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Scientist Smith YT
Scientist Smith YT
12:11 AM
I have a question. So I had some blue/white powder build up on my positive battery terminal on my car. And I scraped it off and put it in a glass jar. I then put some hydrogen peroxide in the jar. And it bubbled a lot and very fast. And it had some bright red colored stuff left over. And then that was it. What could that powder be? And what was left over that was like a bright rusty red color?
 
 
2 hours later…
rob
rob
2:32 AM
So I frequently start comments, especially aimed at new users, with the salutation “Greetings!”
And a couple of times a month, my iPad will notice the correctly-spelled word “Greetings!” at the beginning of a physics.SE comment box, and helpfully change it to “Retinas!”
I have no idea why this happens.
So far I think I have caught them all.
But eventually I will miss one.
When you guys notice that I’m dispensing advice about site policy in comments which begin with the exclamation “Retinas!”, it’s probably not because I have gone insane.
…. probably.
Anyway, ligaments for tonight.
 
 
2 hours later…
More Anonymous
More Anonymous
4:30 AM
@rob Try to turn off google translate on your browser? I suspect that might have a bug and messing things up?
 
John Rennie
John Rennie
5:18 AM
@ScientistSmithYT The white powder is probably lead (II) sulphate, PbSO₄. The battery connectors are lead and there is always sulphate around from the sulphuric acid in the battery. When you add peroxide the lead sulphate is oxidised to the appropriate named "red lead", which is an oxide containing a mixture of Pb (II) and Pb (IV). The blue stuff is copper sulphate, which is unaffected by the peroxide and just goes into solution.
 
 
2 hours later…
DatBoi
DatBoi
7:26 AM
Hello everyone! I was looking for a source which talks about how unequally charged capacitors behave in RC circuits(dc), and how the general charging discharging equations vary in this case. I couldnt find any by myself. Can someone help me with this?
 
John Rennie
John Rennie
@DatBoi hi :-)
 
DatBoi
DatBoi
Hello there!
By unequally charged, I mean that the plates have different charges on them
 
John Rennie
John Rennie
You analyse circuits like this by writing an equation for the current. That gives you a differential equation for the charges on the capacitors and you can solve this to get the charge as a function of time.
@DatBoi Ah, you mean a single capacitor but with an unequal charge on the plates?
 
DatBoi
DatBoi
yes!
 
John Rennie
John Rennie
If you have a capacitor with unequal charges on the two plates than what happens is that the charge spreads itself between the inside and outside surfaces of the plates.
There are two rules that we can use to find out how the charge is distributed.
The charges on the two inner surfaces are equal and opposite, and the charges on the two outer surfaces are identical.
I can draw a diagram to show what I mean if it would help.
 
DatBoi
DatBoi
7:41 AM
Im fine with that
 
John Rennie
John Rennie
Ah, yes, that first diagram shows exactly what happens.
 
DatBoi
DatBoi
yep
 
John Rennie
John Rennie
Then the potential difference is just due to the inner charges.
 
DatBoi
DatBoi
oh
 
John Rennie
John Rennie
i.e. Q = CV where Q is the charge on the inner surfaces.
 
DatBoi
DatBoi
7:43 AM
Then I guess we just replace Q with Q1-Q2/2 everywhere?
 
John Rennie
John Rennie
Yes
 
DatBoi
DatBoi
I see. So the outer surface charges do not affect the circuit at all?
 
John Rennie
John Rennie
Correct
 
DatBoi
DatBoi
Interesting. Do you have some reference for this last point?
 
John Rennie
John Rennie
Not offhand, though it's kind of obvious. As the electrons move round the circuit they are moving away from one outer charge and towards another identical outer charge, and the forces from the two outer charges balance each other out.
 
DatBoi
DatBoi
7:49 AM
I get it, thanks for the time!
 
John Rennie
John Rennie
:-)
 
 
1 hour later…
Emilio Pisanty
Emilio Pisanty
9:02 AM
1
Q: Is there a backside of a black hole?

CompSciFlyFrom all that I can gather, a black hole is thought to be spherical. In this case, would it be theoretically possible to travel around (not inside) the black hole in order to see the backside? If so, would the backside look the same as the front side (i.e. a black hole)? Everything I read about b...

black-holes
our next HNQ?
 
 
4 hours later…
PM 2Ring
PM 2Ring
12:52 PM
In Australian English, "backside" is a common neutral term for "buttocks". Another term is "bum", which is used as a mild swear word. Some Aussies (particularly younger ones) use the American term "butt" rather than "backside".
 
fqq
fqq
1:10 PM
so, there is a black hole in a backside, and the question is about the reverse
(sorry I'll see myself out)
 
PM 2Ring
PM 2Ring
1:24 PM
I once read that Russians prefer to use the term "collapsar" because the direct Russian translation of "black hole" has strong anatomical connotations.
 
ACuriousMind
ACuriousMind
and collapsar sounds much cooler, honestly
 
PM 2Ring
PM 2Ring
It does.
 
rob
rob
@PM2Ring A question about “does a black hole have a butt?” could in principle be answered with explanation about how some of the nutriment which “feeds” a black hole is rejected from the accretion disk in violent jets aligned with the hole’s rotation axis. I’m not sure this can be done in a classy way, though.
2
 
PM 2Ring
PM 2Ring
We also need to mention the expulsion of gas.
Dear lurkers, we aren't actually a bunch of overgrown teenage boys. ;)
2
 
 
3 hours later…
EVO
EVO
4:24 PM
How to fix this. So I opened PSE on edge and this is what I got. I've no issues with other SE sites. The UI looks normal when I open PSE in incognito.
 
ACuriousMind
ACuriousMind
@EVO that's the mobile site view - scroll down and click on "full site" in the footer
 
Shashaank
Shashaank
Many answers here state that there is no such principle as the principle of general relativity ( and general covariance is vacuous ). Why is that the case...If I am accelerating in a car, my acceleration would be something measured by
an observer at rest wrt some inertial frame, whereas my acceleration would be something else measured by an observer who is accelerating at some rate with respect to that inertial frame
Would anyone like to comment
@Slereah is that correct, there is no principle of general relativity and Einstein was wrong about what general covariance tells
 
ACuriousMind
ACuriousMind
4:40 PM
@Shashaank can you link an example of such an answer?
 
Shashaank
Shashaank
@ACuriousMind sure. There a couple of those. Just a minute
 
ACuriousMind
ACuriousMind
also, what exactly do you mean by "principle of general relativity"?
 
Shashaank
Shashaank
physics.stackexchange.com/questions/263954/… Especially the comment by Physics footnotes
 
ACuriousMind
ACuriousMind
Ah, yes. The coordinate thing is indeed unfortunate - it is not special to general relativity that one can formulate the laws of physics in a co- or invariant way w.r.t. arbitrary coordinate transformations
 
Shashaank
Shashaank
And links therein. Particularly this paper by J Norton
 
ACuriousMind
ACuriousMind
4:45 PM
it is special to general relativity that you must use such a formulation if you are to make sense of it, which is why the confusion arises
 
Shashaank
Shashaank
@ACuriousMind why is it necessary in GR to make sense of it
 
ACuriousMind
ACuriousMind
@Shashaank because you have the metric that varies with each point - there is no class of distinguished "frames", there's just arbitrary coordinates
In most other contexts you can get by by restricting yourself to a special and simple class of coordinates, e.g. the global inertial frames of Newtonian mechanics
 
Shashaank
Shashaank
@ACuriousMind I mean by the principle of general relativity that - 1) All frames inertial or not are equivalent with respect to formation of physical laws. 2) Acceleration is not absolute but relative
The point 2) is mine
 
ACuriousMind
ACuriousMind
but since suddenly we have a varying metric and are not longer on simple $\mathbb{R}^n$ but some arbitrary spacetime, the easy notions of "special" frames are not longer accessible
 
Shashaank
Shashaank
Well you can cast Newton’s law in covariant form as in Lagrangian or Hamiltonian mechanics. The resulting Euler Lagrange or Hamilton eqn are invariant but the eqn of motion that we deduce from them wouldn’t be same. Whereas in GR, all the physical laws are invariant under arbitrary transformation. The eqn of the law remains same in accelerated frame.
 
ACuriousMind
ACuriousMind
4:53 PM
@Shashaank you can make any Hamiltonian system generally covariant, see e.g. physics.stackexchange.com/a/194925/50583
 
Shashaank
Shashaank
But in Covraint Newtonian mechanics only the Euler Lagrange or Hanilton eqns are invariant. The eqns of motion resulting from them aren’t invariant. You get pseudo forces which have no natural origin.
To put in short doesn’t what I have said above imply that “GTR obeys a print pile of general relativity but Newtonian mechanics doesn’t “ ....where I have defined the principle of general relativity as above.
 
ACuriousMind
ACuriousMind
really, I'm not even sure what content either of your two points there have if you try to express them mathematically
We can write down Lagrangian or Hamiltonian mechanics entirely in coordinate-free language - the notion of "frame" then doesn't even enter into it
 
Shashaank
Shashaank
The first point is straight out of Wikipedia, the 2nd one is also what Einstein believed ( as far as I have read)
Ok maybe I ask a very simple question and then be happy with the answer
Answer
 
ACuriousMind
ACuriousMind
This is what people mean when they say the principle is vacuous - frames and "covariance" seem really important if you do physics in coordinate-laden language, but disappear almost entirely if you switch your mathematical formulation
 
Shashaank
Shashaank
Like velocity is a relative concept, isn’t acceleration also relative. Like an inertial observer quotes that I am accelerating at 10m/s^2. An observer accelerating at 5m/s^2 with the inertial frame says I am accelerating at 5m/s^2. Everywhere I see that it’s written acceleration is an absolute thing unlike velocity.
Am I wrong in saying that acceleration a relative concept
 
ACuriousMind
ACuriousMind
5:05 PM
@Shashaank What they mean by "absolute" there is not that everyone else sees you accelerating with the same acceleration even if they themselves are accelerating
"absolute" means that you can detect what your acceleration is
e.g. when you sit in a car, you can tell that the car is accelerating even if you close your eyes - i.e. you can tell acceleration without measuring it relative to something
 
Shashaank
Shashaank
Ahh I see @ACuriousMind and is it only necessary for me to detect that I am accelerating or do they also mean that I can suspend a pendulum from the ceiling of the car and detect the exact value (wrt an inertial frame) of my acceleration.
 
ACuriousMind
ACuriousMind
yeah, they mean that "acceleration" is a well-defined quantity without having to specify from what frame you're measuring it - you just need to be careful in how you're measuring it - any observer could look at your pendulum and therefore determine the same acceleration value for you, independent of their own acceleration
this isn't possible for velocity - which is why velocity is "relative" (you need external reference points to determine it) but acceleration is "absolute"
 
Shashaank
Shashaank
5:28 PM
“ any observer could look at your pendulum and therefore determine the same acceleration value for you, independent of their own acceleration”- isn’t it back to what i was saying earlier. If an inertial observer measures my acceleration to be ‘x’ an observer accelerated to the inertial observer at ‘y’ would measure my acceleration to be ‘x-y’. Isn’t it...
 
ACuriousMind
ACuriousMind
@Shashaank the angle of the pendulum doesn't change for any observer, regardless of how they are accelerated!
if you hang the pendulum in your car and I drive next to you matching your acceleration, the pendulum doesn't magically hang straight down for me when I look at it
 
Shashaank
Shashaank
So when I said - “ Like an inertial observer quotes that I am accelerating at 10m/s^2. An observer accelerating at 5m/s^2 with the inertial frame says I am accelerating at 5m/s^2.” I was wrong, right... the accelerated observer will measure my acceleration to be 10 ( I don’t know how he will measure without a pendulum, but he will measure it to be 10), right
 
ACuriousMind
ACuriousMind
you're wrong if you intended them to measure it by any process that relies on $F=ma$ like the pendulum
you'd be right if you intended them to measure it naively by trying to track your changes in velocity (which is relative to them, after all)
 
Shashaank
Shashaank
Yeah I got the caveat . They will measure by acceleration to be same with respect to an inertial frame. They will not measure my acceleration to be the same with respect to themselves. This was what I was saying. This is more evident in rotational motion.
@ACuriousMind “you'd be right if you intended them to measure it naively by trying to track your changes in velocity (which is relative to them, after all)”- is there a reason to state that the observations of an accelerated observer are not correct. Like an inertial observer will say I am accelerating, an accelerated observer will say I am not accelerating.
Is there a reason to state that what the inertial observer says ( that I am accelerating wrt to him) is the correct thing and what the accelerating observer says (that I am not accelerating wrt him) is not the correct
 
ACuriousMind
ACuriousMind
I'd be cautious with the word "correct"
 
Shashaank
Shashaank
5:42 PM
thing
What would you like to use in place of correct
 
ACuriousMind
ACuriousMind
their observation is not wrong but what they are computing is not what we mean by "the acceleration"
or, really, in some cases it might be
it's not "the acceleration" that appears in the statement "acceleration is absolute", at least
 
Shashaank
Shashaank
“or, really in some cases it might be”- with respect to this if I go onto to says that the principle of general relativity ( not GR in whole), is just that the observations of an accelerating observer are also facts of nature, his observation is also an observation of the laws....his observation is equally correct...( just like we do or inertial observers)
Do you agree with the above statement ( I guess you should since you agreed that in “in some cases it might be”)
 
ACuriousMind
ACuriousMind
yes
 
Shashaank
Shashaank
Because then I would say that it should be possible to state laws of nature in accelerating frame ( and refer to the principle of general relativity- above). And further that the law should not just be invariant under transformations to inertial frames but also to transformations to a accelerated and arbitrary frames- noting that the observation of an accelerated observer is also a fact of nature
GR allows us to do that and thus we can conclude that there is a physical meaning to the principle of general relativity. General covariance is not vacuous
 
ACuriousMind
ACuriousMind
what do you mean by "invariant" there?
laws of motion, for instance, can never be "invariant" - they involve solving for position and position is never invariant under translation or rotations!
 
Shashaank
Shashaank
5:53 PM
The form of the equation remain same. I just extended the principle of relativity to accelerated frame
 
ACuriousMind
ACuriousMind
yeah, that "the form of the equation remains the same" is something that makes intuitive sense but is hard to make precise
 
Shashaank
Shashaank
Continuing the 2nd last comment of mine....
 
ACuriousMind
ACuriousMind
as I said, you can write down even non-GR mechanics in an entirely coordinate-free way - in that case your laws are necessarily "the same" under transformation of coordinate systems because you're not making any reference to coordinates at all
 
Shashaank
Shashaank
So you mean that laws of Newton and SR can be written in such a way that the form of the eqn (the law) remains the same even in the accelerated frame (or arbitrary frame )
Newton’s 2nd law doesn’t maintain its form in an accelerating frame, right
Ahhhhh how can I forget SR can be done in arbitrary coordinates
Do you know of any source where Newton’s law are made covariant under arbitrary transformations. Like Newton’s laws being left invariant under arbitrary (including acceelrated) frames
 
ACuriousMind
ACuriousMind
they won't get covariant in the sense you expect
 
Shashaank
Shashaank
6:04 PM
Any source where I can see how they derive such a thing. For SR I know just do the semi coma goes to colon rule, etc. But for Newton’s law, do you know an explicitly sources that shows how to do so
 
ACuriousMind
ACuriousMind
you get fictitious forces in the non-inertial frames, as you are well aware
but see e.g. this answer that Lagrangian mechanics can deal perfectly well with non-inertial frames
 
Shashaank
Shashaank
@ACuriousMind Will the equation of the law remain invariant or not
Does making a law covariant means both sides of the an transform like one thing or does it mean the eqn of th law is invariant under the transformation
 
ACuriousMind
ACuriousMind
I really prefer trying not to talk about laws being invariant/covariant :P
it's a confusing subject that adds very little of substance - if you just do the math properly you will never run into a situation of "oh no this law should be invariant but it isn't" or something like that
for instance, take Maxwell's equations - are they "Lorentz covariant"?
They are "manifestly so" if you write them in their "covariant formulation" form, but these covariant equations involving $F$ are equivalent to the traditional equations involving $E$ and $B$
so what does it mean to say one of them is covariant and the other is not if they are equivalent?
mathematically, there is no such thing as the "form" of an equation, it's a silly concept, really :P
 
Shashaank
Shashaank
I see what you are saying. Proving that those 3 vectors eqns remain invariant is very long task while it is easy to do for the four vector formalism
But my lecture notes really say that Maxwell’s eqns are invariant under Lorentz transformations...
How would you define covariance ( any Lorentz covariance or Galilean Covariance or General Covariance), please...
What the most rigorous way to define those
 
ACuriousMind
ACuriousMind
As I said, I would avoid talking about it :P
 
Shashaank
Shashaank
6:18 PM
Like you said Maxwells eqns are Lorentz Covariant. What did you mean by that
Well then I will do some searching on the interner
But thanks for the discussion
 
ACuriousMind
ACuriousMind
@Shashaank well, the "manifestly covariant" version has $\partial_\alpha F^{\alpha\beta} = \mu J^\beta$
this is certainly not invariant - both sides are vectors and so the numerical values will change under Lorentz transformations
but if you only look at the "form" you might say it's invariant because it holds always
 
Shashaank
Shashaank
yeah I know that but what does covariance mean
 
ACuriousMind
ACuriousMind
but this clashes with the usual language that it is a scalar that is invariant
and vectors and covectors transform covariantly and contravariantly
so the terminology is a mess really and I suspect most people that talk about "laws" being invariant/covariant/whatever don't think all too deeply about it
 
Shashaank
Shashaank
Yeah I see. And if I ask you what does it mean when some one says Newton’s law can be formulated covariantly, what would you say ( if you’d like to say ). Would you say that writing Newton’s law in such a way that both sides of the eqn transform in the same way ( again if you’d like to say).
 
Charlie
Charlie
"what does covariance mean"

oh no here we go :p
 
ACuriousMind
ACuriousMind
6:25 PM
@Shashaank with Newton's law you run into issues that you have to specify under which transformations you intend it to be "covariant"
Newtonian mechanics assumes a Galilean universe
so of course it makes little sense to expect to be able to apply the Lorentz transformations of special relativity to it
if you're silly you might say "Newton's laws are not invariant (covariant) under Lorentz transformations"
but that's starting at the wrong end - the whole edifice of Newtonian mechanics simply isn't built with special relativity in mind
 
Shashaank
Shashaank
Yeah but then it also doesn’t make sense to apply transformations to accelerated frames, because the Galelian group doesn’t constitute such transformations, right
 
ACuriousMind
ACuriousMind
that you can't figure out how to apply the transformations to the equation of motion should really be the least of your problems when trying to mesh SR and Newtonian mechanics together
 
Shashaank
Shashaank
Going in circles :(
 
ACuriousMind
ACuriousMind
@Shashaank you can certainly do a time-dependent transformation $x\mapsto x + f(t)$ where $f(t)$ is a fixed function of time
that's certainly something you can do on Galilean spacetime
and you can apply this to Newton's laws! it gives you fictitious forces!
why do we have to worry about whether this constitutes "covariance"?
the physics is in the fictitious forces, not in playing word games
 
Shashaank
Shashaank
Yeah I see your point.
It’s all just a mathematical trickery. Writing eqns in different coordinates/ frames
 
ACuriousMind
ACuriousMind
6:32 PM
@Charlie would you rather hear the rant about whether or not GR is "diffeomorphism invariant" again? ;)
 
Charlie
Charlie
General covariance means "the relevant equations involve tensors", but the usage of "covariance" as opposed to invariance is a slightly different context
I would not :P
 
Shashaank
Shashaank
Of course they will be true, it’s just that how you interpret the results
 
Charlie
Charlie
The real question is whether GR is invariant under passive or active diffeomorphisms!
 
ACuriousMind
ACuriousMind
::eye twitches::
 
Charlie
Charlie
It's not really mathematical trickery, different coordinate systems correspond to physically different things
Unfortunately there's often zero distinction made between the two (slightly different) uses of the phrase "covariant" in physics
 
Shashaank
Shashaank
6:35 PM
Well then is it right to say that the covariance business and writing eqns in different coordinates isn’t something new that came with GR and was the crux of GR @ACuriousMind it existed before GR as well and wasn’t the crux or takeaway of GR
 
ACuriousMind
ACuriousMind
one shouldn't forget that GR was invented in a very different environment than today
I do think that the idea of coordinate systems etc. perhaps wasn't as much thought about prior to GR
 
Charlie
Charlie
You can talk about coordinate changes on manifolds without any reference to GR, although chronologically how they were discovered doesn't really affect anything at hand
 
ACuriousMind
ACuriousMind
and perhaps the success of GR was what sparked more geometric treatments of other theories as well, I have no idea
 
Slereah
Slereah
It certainly was
that was basically the big idea in the 1910's
 
Shashaank
Shashaank
Didn’t guys at that time knew we can write Newton’s eqns in different arbitrary coordinates. That We can write Lagrangian in different coordinates yet get the same Euler Lagrange eqns ( just asking out of curiosity; this looks trivial now)
 
ACuriousMind
ACuriousMind
6:37 PM
physics has an unfortunate tendency to teach things through a very historical lens, so the emphasis on coordinates and transformations when doing GR is a relic even though today we could do it very differently pedagogically
 
Shashaank
Shashaank
@Charlie all my GR lecture notes have the line “physics is independent of coordinates” in atleast each chapter
 
Charlie
Charlie
Yeah unfortunately blanket statements like that can be found in even the best textbooks
 
ACuriousMind
ACuriousMind
that's another word game, "independent" can mean a lot of things :P
 
Charlie
Charlie
A huge issue I have with learning physics is that a lot of the material (especially in more advanced topics like GR or QFT) assume significant familiarity with the "colloquial" language
And it seem like something you either love or you hate
 
ACuriousMind
ACuriousMind
@Charlie that's where sitting in an actual lecture and being able to annoy the lecturer with questions about that helps ;)
 
Charlie
Charlie
6:43 PM
Very true :P
 
ACuriousMind
ACuriousMind
I don't think I would've had the patience to learn physics from books
 
Charlie
Charlie
I've always had a distrust for lecture notes and opted to read books instead, which in hindsight probably comes from chemistry lecture notes being unsatisfying
if you think colloquial language obfuscates physics, chemistry will drive you insane
 
ACuriousMind
ACuriousMind
I have some idea about that :P (my parents are chemists by training, though not university-trained)
 
Charlie
Charlie
I guess it's the price you pay for working at a higher level of abstraction, there are so many variables at that point that it's hard to have precise terminology
I remember struggling to understand what "crashing out" a solid meant and I just googled it and found the exact reddit post I made 4 years ago in my quest to find out what it actually meant because it was never explained
good times
 
bolbteppa
bolbteppa
I think I would melt if I picked up a basic chem book and tried to make sense of it again
 
Slereah
Slereah
6:51 PM
I have one
It's not too hard but no way am I remembering all that
 
ACuriousMind
ACuriousMind
@Charlie well, at least you're consistent in what you don't understand ;)
 
Charlie
Charlie
It's funny I actually googled the exact title of the post too so apparently my brain hasn't changed much in 4 years :p
 
bolbteppa
bolbteppa
I remember what a cyclohexane is, so that's something
 
Charlie
Charlie
Probably the best example of confusing terminology is chemical names, there's a standard naming system (the IUPAC system) that names things systematically. And then there's the million other names people have for each compound that they use instead
 
Shashaank
Shashaank
7:07 PM
And here I am still stuck thinking what did @ACuriousMind meant precisely by saying that “independent” had different meanings in the context what Charlie said and what I said
Btw @ACuriousMind which of the three 1) MTW, 2) Wald, 3) Weinberg did you find the best
There is recently another good one by Padmanabhan
 
ACuriousMind
ACuriousMind
if you mean the GR books, I haven't read any of them :P
 
Shashaank
Shashaank
Oops then where did you learn it from initially
Any other people here, which of the 3 did you like
 
Slereah
Slereah
It depends what you want to do
Weinberg is probably best for doing down to earth GR stuff
 
Shashaank
Shashaank
@Slereah and for black holes
 
ACuriousMind
ACuriousMind
I didn't know there was GR stuff down here on earth
 
Shashaank
Shashaank
7:13 PM
Weinberg doesn’t write a word about them
 
Slereah
Slereah
All GR books talk about black holes
@ACuriousMind How do you think apples fall
 
ACuriousMind
ACuriousMind
@Slereah fairies
flying above us, pushing everything down with their wings
 
Shashaank
Shashaank
@Slereah not weinberg
 
Slereah
Slereah
Ah well
idk, Carroll?
It's a standard introduction
 
ACuriousMind
ACuriousMind
we have a res. rec. question with lots of good answers for GR here
 
bolbteppa
bolbteppa
7:15 PM
 
Shashaank
Shashaank
I am afraid to pick up Wald
 
bolbteppa
bolbteppa
Those videos are a good reason to go with the Paddy one
 
Slereah
Slereah
Wald is probably not best for an introduction
 
Shashaank
Shashaank
Yes this guy Paddy has really a very good book
 
 
2 hours later…
fqq
fqq
9:01 PM
I really like Wald but I agree it's probably not the best introduction
I like the maths parts, the appendices etc though
 
Slereah
Slereah
9:24 PM
tbh I have read a lot of GR, and the notion of general covariance doesn't come up that much
They will bring it up once in a while but it's never particularly useful
 
Charlie
Charlie
10:16 PM
Am I understanding this correctly, if we say that operations like normal and time ordering "act on symbols not operators", we mean that there is no expectation given, say, $\mathcal T\{\hat O\}$, that the time ordering can be "undone" using commutation relations. And that anything written inside of a time ordering operator is strictly to be interpreted as "nicer notation" for the correct expression
Maybe the tl;dr is that anything goes under the time ordering "operator" since everything is assumed to commute in the interest of tidier looking notation
 
ACuriousMind
ACuriousMind
@Charlie if it could be "undone" using commutation relations, then $\mathcal{T}(\hat{O}) = \hat{O}$ would hold, no?
but this is not the case - normal ordering and time ordering change the operator to something different if it was not already written in that order
 
Charlie
Charlie
10:43 PM
Yeah I guess so, I guess I can live with it
 
Ryan Unger
Ryan Unger
what is general covariance
 
bolbteppa
bolbteppa
11:35 PM
2
Q: Meaning of general covariance

yjcQuoting from Wald's GR: In the context of special relativity, the principle of general covariance states that the spacetime metric $\eta_{ab}$, is the only quantity pertaining to spacetime structure which can appear in any physical law. What other quantities "pertaining to spacetime structu...

general-relativity spacetime metric-tensor covariance
This discussion above has certainly confused me, what's the difference between Newton and Einstein if everything can be made covariant in the earlier discussion...
 

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