the place: comments, chat, whatever.
I guess I didn't think it was necessary to rehash my written arguments (with lots of upvotes) elsewhere.
You seem to be saying otherwise.
user128101
@JohnRennie, so how does a concrete isilated object create an electron withoutpair production?
@DanielSank Ah, there was no need to retype; a brief summary (could have been like 3 lines) and a link would have been sufficient.
08:14
@DavidZ Heh, but nobody would upvote that.
I'll try though. Let's find out.
@DanielSank If they agreed with it, they would.
@user104372 NB pair production is a term normally used to describe creation of an electron and positron from a photon. You wouldn't use it as a general way to describe creation of particles.
@DavidZ I doubt it. They'd have to follow a link and read the entire construction I put forth in my post again.
user116211
Hey, @JohnRennie, would you mind checking my query above?
Note, by the way, that my meta question/answer pair got more up votes than any of the other homework related ones (I think). To me that said the feeling of the community was that I was mostly onto something.
user128101
08:16
@JohnRennie, can you give me a link to see how an electron is created when a neutron decays? can you gloss your comment on the pointlike electron comment?
...and I think that's because I stuck to one pretty simple issue instead of getting into the purposes of the site, issues about how people decide to cast votes, etc. etc.
Just, rename the policy.
But now I'm speculating.
@user104372 The creation of the electron is described by quantum field theory. You're looking for some intuitive handle on what happens, but there isn't one.
If we take the wavefunction for a neutron and evolve it forward in time we find that it evolved into a mixed system containing a contribtuion from the proton/electron/neutrino system.
So there is a probability greater than zero that a neutrino can evolve into a proton/electron/neutrino.
But if you're looking for some simple intuitive explanation of precisely how this happens then I'm afraid there isn't one.
@DanielSank sure, you were on to something, but it got a lot of upvotes when your proposal was being compared to doing nothing. The later questions were meant to compare different proposals against each other. If your proposal is truly the favored option of the community, it should get lots of upvotes in the comparison to other people's suggestions as well. (This is in the hypothetical scenario where it was posted when the question was fresh.)
user128101
@JohnRennie, OK, in conclusion a loose neutron that lost a positron through betadecay is perfectly similar to any other neutron, Is thet so? Can you tell me what was wrong with my answer at the pointlike electron?Do you really think anelectron has no size, or is it a concrete extended massive object?
@user104372 All neutrons are identical, regardless of how they were created. Likewise all protons, all electrons etc etc
08:21
@DavidZ I see your point, but note that in my post, there was maybe one or two sentences which could have been refined. Instead, we're now talking about the goals of the site.
@user104372 although it's commonly said that an electron is pointlike this doesn't mean wht you think it does because fundamental particles don't have a size.
In fact, discussion of the goals of the site is now a featured meta post.
Quantum field theory is only theory we have that tells us what a particle is.
@DanielSank yes, we're talking about the goals of the site because that is what the community chose to do, out of the options that were presented.
@DavidZ That's what heather chose to do.
08:23
Earlier theories just assumed particles existed.
But when you look hard at QFT and ask what a particle is they turn out to be remarkably elusive objects.
Jim's answer (which lead to heather's post) didn't even address the question asked in the meta post.
@DanielSank And Jim. And all the people who upvoted his answer.
Bah, why am I complaining about this?
@DavidZ Yes, people upvoted his answer. But here's an analogy of what I think happened there:
user128101
@JohnRennie, OK, that is QM point of view, but if we assign an extension to any unit of mass, then was my rationale wrong?
DZ: How should we reword the homework policy?
Jim: You know what's cool? Octopuses. And chocolate. Let's talk about that.
Everyone: Have an upboat.
08:25
@user104372 When you say assign an extension to any unit of mass do you mean just assume that a particle has some minimum radius?
@DanielSank that is a deeply flawed analogy.
Perhaps I'm being unkind and/or seeing things in a way to justify my own views on the homework issue, but that's how I see a lot of the talk in meta.
@DavidZ Perhaps.
but I think not.
user128101
@JohnRennie, I assume that twice mass has twice extention, it is a plausible and viable hypothesis, after all QM is not the Truth,and my post did get 7 upvotes!
user128101
The point is that your comment was rather malicious
@user104372 It isn't a plausible and viable hypothesis because it contradicts QFT, and QFT has been experimentally proven over and over again.
This isn't a religion we are preaching, QFT works. It works extraordinarily well.
Every day the LHC confirms that QFT is a good description of physics.
user128101
08:28
@JohnRennie, sure also chemio works, and euthanasia :)
@DavidZ Jim's answer does not actually answer the question. It just suggests other questions. On the main site, we delete stuff like that.
@user104372 When I say QFT works I mean we can make detailed predicitions of the outcome of collider experiments and experiment shows that our predictions are correct - every time. That's a very specific definition of works.
user128101
@JohnRennie, What surprised and hurt me is that you did not criticize the rationale, but the detail that effective mass is 1%, which you know it's true
Now we have to contend with the fact that we have an upvoted answer which doesn't actually answer the question.
user128101
@JohnRennie, that is not your style. Anyway,thanks for your time, and again, please do run for president! Bye
08:31
Also, @DavidZ, I think you're pushing me around unfairly.
Rereading Generalizing the homework policy, I see two questions:
1) Are there a significant number of questions which are off topic under our current homework policy which would be on topic under the new policy? If so, should they be on topic?

2) Exactly what sorts of questions would become off topic under the new policy which are not covered by current close reasons? Do we want them to be off topic?
@DanielSank yeah, but this is not the main site. Things are looser on meta, because we're using the Q&A system for inherently discussion-y topics.
1) No
2) None.
I fail to see how the questions posed in that meta post admit my stated opinion about how to deal with the homework policy as a sensible answer.
In other words, I think the questions posed in that meta post, while interesting and worth discussion in some right, are unimportant compared to a simple rewording of the policy.
@DanielSank Those are not what the question itself is asking. To be fair, looking back at it, I see that I neglected to actually ask what I meant to ask, but nobody brought that up at the time.
So I think you're criticism that I should have answered that meta post is just off the mark.
@DavidZ Yes.
As I keep saying, the meta posts are generally very unclear.
The result is that people post whatever the hell they want as answers, get upvotes, and then we're trying to somehow extract useful information from that.
Not good.
@DavidZ Yeah, well, my reaction was "I don't understand this. I guess I have nothing to say".
And now I'm being criticized for not having answered ;)
I wonder if we need to stage meta posts.
Is there any way to do that? Post it, delete it, and ask the 10k+ users to review before making the post public?
It's technically possible, sure
I prefer to post it, ask everyone to review it, and have it public the whole time
08:40
@DavidZ Problem is that we get stuff like we just saw: the post doesn't actually ask a question, and now interest is spent.
That's not great.
Anyway, the core question I should have included in that post was from the chat session: what exactly should be on or off topic under the new policy?
@DavidZ Yes.
I missed that, unfortunately.
But in any case, we were talking about the meta.
Would you like to make a meta post which says "What questions should be on and off topic under the replacement for the homework policy?"?
No, it's not :)
Yes it is.
08:42
That post says:
> "In particular, what are better ways to characterize our actual reasons for closing questions where we currently use the "homework-like" close reason?"
IT says so right in the abstract.
That's a different question.
And right before that it says "what kinds of questions do we really want to see closed?"
Particularly because the post contains the survey data, it seems to focus entirely on "why exactly are we voting how we're voting?"
@DavidZ Yes, there are multiple questions, which is why I didn't respond. I couldn't address everything being asked there, and I was stumped about what to do with the data.
Well, if you think there's a need for a post that simply asks what should be on topic and off topic, feel free to make it.
08:44
Before we go on, I need to reassure you that while I'm criticizing your meta posts, I'm not criticising you.
@DavidZ I don't.
I think we need to reword the answer and be done with it.
@DanielSank Sure, that's been understood
@DavidZ Good.
@DanielSank If that's what you think, put that before meta. You can post a question that asks something like "do we want to stop the discussion at [other question] and [other question] [etc.], drop all other proposed new policies, and immediately use [your proposal] as the replacement for the homework policy?"
@DavidZ oy vey. So you're roughly saying to repost my initial meta post, and prepend it with a note saying "Remember this? Let's do this."
I guess I could do that.
Yep.
Except you don't have to repost; you can link to it, and just include a summary in the new post.
08:49
I'm trying to decide 1) whether that's actually a reasonable thing to do, and 2) whether that would be risking the entirety of the good will I enjoy around here.
The way you worded your suggestion makes it sound like you expect me to be rather dismissive of the proposals put forth by others.
Well, yes. The actual wording is up to you, of course. But if I understand correctly, your suggestion would be that discussing all the other proposals other people have put forth is a waste of time, and we should just use yours. If you want to convey that clearly, I think it is at least helpful, perhaps even necessary, to be dismissive.
@DavidZ I can see I have failed to express my thoughts, and that's really pathetic on my part.
I don't think my proposed wording is necessarily suitable. I just think backing off to a discussion about the goals of the site is unnecessary for refining the homework policy and has expanded the workload to the point of impossibility.
OK, so put that on meta.
You seem locked into thinking I have an egotistical notion that my initial proposal is perfect. This despite the fact that I've just spent hours arguing, and you conceded, that your own meta posts are totally unclear and don't even pose the questions you thought they did. I'm trying to help focus the issue, not just push my own opinions.
I'm surprised if that's not clear yet, but if so it's probably because ACM isn't here to help me past my obviously terrible ability to express myself.
No, that's not an accurate reflection of my view on either count
08:57
@DavidZ then I'm totally lost.
No, it's just 2am. I'm tired.
Bottom line: clearly you think something is wrong with the current process, otherwise you wouldn't be arguing. Whatever problem it is that you see, the way you fix it is by making a meta post.
@DavidZ Perhaps. I hope that identifying the flaws in the existing posts has been useful, if for no other reason than the fact that when we started this discussion we were asking whether votes on meta posts should be used to influence policy.
Given that those meta posts are rather muddled, I think we can see that care is needed in interpreting the votes.
That's one of the main points I wanted to make here.
The discussion certainly doesn't hurt; I'll take it into consideration.
Thanks for your patience.
Enjoy the C++.
oh, looking forward to it already
09:01
very good
I'm looking forward to biologically beneficial unconsciousness.
 
2 hours later…
user116211
Okay, I got it; since there would be two degrees of freedom if $q_3$ is dependent on $q_1$ and $q_2$; then $\frac{\partial q_2}{\partial q_1}= 0= \frac{\partial q_1}{\partial q_2}\,.$
user116211
@Secret WoW!
I actually kinda agree to it somewhat, given that despite I am known among my friends to be quite self conscious, there are people like Kelvin (my honours co-supervisor) and Acuriousmind, point out behaviourial and personality traits that I am never aware of
 
1 hour later…
12:18
@JohnRennie @ACuriousMind: iS THERE ANY LIMIT T to mass a body can have due to the restrtcition of speed of light
because F = G M1 M2/r^2 suppose M2 is 1kg and distance is not quite large so is there any restriction on how much mass M1 can have?(so that it doesn't produce acceleration excedding 3 x 10^8 m/s^2
12:36
@JohnRennie : it isn't true. The mass of the hydrogen atom is the mass of the electron plus the mass of the proton. There is no thing that is made of negative energy. There is no magic. But there is a mass deficit.
Lol
@DanielSank : I know the answer to that one.
@user104372 : electrons are not point particles. That's a myth. Check out the wave nature of matter.
@Xasel 1. Please do not ping me with general questions for which you have no reason to believe I'm somehow uniquely qualified to answer. 2. Please pay a bit more attention to orthography and proper capitalization when writing. 3. There is no maximum mass, and there is no maximal acceleration.
@Secret : you aren't really conscious. You only think you are.
12:52
@0celo7 Yes, there is an argument that one-dimensional systems are not degenerate. I find it somewhat dissatisfying to get the non-degeneracy of the SHO from that because you're not using any properties of the SHO itself for that, however.
@ACuriousMind Did you hear about ample line bundles in algebraic geometry?
@Danu yes
@ACuriousMind Why is that unsatisfying? It works for any system
So the definition I have is the following
Seems good enough for me
12:58
A line bundle $L$ is called ample if for some $k>0$ and some linear system in $H^0(X,L^{\otimes k})$ the associated map $\varphi$ is an embedding.
where $\varphi$ is the map that maps a space, minus the "base locus" of a holomorphic line bundle, into $\mathbb P^n$
Does this construction sound familiar to you?
I think (very) ample are related, btw. Cf. wikipedia.
@Danu No, because we didn't work in the holomorphic setting at all
That's a shame :P
So did you ever find any use for non-complex algebraic geometry, in physics?
I think this might somehow translate to the stuff with divisors and ample bundles we did, but this was at a point in the lecture where I didn't really follow it anymore
@ACuriousMind It's very closely related to divisors, indeed.
The map $\varphi$ is constructed using the divisors associated to sections of the line bundle
@Danu Nope
13:02
Did you ever find any use for complex algebraic geometry? :P
(I just know mirror symmetry)
Just wondering, btw, do people typically do alg.geom. over any algebraically closed field, "just because we can", or also over other fields? And why?
@Danu I'm not clear on the distinction between complex geometry and complex algebraic geometry :P
@ACuriousMind Okay :P
@Danu My alg. geo. course did most of its stuff not over any field, but in the abstract scheme-theoretic setting.
It's not so clear in general AFAIK
@ACuriousMind Ah, okay
Schemes...
It's the "next step" after sheaves ;)
There you often have a base scheme, which corresponds to the base "field" if you choose it to be the Spec of the field, but it can be anything really
13:06
okay
We only specialized to $\mathbb{C}$ for Riemann-Roch in the end.
I don't know what Spec is
@Danu You don't know what the spectrum of a ring is? :O
When you start talking about Spec I think it's safe to say you're outside complex geometry
@ACuriousMind No need for it in Huybrechts, as far as I can tell.
Space of prime ideals with Zariski topology?
13:07
I read the definition on wiki, yeah.
Also Zariski topology does not feature in complex geometry as far as I can tell
@Danu Yes and no. Complex geometry typically uses the analytic instead of the Zariski topology, but every complex analytic variety is also one in the spectral sense, that's Serre's GAGA theorem.
I'm sure it is---so you can use GAGA to draw a nice line
Which side of GAGA you're on tells you if you're doing algebraic geometry or complex geometry ;)
Since the Zariski topology is rather...clumpy, there's no reason to ever use it if you've got a better one available :P
Although the drawings of e.g. $\mathrm{Spec}(\mathbb{Z})$ tend to be rather funny
This is $\mathrm{Spec}(\mathbb{Z}[X])$ according to Mumford:
Challenge for @Danu: Draw this in TikZ (without looking up the existing solutions) ;)
@ACuriousMind This is very easy except for the clumps
The clumps... no idea
You can't use solid black bubbles because the geometers will then complain that doesn't capture the "fuzziness" of the points :P
13:17
I'll stick to drawing smooth objects, for now.
Regrettably little to draw in complex geometry, so far :P
Mumford?
Jim
Jim
13:39
Mumford's the word
So side note, a colleague of mine suggested a physics term that I think everyone will agree should be used
I was telling him about the constant energy density of dark energy and he pointed out that if the total amount of dark energy increased proportional to $a$, then dark energy, or rather the rate of its accumulation, was a good indicator of the rate of expansion in the universe
Then he said, "dark energy per unit time. That's dark power"
Yes. We should absolutely be measuring the dark powers of the universe
@Jim 1. Heh. 2. Too bad that if the universe is infinite, "total dark energy" at constant energy density will always be infinite, and doesn't grow. Although I guess this then means that the dark power is already infinitely strong.
Jim
Jim
@ACuriousMind you could measure the density of dark power or the dark power in a finite volume
Though the measurements may be skewed a bit should Darth Vader enter the room
13:58
Sorry won't concern you from now since it' bothers you(I just thought that since you are theoretician you know much better than me and can identify error in my reasoning)
14:49
OMG the PSE is offline for maintenance. What will I do?
Last night dream: Some time in h bar, there's a user called secretstatus asking Danielsank help to help him on building a set based on what he dreamt of last night, which involve some kind of mythology god
like characters and settings. Danielsank is initially puzzled on one of the placement of a concrete plane, while secretstatus insists that it has to be carried out because that is exactly what the setting is based on Mid way through the conversation he noticed me chatting and thus he changed his username into stablestatus to prevent confusion. eanwhile, daneilsank said that unless in the rare event that secret become active
again, secretstatus can retain his original username for now. While it is true that I only have spoken once during the conversation, I am actually watching the entire chat flow to see what they are talking about
@JohnRennie Well, maybe drink some more coffee ? :)
@Secret I could do some work I suppose :-)
It's back! Phew :-)
@JohnRennie It's online here
Ah, I see you've already gotten it back, too
@ACuriousMind It dropped out for a few minutes. I assume they ran into some problem with the servers. When I tried to open the main site I got a 30 second wait then a message saying "down for maintenance".
14:55
Huh, I didn't notice that, shows I'm not a complete fanatic for this site ;)
I would guess that if the front end servers time out a database request they default to a "down for maintenance" page rather than spitting out some gobbledygook error message.
So "down for maintenance" actually means "Oh sh*t, something is broken" :-)
Recently I am trying to use lagrangian mechanics to model some physics found in portal games, however some details need to be ironed out before I can discuss. For now I can show the trajectory of such scenario and that the major issue I need to figure out is the domain of the Lagrangian in order to handle the discontinuity in the model (pics incoming next message)
@ACuriousMind What is Mumford??
@0celo7 Did you try searching for it, perhaps together with keywords from the context in which I used it?
@ACuriousMind Yup.
No luck.
15:00
You suck at Google :P
"Mumford Spec(Z)" brings up several hits which make it clear for me
what's spec(Z)?
If Mass = 4496005299291579392 kg .AIn't it will produce acceleration of 3*10^8 m/s^2 on a body 1 kg at a distannce 1 m form it?
which will certainly violate c(speed of light)?
@0celo7 The spectrum of $\mathbb{Z}$, i.e. the set of its prime ideals endowed with the Zariski topology.
@Xasel No it won't. You can't apply Newtonian physics and expect the result will respect relativity.
@ACuriousMind wtf is that
@0celo7 Now, "prime ideal" and "Zariski topology" are things you can certainly look up on your own.
15:09
@ACuriousMind You know I don't know any algebra
How is that relevant?
You won't suddenly learn more algebra just because it's me regurgitating these standard definitions
@ACuriousMind $\overline{A\times B}=\overline A\times\overline B$, right?
Aha, google tells me yes.
In other news, a brief skim of the principles of classical mechanics and quantum mechanics (at least those covered by susskind), it seems discontinuities in motion like those in portal physics seemed to break a lot of continuity conditions that prevent nice formula such as EL from being used, while quantum seemed to be largely intact
Meanwhile, reading my topology study notes
We are also assuming the details of the portals are unimportant, thus we treat them as identification of two points in space and ignore for now general relativistic treatments
Typo: The two "ax" expressions in the diagram accidentally have their signs interchanged
15:27
@Xasel there is no limit to acceleration in relativity. In fact the acceleration can become infinite - subject to defining precisely what you mean by acceleration.
There is a limit on locally measured velocities, and this limit is sort of why we get black holes. But there is no limit on acceleration.
A very large mass will inevitably become a black hole, but a black hole can be as large as you want, with no upper limit to its mass.
Incidentally your mass of 4496005299291579392 kg is 0.0000000001% of the mass of the Sun, so it's obviously not an upper limit for the mass of a body.
@ACuriousMind: my attempt to answer the unanswerable ...
1
A: How do symmetries “define” physical laws?

John RennieA theory is typically described by a Lagrangian, and varying this gives us the equations of motion of the system. The symmetries you describe are symmetries of the Lagrangian i.e. they are transformations that leave the Lagrangian unchanged. It would be nice to think that the Lagrangians that de...

Please downvote without being wracked with guilt :-)
@JohnRennie Your first two paragraphs are correct but very general; your last two paragraph don't make a whole lot of sense to me. What does "imposing a $\mathrm{U}(1)$ symmetry on the Lagrangian for quantum electrodynamics" mean? What is the Lagrangian you're starting from here, and how do you end up with the "correct" one?
user218912
@0celo7 is the last term $m^2$?
user218912
for the wrt. $A_\alpha$ derivative
I guess you're commenting on the way I've worded this since we both know what I mean. I'll have a reread and see if I can make it clearer.
@JohnRennie I'm not sure I know what you mean, I'm afraid.
15:36
ok back..lets scroll up what hapened till now :0
@JohnRennie Yes, but now I think you're dodging the question because it asks how we are led to these Lagrangians (at least in my reading)
user218912
@ACuriousMind can you please show me how to take the derivative of vector fields with indices? like how do I compute $\frac{\partial}{\partial A_\alpha}$ of $\frac{m^2}{2} \eta^{\mu\nu} A_\mu A_\nu$?
user218912
we didn't learn how to do it yet
user218912
is it just like normal derivatives?
user218912
15:40
how do I treat the different indices?
@ACuriousMind now I think you're dodging the question - ah, you spotted that :-)
There is no definitive answer is there? The QED Lagrangian is a guess. But it's a guess from a restricted subset of Lagrangians that are invariant under a local U(1) gauge symmetry.
@IceLord In $A_\alpha$, the $\alpha$ is arbitrary, but fixed, so you're just taking an ordinary derivative w.r.t. scalar variable $A_\alpha$. There's nothing much to learn once you've figured out what $\frac{\partial A_\mu}{\partial A_\alpha}$ is.
Jim
Jim
@JohnRennie Noether's theorem? Seems like an obvious thing to include for symmetries leading to physical laws
user218912
@ACuriousMind what is it? xD
user218912
i don't know the answer so I can't use that to figure it out.
15:44
@Jim I was tempted to discuss Noether's theorem, but the question was obviously about the local gauge symmetries used in the standard model, and Noether's theorem isn't useful there.
user218912
@ACuriousMind do I also use product rule?
But then why sun is not causing acceleration of particle stream near it at such rate...secondly is there any alternate definition of acceleration and I disn't understand what do you mean by locally measured velocity?
@JohnRennie
is therere any local or global measurements of velocity
@JohnRennie Well, I do think that the pure Yang-Mills Lagrangian is very natural if one starts from the notion of a local symmetry and a gauge field - it's basically the only invariant term in the field that you can write down in all dimensions. And then the "minimal" coupling to matter also comes very natural: Replace all ordinary derivatives in the matter action by covariant ones, done. Then you have left to figure out where the matter action comes from, and you have to explain "naturalness".
But you're right in so far as there's no logically necessary train of thought that leads us to the Lagrangians that we use
@ACuriousMind the physicists I've asked about this tell me the standard model Lagrangians are pretty obvious, so I've rather overplayed the role of guesswork in my answer because they are obvious guesses. But I think my answer addresses the spirit of what the OP was asking.
user218912
@ACuriousMind at least can you tell me where to read about how to do it?
user218912
15:49
it's not in my book
@ACuriousMind I'm missing something conceptual. In a general topological space, consider a set. If each point in that set has an neighborhood in the set, why is it open? Because it's the Union of neighborhoods, which are open?
Why is Union capitalized, phone?
@IceLord Figuring out the answer to problems where you don't know what the answer must be is a valuable skill. In this case, it should not be hard: What $\frac{\partial A_1}{\partial A_1}$ is should be obvious, and what $\frac{\partial A_\mu}{\partial A_1}$ for $\mu\neq 1$ is is something for you to think about if it's not obvious.
@Xasel the Sun is big, very big, so its surface gravity is quite low even though it's very massive. As for what we mean by acceleration, to get some idea of the complexities involved see:
20
Q: What is the weight equation through general relativity?

user17093The gravitational force on your body, called your weight, pushes you down onto the floor. $$W=mg$$ So, what is the weight equation through general relativity?

user218912
@ACuriousMind do I also use product rule because there are 2 vector fields?
@0celo7 Because it's often used in proper names like "Western Union Bank"?
@0celo7 Yes
@IceLord You use whatever rules for the derivative you wnat/need to use
15:54
Where did you get Western Union Bank from? That's awfully specific.
@JohnRennie Sigh...see what you did, now it's going hot
@JohnRennie Next time they tell you that, ask them why it took them decades to come up with the obvious guess for QCD, then :P
@0celo7 It was a proper name with union in it that popped into my head. No specific reason
@ACuriousMind Right. I'll be keeping my eye on you.

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