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Jul
24
comment Why general relativity over other similar theories?
@ViktorToth The equivalence principle is about gravity. The section you're quoting from is named "Principle of Relativity and Gravitation". It's completely obvious from the get-go that Einstein was seeking a relativistic treatment of gravity. The whole paper is about the implications of gravity to various phenomena, from gravitational time dilation to electromagnetism. I have no idea how one could read it and conclude that Einstein wasn't concerned about reconciling relativity and gravity, and conclude instead that it accelerated frames were the primary motivation.
Jul
24
comment Why general relativity over other similar theories?
@ViktorToth it's rather trivial to treat all frames equally in STR (in the same sense that GTR does): just express your equations of motion in tensorial form. Then no coordinate system, inertial or otherwise, is intrinsically distinguished. The difference in GTR lies in the fact that metric is dynamical and not necessarily flat. ... Saying that Einstein's primary motivation was treatment of accelerated frames is a really bizarre claim. Rather, it was treatment of gravity that obeyed the equivalence principle, a goal presented from the earliest (1907 and 1911) papers on the subject.
Jul
23
comment Why general relativity over other similar theories?
"he was seeking was a generalization of the theory of relativity (later to be known as the special theory) to accelerating frames." -- Just wrong. STR has no absolutely no problems with accelerated frames, and Einstein was actually seeking a relativistic theory of gravity. The oft-repeated claim that one needs GTR to deal with accelerated frames is a very silly myth that has no basis in reality.
Jul
22
answered How can an infinitesimally small object rotate?
Jul
22
comment How can an infinitesimally small object rotate?
@AlecBell The singularity of a spinning black hole is (probably) not pointlike, nor even analogous 'a point in space'. Specifically, the Kerr metric of an isolated rotating black hole has a ring singularity. ... I put in a qualifier of 'probably' because it is is not uncontroversial that the interior of the Kerr metric is a physically realistic description of an isolated rotating black hole. ... Actually, even the Schwarzschild singularity is not really 'a point in space', since it's not a timelike singularity, but that's a different issue.
Jul
22
comment How can an infinitesimally small object rotate?
@AlecBell A region of spacetime separated from the rest of the universe by an event horizon.
Jul
22
comment How can an infinitesimally small object rotate?
In the 1913, Élie Cartan came up with non-tensorial representations of orthogonal Lie algebras, which later came to be called spin(orial) representations. ... More relevantly here, Pauli's matrices (ca. 1926) are generators of the spin representation of the rotation group $\mathrm{SO}(3)$. So in a reasonable sense, the electron really does rotate, and I don't agree with saying that the word 'spin' shouldn't be taken literally. It's completely true that shouldn't be taken classically, but that's a different claim.
Jul
22
comment How can an infinitesimally small object rotate?
The Stern–Gerlach experiment was in 1922, Pauli invented his matrices in 1926, while the Dirac equation was 1928--so by that time physicists have clearly understood and accepted what spin-1/2 means. ... That's in addition to the mathematical notion of spinor going back to the mid-1910s at the latest.
Jul
16
reviewed No Action Needed Rigorously prove that electric field is zero in a perfect conductor
Jul
15
reviewed Approve Why does locking the rear tires on a vehicle cause it to spin?
Jul
13
comment Rocket equation derivation, question about signs
@k-selectride Right, you can remind them of the the definition of derivative of $f$ as the limit of $[f(t+\Delta t)-f(t)]/\Delta t$. This corresponds to $\dot{f} = \mathrm{d}f/\mathrm{d}t$ in infinitesimal form. Since we know $m$ is decreasing with time, $\mathrm{d}m$ must be negative if $t$ is going forward, etc.
Jul
13
answered Rocket equation derivation, question about signs
Jun
7
comment What is the meaning of SI unit $Ns$ (NEWTON.TIME)?
then I'm afraid that I don't understand your question.
Jun
6
comment What is the meaning of SI unit $Ns$ (NEWTON.TIME)?
A newton-second is a unit of momentum. It makes sense to express it that way because force is the rate of change of momentum, $F = \mathrm{d}p/\mathrm{d}t$.
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 How is length contraction reconciled with other objects occupying space?
@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.