@0celo7 If someone makes an attempt to calculate something and gets stuck then that is a legitimate question for this site. There are many books online, but you learn mostly from doing the hard exercises in the books. I've noted that there are quite a few teenagers between the ages of 14 and 18 here studying advanced subjects and getting help with problems here. Some of them may already be studying at university, but most children who are way ahead in physics will not be able to go to university (e.g. they may not be far enough ahead in all other subjects). — Count Iblis2 mins ago
Uh, getting stuck in a calculation is still off-topic.
So I'm not quite sure how the theory deals with CTCs
I recall from that guy's comment that the causality of PDEs depends on the "principal term", whatever that means, and that for scalar fields that is $\approx \partial_\mu \partial_\nu \phi$, which in that theory would depend on the $h$ field
I was reading the quite nice answer of QMechanic on the topic of compact support tachyon fields not propagating faster than light, but this case is a rather simple one, free scalar field in flat space.
Are there any more general theorems on this? Let's say, for a field transforming under the ta...
@Slereah: I think you should somehow include the elaboration here into that question. I see now what the issue is, but it wasn't really clear to me from just reading your question.
"We now derive the full Einstein equations, on the basis of the same self-coupling requirement, but with the advantages that the full theory emerges in closed form with just one added (cubic) term, rather than as an infinite series, and that no special 'gauge’ such as gμν,ν = 0 need be introduced."
@ACuriousMind You'll find this interesting. Prof Denzler asked me the other day why physicists are so interested in the square of the curvature of a bundle :D
"For the conversion of boundary problems into initial value problems we shall be concerned only with that small fraction of the general theory which deals with first-order partial differential equations with the same principal part"
@Slereah It's funny how you can find statements covering the whole range from "GR is a gauge theory" to "GR is very much like a gauge theory" to "GR is a bit like a gauge theory, but fundamentally different" to "GR is not a gauge theory"
@0celo7 Huh? How does it not matter? Is the end of that bar perfectly reflective, i.e. does the block just bounce off the left wall if it is going toward it?
"Quasilinear equation, a type of differential equation where the coefficient of the highest order derivative does not depend on the derivative of the unknown function"
"An equation is called semilinear if it consists of the sum of a well understood linear term plus a lower order nonlinear term. For elliptic and parabolic equations, the two effective possibilities for the linear term is to be either the fractional Laplacian or the fractional heat equation. "
@0celo7 Okay, still, what does "the sign doesn't matter" mean? If the block goes to the left, it just crashes into that wall. If the block goes right, it stretches the spring until it is stopped and then reverses direction, crashing into the wall.
Oh!
Do you mean it is unintuitive that the velocity with which it hits the wall is independent of the initial sign of the velocity?
I agree with you it is somewhat unintuitive, but, well, it's the case - the only energy in that system is the initial kinetic energy and the tension of the spring, and both of these are independent of the sign of the velocity, so the final energy with which the block hits the wall is also independent of it.
This is why I always tell people not to trust their intuition
Introductory mechanics at the sophomore level continues to have corners I hadn't fully appreciated. Taught myself something tonight and now I'm bouncy.
@0celo7 Yeah, FNAL announced that they didn't want people showing up unannounced at the gate anymore last year. You are suppose to have contacted the user office at least two weeks in advance to arrange a temporary (just for getting to the badge office) pass. Or something.
OK. So get the neutron people to call the user office and complain. They are already on the inside so they can get some action more easily than you can.
I was downvoted on the issue earlier today, so I've been thinking carefully. Trying to decide if I might be wrong (though that would mean Goldstein was wrong too).
@0celo7 To make sure you're awake and appreciate the difference.
That or they are engineers and believe in pounds-mass or something.
hmm, @ACuriousMind, in that problem above, is the work due to the spring if the mass moves right by $s$ just $-\frac{1}{2}ks^2$...or do you have to take the angle into account somehow
The problem I just posed is first semester stuff. The students I teach the related material to wouldn't know a tensor if it bit them in the butt, and won't reach that level for a couple of years at a minimum.
Any way, step one is to roll a wheel down the hill (without slipping) and show by that means that the rotational kinetic energy must be accounted for in the W-E theorem. (This is all external forces; to wit gravity.)
Step two is to consider a rotating symmetric system which pulls some of it's mass closer to the center causing a speed up and change in rotational KE. (These are all internal forces.)
I was reading the quite nice answer of QMechanic on the topic of compact support tachyon fields not propagating faster than light, but this case is a rather simple one, free scalar field in flat space.
Are there any more general theorems on this? Let's say, for a field transforming under the ta...
