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May
17
comment Does Special Relativity Define a Number divided by 0?
@garyp not quite. Something's inertial frame is a way to refer to an inertial frame in which it's at rest (and at the origin), but my point is that there are legitimate senses in which light can have a rest frame--but that rest frame cannot be inertial!
May
16
comment Does Special Relativity Define a Number divided by 0?
@CuriosOne I wish more people would say instead, "light has no inertial reference frame", which addresses such questions directly anyway, yet avoid running afoul of, e.g. lightlike coordinates or null four-vectors in a frame field or tetrad.
May
16
revised Time to fall in a non-uniform gravitational field
added 462 characters in body
May
16
answered Time to fall in a non-uniform gravitational field
May
9
comment Could time dilation bend the path of a photon? Does time dilation have a refractive index?
I like this answer, but I'd rather say that the "same cause" is simply that different paths have different lengths (proper times), which is what's suggested by the prior sentences in this answer anyway. ... It's conceptually the same even with vanishing curvature.
May
4
comment Lenght contraction question
@gonenc yuh; I was just obliquely pointing that out. ;)
May
2
comment What is the uncertainty principle?
@Muphrid the differences are that (1) wavenumbers would have no role in that description at all, (2) even Hilbert space, the uncertainty principle is more general than square-integrable functions. So I was recommending that context of your answer to be be explicitly specified. If you don't agree, ok. It's not so important as to fight over.
May
2
comment What is the uncertainty principle?
@Muphrid just that. For example, if do QM in phase space, what you would use is a real-valued quasiprobability distribution $P(x,p)$ that's possibly negative but whose absolute value is bounded by something $\propto 1/h^3$, so you can't localize it arbitrarily, but not for reasons of waves. ... Physically, QM doesn't happen "in Hilbert space"; the Hilbert space is just one description. ... But even in Hilbert space, one should be mindful that all kinds of observables can have uncertainty between them, and the wave/Fourier analogy only works for those with commutator $i\hbar$ or similar.
May
2
comment What is the uncertainty principle?
I think you should specify that you're only concerned with one particular description of one particular pair of observables. Otherwise, this answer does neither the physics nor mathematics all that well... Even for $x,p$, this is only a peculiarity of the Hilbert space formulation; it's not physically fundamental. But there is intrinsic uncertainty between any non-commuting of observables, so even mathematically, the uncertainty principle is not really about waves. (The accepted answer has a similar lack, but it's much more obvious how to generalize an instrumentalist description.)
May
2
comment What is the uncertainty principle?
+1, but this answer would be much better if it was made clear that position and momentum are just one particular case, in that there is uncertainty between many other pairs of observables, although typically in a more complicated relationship.
Apr
27
comment What is a body's momentum really equal to?
@jwg feels like we're on a semantic treadmill here, but in general usage 'outdated' can mean 'no longer used or useful'/'discarded'/'old-fashioned', so inches are not outdated in the first two of those senses and are outdated in the last sense. ... in any case, DavidZ is of the prescriptivist bent, so it's largely moot.
Apr
22
answered The meaning of the phase in the wave function
Apr
21
comment Neutron star: escape velocity
@JohnDuffield Schutz says that gravity to Newtonian order is due to the time-time component of the metric, which is true. This is also half the the reason that light curves, as the leading-order correction to the coordinate speed of light in the weak-field regime is half from the time-time component and half from the spatial components. But Schutz is primarily concerned about redshift, so his statement about light is actually also correct, since redshift is entirely determined the time-time component. Regardless, open a question about Schutz if you want to discuss him.
Apr
19
comment Neutron star: escape velocity
@gamma1954 Yes, I lapsed into $G = 1$ units because they're more convenient. ... Also, if you're wondering about the effective potential, I gave an outline of a derivation here.
Apr
19
answered Neutron star: escape velocity
Apr
19
comment Schwarzschild radius in black hole density
An implicit assumption here is that there is such a thing as 'the' radius, which is actually misleading.
Apr
19
answered Schwarzschild radius in black hole density
Apr
19
comment Schwarzschild radius in black hole density
Very related: Do black holes have infinite areas and volumes?. Basically, the volume of a black hole is not frame-independent, and so is not unambiguously defined. However, for a simple (non-rotating, uncharged, isolated) Schwarzschild black hole, one fairly 'obvious' choice of frame gives the same volume as the usual Euclidean formula with Schwarzschild radius.
Feb
10
comment Why do we theorize that the Big Bang created space?
thrown ball is an an analogy, pointing to a common cause: gravity. Of course gravity is not Newtonian, so ballistics can't be taken true, but what they have in common is that they're both solutions to the equations of a theory of gravity: given an initial condition, all else on the large scale follows from gravity. (In the case of cosmic expansion, the FLRW family of GTR solutions.)
Feb
9
comment Why do we theorize that the Big Bang created space?
if you think it's "without any cause", you're mistaken. There's as much cause as in the trajectory of a throwing object making an arc (etc.). What's actually not understood is the origin of the initial conditions, i.e. for what reasons (if any) was it initially thrown as it was.