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ACuriousMind
ACuriousMind
12:05 PM
@DanielSank That's a generous (and hopefully delicious ;) ) offer! I'd like that :)
 
Slereah
Slereah
A rather rude title
@Secret How do you define the volume if not with the geometry?
 
user116211
Sounds like written by Lumo in disguise.
 
heather
heather
what is that book about?
 
ACuriousMind
ACuriousMind
@heather I'm guessing it's about how THERE WILL BE NO PHOTON ROCKET ;)
How did you find that, @Slereah?
 
heather
heather
@ACuriousMind, well, I was asking because I'm not sure what that is.
 
Slereah
Slereah
12:13 PM
I was looking for a book by another Smilga
 
ACuriousMind
ACuriousMind
@heather I have not the faintest clue what a photon rocket is, either
 
Slereah
Slereah
 
heather
heather
@ACuriousMind, it appears a strange idea:
Photon rocket
A photon rocket is a hypothetical rocket that uses thrust from emitted photons (radiation pressure by emission) for its propulsion. Photons could be generated by onboard generators, as in the nuclear photonic rocket. The standard textbook case of such a rocket is the ideal case where all of the fuel is converted to photons which are radiated in the same direction. In more realistic treatments, one takes into account that the beam of photons is not perfectly collimated, that not all of the fuel is converted to photons, and so on. A large amount of fuel would be required and the rocket would be a...
The wikipedia article cites that book! =P
 
Slereah
Slereah
Photon rockets are somewhat attractive because you don't really need to bring fuel on board
but they're pretty inefficient
 
Secret
Secret
@Slereah Well take the most common demonstration of an expanding universe, before and after the balloon is blown up, the surface area of the balloon actually increases as the galaxies on it become further apart. But is this what is really happening in the real thing, that there is literally more space between two objects, or that the whole thing (assuming we are still at some earlier history in the universe where it is of finite size) has the same spatial volume except the geometry curves so that some points become more further apart because of the curvature?
 
Slereah
Slereah
12:16 PM
Well no
Don't take the analogy
Because the analogy isn't what we do
 
heather
heather
quantum mechanics by landau and lifschitz - would I be able to get through it? (assume for the moment that I have learned basic calculus, because I am in the process of learning it currently)
 
Slereah
Slereah
Basic calculus is a bit light to go there
I mean it's not too bad
 
ACuriousMind
ACuriousMind
I don't think L&L are a good place to start any subject, at least judging by what I've heard about them
 
Slereah
Slereah
Landau doesn't even talk about Hilbert spaces
But it still has a lot of math
 
heather
heather
oh, okay. especially considering I don't really know much about quantum mechanics, sounds like a poor idea. but then, would shankar be okay (again, once I learn basic calculus)?
 
Sanya
Sanya
12:21 PM
@heather Shankar will probably be an easier start than Landau Lifshitz - those latter books are a bit of a religious matter
 
user116211
@heather It works greatly as a reference book when you know already the content. It's not a book to learn anything from for the first time.
 
heather
heather
@MAFIA36790, Shankar is, or Landau/Lifschitz is a reference book?
 
Sanya
Sanya
I tend to like them but they are a bit lacking in mathematical depth and their structure is often ... peculiar
 
user116211
L&L.
 
rob
rob
Heh, a photon rocket question was one of the first things I answered here.
4
Q: Rocket propelled by a giant monochromatic laser

physguyI am preparing for my quals and stumbled across the following problem, and although it only requires undergraduate-level physics, I feel I can't piece everything together. "A rocket of mass $m_0$ is propelled by a giant monochromatic laser mounted on the back of the rocket. The laser emits a bea...

homework-and-exercises special-relativity laser rocket-science
 
heather
heather
12:22 PM
ah, okay. Sounds like shankar is a much better choice.
 
Secret
Secret
@Slereah In the FLRW metric, the scale factor which keep track on the comoving distance of two objects increases for an expanding universe. How to interpet that, if the balloon analogy is inaccurate, then it means the scale factor is not really a measure of the spatial volume of the universe. Then if it is not the volume, what is being increased that lead to objects became further apart?
 
Slereah
Slereah
Define "volume"
The distance between two stationary points in the FLRW metric will increase, if that's what you want to know
Distance defined independantly from coordinates by a two way light beam
 
heather
heather
^looks pretty cool, and the preview intrigues me even further...
 
Jim
Jim
@Slereah Define "define"
 
user228700
@MAFIA36790: It looks like an identity relation is defined even when all $x$ belonging to $A$ are not included. Secondly, this is true for symmetric and transitive relations too. The only relation in which it is absolutely necessary to have all possible ordered pairs $(x,y)$ is the reflexive relation.
 
user228700
12:29 PM
Correct or not?
 
Slereah
Slereah
Well the volume is only defined up to a foliation
and it depends on the geometry
So I'm not sure what he's asking
 
Jim
Jim
@Slereah Incorrect. Define: state or describe exactly the nature, scope, or meaning of.
 
Slereah
Slereah
You're cruising for a bruising, Jim
 
Jim
Jim
always
I'm always cruising for a bruising
 
heather
heather
@Sanya, do you know any good introductory general relativity books?
 
user228700
12:32 PM
@heather Omg.
 
Jim
Jim
@heather Spacetime and Geometry, by Sean Carroll
 
heather
heather
@Jim, how much math does it require?
@Kaumudi, what?
did I say something offensive? if so I apologize!
 
Jim
Jim
@heather if you're asking that question, there doesn't exist an introductory general relativity book for you. GR is all heavy math
 
heather
heather
@Jim, what level of heavy math? I guess I just need to get an idea of what I need to learn.
 
Jim
Jim
advanced calculus, PDEs, basic tensors
 
Secret
Secret
12:35 PM
I think volume can be defined using the metric tensor in a pseudoriemannian manifold. Using each of the 4 coordinate (something), a 4-volume form can be constructed from the metric tensor, which can be integrated over the region of the manifodl to give a notion of the volume of a manifold

So suppose I have a square region of minkowski spacetime, and two events A and B some spacetime interval apart. Now the spatial components is being expanded uniformly at the midpoint M of A and B (this would end up curving the spacetime in the vicinity of M, The spacetime interval of A and B should increa…
 
Jim
Jim
it will cover manifolds, sets, and groups (I think) briefly, but it doesn't hurt to know them
 
user228700
@heather Lol, no. I was just taken by surprise.
 
user228700
@MAFIA36790: Nvm.
 
heather
heather
@Jim, oh, geesh. okay, I certainly don't know advanced calculus, partial differential equations...I don't even know what the last thing is. I know a bit about set theory, and a tiny bit of manifolds thanks to 0celo7, but otherwise, I'm thinking I probably should learn some of that stuff. =P
 
Sanya
Sanya
@heather no; but I would stick to mechanics, quantum mechanics, electrodynamics and statistical mechanics first - once you feel comfortable with that, you can go and explore field theories and GR
 
Jim
Jim
12:37 PM
Carroll does a good job introducing the harder maths, but be prepared to be confused at first. It also introduces einstein tensor notation, I think, so you might be able to get away without knowing much tensors
 
Sanya
Sanya
even if I realise the attraction the latter two might have
 
Slereah
Slereah
I prefer Callahan for a soft intro to GR
 
Jim
Jim
@Slereah how rigorous is it?
 
Slereah
Slereah
It's alright
 
heather
heather
@Sanya, okay. I was asking because Christmas is coming up (and my mom is already asking me what I want - !), so I was looking around for various books and such. =)
 
Slereah
Slereah
12:38 PM
It spends a lot of time on extrinsic curvature as a pedagogical example
 
Jim
Jim
which is probably good, because that's a tough concept to get without lots of practice
 
heather
heather
@Jim, I see. I'm looking at the amazon preview to get an idea.
 
Jim
Jim
@Slereah what's the title of the book? I feel like giving it a look through
 
user116211
@Slereah The picture book by Callahan?
 
user116211
His Multi. Calc is full of pics.
 
Sanya
Sanya
12:40 PM
@heather I see the point ... well, if I was beginning my studies again I'd actually spend 2 years doing only math, so I'd first go shopping in that department :D
 
user116211
We don't need pics for mathematics. Huh!
 
Jim
Jim
@Sanya Yeah, that's good advice. I wish I'd done that. Too bad it's just so darn unappealing
 
heather
heather
@Sanya, hmm, yeah. I should probably start looking into those as well. (my mom is going to laugh so hard at my list, because it is going to be all books) =D
 
Slereah
Slereah
@Jim The geometry of spacetime
 
Jim
Jim
cool, thanks
 
0celo7
0celo7
12:43 PM
Why not just read Hawking Ellis? It just requires basic calculus and algebra.
 
heather
heather
@Slereah, I'm looking at the amazon preview, and it looks like it might be managable.
 
user116211
You should start reading set theory.
 
Sanya
Sanya
@Jim that depends on the perspective ... if the university had let me ditch all those experimental physics lectures and labs in exchange for more math, I'd have been in. It's only a problem once you go out of university and no one is interested in the theoretical stuff anymore
 
Slereah
Slereah
No start by reading logic
 
heather
heather
@0celo7, what is the title?
@MAFIA36790, set theory book recommendation...?
 
0celo7
0celo7
12:44 PM
There is only one Hawking Ellis.
 
user116211
I will not say Jech; go with Naive Set Theory by Halmos.
 
heather
heather
@0celo7, large scale structure of spacetime?
 
Jim
Jim
@Sanya True. If I had been able to do that in undergrad, I would have. Unfortunately I though it best to choose some core physics courses over advanced math
 
user116211
Next study Calculus; Apostol as I said earlier.
 
heather
heather
@MAFIA36790, right, that makes sense.
 
Sanya
Sanya
12:46 PM
@Jim I didn't have any choice anyway ... And honestly, at the end, I'm pretty disappointed by my study plan/lecture contents insofar as we never actually hit the interesting stuff :/
 
heather
heather
@0celo7, I think I could maybe make it through if I had a set theory book handy for some of the notation. (hawking and ellis, I mean)
wait, actually, it has partial differential equations @0celo7...
 
0celo7
0celo7
What does?
 
ACuriousMind
ACuriousMind
@Sanya I do think that those labs and at least some of the experimental lectures are things any physicist should have done at least once.
 
user228700
Hey @MAFIA36790: Division is not a function? (I'm sorry for pinging you :/)
 
Secret
Secret
@Kaumudi Of all reals, one number cannot be mapped by division
 
Sanya
Sanya
12:48 PM
@ACuriousMind of all the people I'd have expected to contradict me there, you'd have been the last
 
0celo7
0celo7
@heather the preface says you need basic calculus and algebra
 
user116211
You have the definition of function; see if it is valid for the division operation and your concerned domain and range.
 
Sanya
Sanya
anyway, yeah, some, maybe
 
ACuriousMind
ACuriousMind
@Kaumudi That depends - from which source to which target is it supposed to be a function?
 
Sanya
Sanya
not the whole load of wasted time we went through though
 
user228700
12:49 PM
@Secret Do u think u could explain it to a person who just graduated high school?
 
user228700
@ACuriousMind Defined on $R$.
 
heather
heather
@0celo7, Hawking Ellis has partial differential equations in the first chapter
 
Slereah
Slereah
also topology
 
0celo7
0celo7
It does?
What's the PDE?
 
heather
heather
in the chapter about differential geometry
 
Secret
Secret
12:50 PM
@Kaumudi Simplest explanation, 0 times any reals (including itself) is zero, division reverses this, but if any number times 0 give 0, is it possibel to reverse it to a unique number?
 
ACuriousMind
ACuriousMind
@Sanya I know - I'm all for more math, but I'm not for less of the labs and such because I've known many people who thought they were going to be theorists and then ended up doing more experimental things anyway, and that would have been a lot more difficult without the mandatory experimental part
 
user116211
@0celo7, Bourbaki says in his preface one doesn't need any mathematical background to read the book.
 
user116211
Because his book is the mathematics? Anyways, but that doesn't mean one can learn things from it for the first time.
 
user228700
@Secret Hm, no...OK, thanks! :-)
 
0celo7
0celo7
Bourbaki is not a he
 
user116211
12:51 PM
They; I know.
 
Sanya
Sanya
@ACuriousMind I've done experimental work in my thesis - I don't think any of the labs greatly prepared me for that, to be honest
so I'm not too sure of that argument
 
0celo7
0celo7
@Sanya what year are you, anyway
 
ACuriousMind
ACuriousMind
@Sanya It...might be highly dependent on the kind of tutors you get
 
Sanya
Sanya
@0celo7 graduated
 
0celo7
0celo7
@ACuriousMind tutors?
 
heather
heather
12:53 PM
@0celo7, the PDE is $(\frac{\partial f}{\partial t})_\lambda\mid_t = \lim_\limits{s\rightarrow 0} \frac{1}{s}\{f(\lambda(t+s)) - f(\lambda(t))\}$
 
Sanya
Sanya
@ACuriousMind I'd guess; the point is just - our labs in physics were always perfectioned and you just had to go through the motions of starting the measurement machines or similar - that's not how experiments work
 
ACuriousMind
ACuriousMind
@0celo7 The people who supervise the labs
@Sanya Hmmm, true, some of the labs were like that
 
heather
heather
@0celo7, except the first $\lambda$ is right next to the tall line, down at the bottom like $t$.
 
0celo7
0celo7
Is that a mistranslation
 
Secret
Secret
FYI: The most fundamental reason why all extensions of the reals (which must be at least one side distributive) does not allow division by zero is the same reason why $0+0=0$
 
0celo7
0celo7
12:55 PM
@heather that's not a PDE
It's the definition of the derivative
They don't even assume you know calculus in HE
 
ACuriousMind
ACuriousMind
Stop trying to get her to read HE, @0celo7 :P
 
heather
heather
@0celo7, seriously? Oh, oops.
 
user116211
Before starting HE, better read Munkres and Kelley.
 
heather
heather
@MAFIA36790, I didn't realize there were two volumes to Apostol, cool! Munkres and Kelley...okay (my list is growing =)
 
Sanya
Sanya
@ACuriousMind if you'd give people time, measurement devices and a task and let them think through it by themselves, figure out what to do - that would actually be a lot more helpful (and more fun) - thing is just, it takes even more time and it is harder to supervise and well ... our department was overcrowded anyway
so better get them through quickly
 
Jim
Jim
12:58 PM
@Secret Yeah, I'm pretty sure that $f(x)=1\over x$ is considered a function. Just because it doesn't map each input from the domain of all reals to exactly one output, doesn't mean it isn't a function. You can define it over the domain of all numbers other than zero and it satisfies even the strictest definition of "function". Although, many say that even with zero included it is considered a function
 
heather
heather
@MAFIA36790, wait, what is the title (for Munkres and Kelley)?
 
ACuriousMind
ACuriousMind
@Jim It's not a function in the formal sense if you include 0 in the inputs.
That people sloppily may talk about it as a function on the reals doesn't make it one
@Sanya I fully agree with that
 
Secret
Secret
@Jim The thing is kamudi's example the domain is all reals, and f(0) does not map to anything. But a function must have all elements in its domain to be mapped to something that is not empty (If I recall what Munkres said)
If we restrict the domain to the usual $\mathbb{R}/ \{0\}$ then f is a function
 
Sanya
Sanya
@ACuriousMind in the end it all boils down to the fact that we need a real academic university again - people spending 10 years before graduating, free of financial pressure or anything else; a place for a small number of people deattached from reality and time limits
 
Jim
Jim
It's a function plus or minus one element in its domain
the uncertainty covers it
 
0celo7
0celo7
1:03 PM
I like how @heather has only math books on her list
 
heather
heather
@0celo7, well, actually...um, I also have shankar's principles of quantum mechanics, nielsen and chuang's quantum computing and quantum information, and a few others in that field.
 
0celo7
0celo7
Did I tell you to put Shankar on there?
NC is Daniel's doing
@ACuriousMind :(
 
Secret
Secret
@0celo7 , @acuriousmind, @Slereah
Define the 4-volume form using the metric tensor in a pseudo-riemannian manifold $g$. Using each of the four coordinate forms which is specific for each point in spacetime, a 4-volume form can be constructed from the metric tensor $$dV=\sqrt{|g|}dx^0dx^1dx^2dx^3$$ dV can then be integrated over some region of the manifold to give a notion of the volume of a manifold. Suppose I have a square region $\omega$ of minkowski spacetime, and two events A and B some spacetime interval apart. Now the spatial components is being expanded uniformly at the midpoint M of…
 
user116211
@heather Yeh, 1 is on analytic geometry and one-variable calc; other is an intro to linear algebra and Multi-variable calc.
 
user116211
@heather Both are on general topology.
 
heather
heather
1:10 PM
@MAFIA36790, which would you say is more accessible, munkres or kelley?
 
user116211
Munkres.
 
heather
heather
okay, thanks!
 
user116211
It has many examples and his language is very lucid.
 
Secret
Secret
Munkres has a touch of order theory in the Ch. 1, which is very useful in getting your head around those homomorphism related proofs
 
user116211
So does Kelley.
 
user116211
1:12 PM
But his definitions are weird.
 
heather
heather
@0celo7, I've gotten three recommendations for a general relativity book: Spacetime and Geometry by Sean Carroll, The Geometry of Spacetime by James Callahan, and Hawking Ellis. now I'm debating which one. =)
 
user116211
I would advice to stick to mathematics first; strengthen your maths concept and then you are free to read any physics.
 
heather
heather
@MAFIA36790, okay. So to summarize the current list of math books, Halmos for Set Theory, Apostol I and Apostol II for calculus, and Munkres for topology.
 
user116211
@heather Good!
 
heather
heather
@MAFIA36790, any other fields of math =)
 
user116211
1:16 PM
Yes, you should do some geometry.
 
user116211
Analytic Geometry.
 
user116211
Solid analytic Geometry.
 
user116211
Projective Geometry.
 
user116211
I have no strong recommendation for these. However, you can check Adrian Albert; it's still in print, I guess.
 
Slereah
Slereah
I recommend
 
user116211
1:21 PM
There are other century old books; I don't think they are separately taught nowadays in any freshman curriculum.
 
heather
heather
okay. geometry. I'll check that out as well.
 
Slereah
Slereah
A good geometry book btw
 
Secret
Secret
is my refined question about volume making sense to anyone?
 
Sanya
Sanya
1:53 PM
0
Q: Equations of motion for a vector field

slothwayneCurrently working through some exercises in quantum field theory, however I'm completely lost with this problem. Let $L$ be a Lagrangian for for a real vector field $A_\mu$ with field strength $F_{\mu\nu} = \partial_\mu A_\nu - \partial_\nu A_\mu$, gauge parameter $\alpha$, and external curre...

homework-and-exercises electromagnetism lagrangian-formalism gauge-theory variational-calculus
is that acceptable? In the end, the answer boils down to "use the E-L-eqs" if I see it correctly ...
 
ACuriousMind
ACuriousMind
@Sanya It's just a homeworky question asking someone to apply the E-L equations correctly for them, therefore off-topic in my mind. Not going to mod hammer it, it already has a close vote and I trust the reviewers will see it the same way.
 
Sanya
Sanya
@ACuriousMind ok, it came up in first post review and I wasn't sure about it
 
ACuriousMind
ACuriousMind
Well, if you're not sure, the proper action is to not vote to close it ;)
 
Emilio Pisanty
Emilio Pisanty
@heather nah, forget GR, just go for the full geometry shebang
gorgeous book
 
Sanya
Sanya
@ACuriousMind that's why I posted it here instead of flagging the post
 
ACuriousMind
ACuriousMind
2:00 PM
@Sanya Then again, below 3k your close flags only push things into the queue, and since this one already has a close vote (I know you can't see that), whether or not you flag this specific question as off-topic is completely irrelevant.
 
Emilio Pisanty
Emilio Pisanty
@ACuriousMind not completely irrelevant
 
Sanya
Sanya
yep, but as I don't see it, I assume it needs taking care of if I see it in the queue
 
Emilio Pisanty
Emilio Pisanty
it may well bump it to earlier in the queue
 
ACuriousMind
ACuriousMind
@EmilioPisanty It may?
 
Emilio Pisanty
Emilio Pisanty
@ACuriousMind not sure how the queue is ordered tbh
 
ACuriousMind
ACuriousMind
2:02 PM
Are you saying the amount of off-topic flags increases the priority of a review, or something like that?
 
Emilio Pisanty
Emilio Pisanty
it's a bit of a contentious issue
what with the train wreck that is SO review queues
or at least were
@ACuriousMind it's at least possible
 
ACuriousMind
ACuriousMind
I've not heard of that, but given the often arcane design decisions in the review system, I'd not be surprised
 
Emilio Pisanty
Emilio Pisanty
@ACuriousMind it's also possible that the queue ordering system has changed over the years
it's quite reasonable to put something with a large number of flags higher up the queue
or at least something with a higher flags-to-views ratio
This one is good for morale, though, when you think the close review queue is just too long
currently at 10% of its historical record
 
Sanya
Sanya
9k O_O
 
Emilio Pisanty
Emilio Pisanty
@Sanya precisely
 
Sanya
Sanya
2:06 PM
I am doing something wrong here ... every time I tell people to elaborate on their first questions, add some details, I get comments as answers
no one seems to understand that there is an edit option
 
Emilio Pisanty
Emilio Pisanty
@Sanya then make it clear that you want them to edit
 
Sanya
Sanya
probably necessary, yup
 
ACuriousMind
ACuriousMind
@Sanya They are probably used to forums/imageboards and just think responding to your comment is the proper course of action. Getting used to SE precisely not wanting threads to look like conversations takes a bit of time
2
 
Emilio Pisanty
Emilio Pisanty
highest I can find on the wayback machine
it was a big thing at the time
433
Q: Let's burn down the close queue!

Shog9 Stage 2 completed: The initial phase of the burndown was completed on 2014-03-03 10:48:49; the second phase completed on 2014-03-08 at 19:41. Detailed statistics on how these played out can be found on Phase 1 results and Phase 2 results. There remains much work to be done! You can find r...

discussion review vote-to-close
 
Sanya
Sanya
@EmilioPisanty at that point, I'd rather wonder whether the system of "peer-review" works
well, actually still with 9k
I'm happy PSE is not at that point
 
Emilio Pisanty
Emilio Pisanty
2:13 PM
It's just the humongous traffic on SO
It led to other problems too
with people breezing through the reviews just to get the badges
often with automated tools
 
0celo7
0celo7
what's poppin, people
 
Emilio Pisanty
Emilio Pisanty
so they ended up needing to put in audits to check that people weren't messing up
 
Sanya
Sanya
oh my ... well, let's keep fingers crossed for this small PSE then ...
 
Emilio Pisanty
Emilio Pisanty
@Sanya I find the prospect of PSE ever growing to the current size of SO highly unlikely
 
Secret
Secret
0celo7, is my volume question making sense to you?
Sanya, Emilo and ACM are discussing about people commenting and other PSE growth stuff
 
0celo7
0celo7
2:16 PM
I did not see it
 
Sanya
Sanya
@EmilioPisanty lack of interest (ed people)?
 
Emilio Pisanty
Emilio Pisanty
@Sanya have a look at the charts
PSE is at 92 questions per day
SO currently clocks 8k/day
that's a two orders of magnitude gap
 
0celo7
0celo7
lol
 
Sanya
Sanya
well, no one needs 8k physics questions per day :D
 
0celo7
0celo7
Holy shit, 2 Chainz mixtape, Meek Mill album, Jeezy album
crazy
 
Secret
Secret
2:22 PM
@0celo7
Define the 4-volume form using the metric tensor in a pseudo-riemannian manifold $g$. Using each of the four coordinate forms which is specific for each point in spacetime, a 4-volume form can be constructed from the metric tensor $$dV=\sqrt{|g|}dx^0dx^1dx^2dx^3$$ dV can then be integrated over some region of the manifold to give a notion of the volume of a manifold. Suppose I have a square region $\omega$ of minkowski spacetime, and two events A and B some spacetime interval apart. Now the spatial components is being expanded uniformly at the midpoint M of A and B (this would end u…
 
0celo7
0celo7
Orientable manifold I'm assuming?
 
Secret
Secret
yup orientable
 
0celo7
0celo7
What exactly did Slereah say?
 
Secret
Secret
> Define "volume"
The distance between two stationary points in the FLRW metric will increase, if that's what you want to know
Distance defined independantly from coordinates by a two way light beam
> Well the volume is only defined up to a foliation
and it depends on the geometry
So I'm not sure what he's asking
> Well no
Don't take the analogy
Because the analogy isn't what we do
Elaboration: By analogy ,he mean the balloon expansion demonstration
and the following is the original version of my question:
2 hours ago, by Secret
@Slereah Well take the most common demonstration of an expanding universe, before and after the balloon is blown up, the surface area of the balloon actually increases as the galaxies on it become further apart. But is this what is really happening in the real thing, that there is literally more space between two objects, or that the whole thing (assuming we are still at some earlier history in the universe where it is of finite size) has the same spatial volume except the geometry curves so that some points become more further apart because of the curvature?
3 hours ago, by Secret
@JohnRennie actually, in GR, when we said spacetime expands, does the volume of spacetime literally increase (as in spacetime was created between the two objects thus making them more far apart form each other), or the geometry curved in a way to give an impression of an increased distance between two points?
 
0celo7
0celo7
@Secret what does that even mean?
 
Secret
Secret
2:28 PM
I am guessing, because spacetime in general is curved, and the volume form depends on a set of coordinate forms, these coordinate forms can differ from point to point in a manifold (otherwise we won't need to do parallel transport related stuff and compute the connection coefficients). So in general the volume will depend on the curvature of spacetime at that point
 
0celo7
0celo7
@ACuriousMind !!! According to MO, $A\otimes B=0$ $\not\Rightarrow$ $A=0\lor B=0$!!!
why not?
$A\otimes A=0$ does not mean $A=0$ 0.0
 
John Rennie
John Rennie
 
ACuriousMind
ACuriousMind
@0celo7 Take $\mathbb{Z}\otimes\mathbb{Z}/2\mathbb{Z}$ as $\mathbb{Z}$-modules. Then $2\otimes 1 = 2(1\otimes 1) = 1\otimes 2 = 1\otimes 0 = 0$.
 
Slereah
Slereah
already gave that link
 
0celo7
0celo7
@ACuriousMind I don't know what any of that means. I'm only concerned with vector spaces over $\Bbb R,\Bbb C$.
 
ACuriousMind
ACuriousMind
2:33 PM
@0celo7 For vector spaces/over fields the implication holds. It fails only if modules can have torsion.
 
0celo7
0celo7
Module?
 
ACuriousMind
ACuriousMind
A module is a vector space over a ring, basically
Anyway, you can ignore all of this and be content that your implication does hold for vector spaces.
 
0celo7
0celo7
@ACuriousMind I'm sorry. I was trolling subconsciously.
I know what a module is
 
ACuriousMind
ACuriousMind
@0celo7 ???!!!!?!?!?!!?!?!
 
0celo7
0celo7
But I don't remember the tensor product of modules
I learned it, then quickly forgot
I only remember the one for vector spaces via the free vector space of a set
@ACuriousMind What is confusing?
@Secret No, volume is coordinate independent.
 
ACuriousMind
ACuriousMind
2:37 PM
That's not confusion, it is exasperation :P
 
0celo7
0celo7
The whole point is that $\omega=\sqrt{g}\text{stuff}$ is a tensor
@ACuriousMind Sometimes my personality randomly splits (pair production) and trolls. I can't help it
 
Sanya
Sanya
@0celo7 and you were the one who got really upset when being trolled yourself :o
 
0celo7
0celo7
trolls are vile
 
ACuriousMind
ACuriousMind
Oct 22 '15 at 1:12, by 0celo7
I'm a hypocrite
 
0celo7
0celo7
That wasn't me, nice try
@ACuriousMind Interesting thing: the derivative of a function is continuous on a dense set (of $\Bbb R$)
 
Secret
Secret
2:41 PM
Guys, just found something, I will have a read and see if it explains it:
Metric expansion of space
The metric expansion of space is the increase of the distance between two distant parts of the universe with time. It is an intrinsic expansion whereby the scale of space itself changes. This is different from other examples of expansions and explosions in that, as far as observations can ascertain, it is a property of the entirety of the universe rather than a phenomenon that can be contained and observed from the outside. Metric expansion is a key feature of Big Bang cosmology, is modeled mathematically with the FLRW metric, and is a generic property of the universe we inhabit. However, the model...
 
user116211
Sep 18 at 5:22, by 0celo7
@IceLord I have MPD.
 
0celo7
0celo7
It's a debilitating illness :(
I'm tired of being bullied for it
@ACuriousMind Did you ever lean this Baire category nonsense?
The terminology is fucked
A $G_\delta$ dense set need not be dense!?!?
And $F_\sigma$ meager is not meager!!?!
 
Physics Guy
Physics Guy
@EmilioPisanty That was a joke about him.
 
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