uh, you cannot go faster than the speed of light, thus there is no way to arrive earth before a year even when travelling arbitrarily close to the speed of light
What's there to reconcile? Your journey takes a day in your frame, and (more than) a year in Earth's frame.
All the while, the light signal stays ahead of you, and in your frame, arrives in less than a day on Earth (which is consistent with the constant speed of light because the distance to Earth is length contracted from your POV)
@Phase There's no spooky stuff, just poorly explained stuff ;)
Once you grok SR, you'll realize all these paradoxes and thought experiments are a really poor way to teach it, yet oddly enough we insist on doing so :P
@Phase Ah, well, I haven't read it but from what I've heard of it I suspect it's not a good introduction to SR if you don't know the basis from somewhere else.
Since I haven't read it you probably shouldn't give too much on my suspicion, though
@ACuriousMind if you take a spacetime basis, like a = (1,0) and b = (0,1), and have that be a 'stationary' co-ordinate system, applying the lorentz transform to the space will result in a new orthonormal basis that isn't euclidean-ly orthogonal, but is according to g, right? But how does this actually transfer into a quantity being changed if there's a vector / path in the space before the transform? I'm struggling to really imagine how to use it.
if its a poorly formed question feel free to tell me
@Phase No quantity is being changed. In this 2d example, given a vector $v$, you can expand it as $v = v_a a + v_b b$. If $a$ is space-like and $b$ is timelike, then that means $v$ has "length" $v_a$ and "duration" $v_b$ from the viewpoint of this frame. After the transform to a basis $a',b'$, you get different $v_{a'}$ and $v_{b'}$ - this is length contraction and time dilation, respectively. But $v$ hasn't changed, just the basis you express it in.
I've heard people talk about the "frame of reference of light", but wouldn't that mean defining a space where you have two parallel lines that are orthogonal to each other?
@SirCumference: 0celo7 doesn't like me saying this, but the best way to understand SR is to treat it as SR i.e. start with the Minkowski metric. Once ou've grasped that underlying principle it all starts to become clear.
My thing with SR is that the things that are interesting in SR are not so interesting in GR, or actually just impossible to study, so it's a pretty different subject.
@SirCumference from personal experience I'd say there's a time when you realise you actually understand SR (or whatever) and that realisation is a wonderful feeling and worth all the pain leading up to it.
@JohnRennie I seldom get that feeling because I never have enough time to think about the material. Contrast with math, which is much slower and gives me time to truly think about the stuff and draw connections. I feel that sense of satisfaction far more in math...
Though I'd probably feel the other way if I were a math major
@SirCumference Hmm, OK, the first year is generally the year they really rush you because they need to get all the basics done. It should be calming down a bit now.
Try looking back at some of the coursework you did in the first year. I bet you'd find it pretty easy now.
@SirCumference When you're learning a new subject it always a bizarre mess at first because it takes a while for you to mentally assemble all the parts and get the big picture. This is entirely normal.
You'll find that with time the stuff you found really hard at first starts to seem simple.
I am a materials science graduate and I wanted to learn statistical physics. Are there any good problem banks online that I can solve to get better at it. Also it would be convenient if the problems were labelled according to difficulty.
We tried to create a Physics homework site on Stack Exchange, but the Stack Exchange admins wouldn't let us. The QandA site was created by one of our members, Kenshin, after our attempt to create an SE site failed. It was deliberately designed to be as close to the SE as possible.
@Abcd Looking at the users page, there only seems to be around 50 or so actual active users...
@SirCumference I certainly haven't done GR to the same 'mathematical detail' as @0celo7 but my experience is the same as his - SR's much harder than GR
@0celo7 It's probably a better desk than my office desk - They still haven't given me my computer yet :(
What are special text codes that must be written to generate various mathematical formulae, symbols like limit, derivative, integral, closed integral etc. (in simple keypad)
For instance, "**" for italics etc.
@JohnRennie I have been thinking about evaporating BHs and infalling particles (or persons) and I found the exact doubt that has been bugging me as a comment of yours on an old question.
"An external observer sees the black hole evaporate in a finte time, but the same observer measures an infinite time before the infalling particle reaches the event horizon. That means the observer will see the black hole evaporate before the particle crosses the event horizon. Is this true, or are my assumptions wrong?"
@JohnRennie yeah. i have to say, you'd probably be wasting your time there - the site doesn't have a lot of the features SE has and moderation isn't enforced very well. it's basically become a copy-paste homework site, i feel like.
@ACuriousMind Academic bullshit: People citing a preprint but the actual published paper doesn’t even mention the result.
I swear my advisor thinks I’m a retard because I can’t find the theorem in this paper he read when he was in grad school. I’m pretty sure he read a preprint!
In any case, it seems the issue is a lengthy backlog due to too few reviewers: If more than one of the regular reviewers skips a review or votes to leave open while the rest votes to close, questions are likely to hand around for rather long in the queue
@Dvij the Hawking radiation calculations have all been done using various approximations, because we don't have a theory of quantum gravity. Typically the calculations assume a fixed background. That means they don't actually describe the evaporation of the black hole - they just tell you what the radiation would be at a moment in time.
Beall's List sometimes overshoots, though it's a good starting point.
I wouldn't say publication there will automatically hurt your admission chances, as especially if you're very junior I'd actually assume you had been naive. What it likely won't do is help all that much - predatory or not, it'...
@Dvij So when you start asking about what happens to observers falling in, and seeing the black hole evaporate before their eyes, there are no rigorous calculations that describe this process.
I have this following theorem: Suppose $K \subset V$ is a polyhedron of codimension $\geq 1$ and $\omega$ a $k$-form. Then there exists an arbitrarily $C^0$-small diffeotopy $h_t : V \to V$ such that $\omega$ can be $C^0$-approximated near $\tilde{K} = h_1(K)$ by an exact $k$-form $d\alpha$.
@Dvij: my own best guess is that an event horizon never forms. That is, the infalling star (or whatever) evaporates before it can form a true horizon. But it's only a guess. I don't think anyone has a really good description of the process.
@JohnRennie I am just spitting the stuff out but wouldn't Vaidya metric do any good? They describe non-static background for an evaporating BH I think.
@Dvij I think the Vaidya metric is actually stationary, though I wouldn't swear to it. In any case it would provide a good description of an evaporating black hole.
@JohnRennie Btw, I am not sure whether it is related to this or not but I am thinking about another (to me) interesting situation about BHs. Could it happen that a BH is sufficiently small so that it evaporates so fast that nothing can fall into it even in the falling person's proper frame? I think addressing this question even more pressingly requires a non-static calculation of evaporating BH metric. Not sure.
@0celo7 This traces back to the holonomic approximation theorem, actually. Try to approximate the formal 1-jet section $J(x, y) = (x, y, 0, -y, x)$ over the circle by holonomic 1-jet sections
You end up approximating the non-conservating field $(-y, x)$ to conservative dudes
@sammygerbil I have to say that I consistently find your comments on questions you consider sub-par, like the one here, to have an aggressive and antagonistic tone that is completely uncalled for, particularly with new users. This is magnified when you are wrong (as in this case - your comment implies that it is obvious that the air pressure inside an airtight box cannot change, when in fact it's quite the opposite) but even if you're right, there are better ways to express it. — Emilio Pisanty12 secs ago
@0celo7 The claim becomes that you can approximate the restriction of the map $J : U \supset S^1 \to U \times \Bbb R \times \Bbb R^2$ to an nbhd $V$ of the perturbed circle in the $C^0$ norm by something of the form $J' : V \to V \times \Bbb R \times \Bbb R^2$, $J'(x, y) = (x, y, f(x, y), Df(x, y))$, right?
But then you'd have to have a $C^0$ approximation of $(-y, x)$ on $V$ by $Df(x, y)$'s
And you can similarly argue by doing path integral along the perturbed $S^1$
What are special text codes that must be written to generate various mathematical formulae, symbols like limit, derivative, integral, closed integral etc. (in simple keypad)
For instance, "**" for italics etc.
