382 reputation
110
bio website
location
age
visits member for 2 years, 4 months
seen Nov 19 at 4:54

Grad student: jlackm.wordpress.com


Oct
28
comment Does GR imply a fundamental difference between gravitational and non-gravitational acceleration?
I think you have it wrong. An accelerometer in free fall would measure $0$ acceleration. The statement that you can't tell the difference between being in free fall and at rest in a vacuum is (approximately) true. You can clearly tell the difference between free fall and upward acceleration in an elevator. In one if you drop a ball it will fall beneath you, in the other it won't. And if you mean downward acceleration of the elevator, then that is exactly free fall so the statement is vacuous.
Oct
21
comment Diffeomorphism Invariance of General Relativity
@twistor59 Do you mean that if $\varphi:M\to M$ is a diffeomorphism, and $\phi$ solves $\eta^{\mu\nu}\nabla_\mu\nabla_\nu\phi=0$, then $\varphi^*\phi$ won't solve $\varphi^*\eta^{\mu\nu}\nabla_\mu\nabla_\nu\varphi^*\phi=0$ where the covariant derivative are now with respect to $\varphi^*\eta$?
Oct
21
comment Diffeomorphism Invariance of General Relativity
Thanks, though it's a bit technical. Do you have a simple example illustrating the difference between a theory that is diffeomorphism invariant and one that is not?
Oct
20
comment Diffeomorphism Invariance of General Relativity
@twistor59 Ok, but $\eta^{\mu\nu}\nabla_\mu\nabla_\nu\phi=0$ isn't a tensor equation, if you do the change of coordinates you get $g^{\mu\nu}\nabla_\mu\nabla_\nu\phi=0$. I still don't see what the problem is, ex: you can solve the wave equation in cartesian or polar coordinates, you just have to do the proper change of variables. The Euler-Lagrange equations are the same in any coordinate system, so what problems do active diffeomorphisms cause?
Oct
20
asked Diffeomorphism Invariance of General Relativity
Jul
31
awarded  Yearling
Jun
8
comment Is Biot-Savart law obtained empirically or can it be derived?
But how I've seen it done, Maxwell's equations are derived from the biot-savart law, which would make this circular.
Jun
8
comment Is length/distance a vector?
I'm not saying it's not standard terminology, I just don't think they are the same kind of vector, and it can be confusing to bag them together...It is standard to call angular momentum a vector, but it's clearly not the same kind as a velocity vector. If you change the place of the origin, the position vector changes, a velocity vector won't.
Jun
8
comment Is length/distance a vector?
I didn't interpret the OP's question in the formal sense of a vector space, that isn't usually what physics people mean when they use the term vector, otherwise anything could be a vector. They usually mean vectors as in velocity vectors, formally tangents to curves or whatever. It makes sense to write the position of a particle at $(0,1)$ as $\hat{y}$ in cartesian coordinates, but how would you do so in polar coordinates? In polar coordinates the same position is written $(1,\frac{\pi}{2})$, but I don't think identifying that with $\hat{r}+\frac{\pi}{2}\hat{\theta}$ works.
Jun
8
comment Is length/distance a vector?
I disagree that position is a vector, position is specified by coordinates, but it's not a vector; it's not a quantity with a magnitude or direction...the displacement vector is a different thing and is a vector. Just thinking in terms of differential geometry, coordinates and vectors are not the same thing. @Oaoa What you are saying would be right in a different context, but not in this one.
Jun
3
comment What exactly is implied by Einstein's insight in this scene from the NOVA series “$E=mc^2$ Einstein's Big Idea?”
I've always wondered about the clock tower thing...was Einstein just really lucky with his reasoning that if he were traveling near the speed of light, the clock would slow down? because I don't see how this implies that light is the speed limit...I mean as long as light has a finite speed, this effect would be observed. It seems like faulty reasoning that luckily led him to the right conclusion, unless I am misunderstanding.
May
30
comment Momentum of particle in a box
One thing I've noticed, is that the "de broglie wavelength" isn't even a possible wavelength, interestingly enough (at least for n=1).
May
30
accepted Diving into a charged (Reissner-Nordstrom) Black hole
May
30
comment Momentum of particle in a box
Ok, only thing is it seems like after you make a measurement of momentum, and the wavefunction collapses to $\int_{-\epsilon}^{\epsilon}dp\,\psi(p)e^{-ipx}$ or whatever, it won't solve the boundary conditions, which seems problematic? One of the justifications I saw online for the statement that there are only discrete momentum values is the de broglie wavelength, with the wavelength being the one corresponding to the argument of $\sin$. This make me wonder is the de broglie wavelength is really good for anything, other than if you know the particle is in approximately a momentum eigenstate.
May
30
comment Momentum of particle in a box
Can you elaborate on why it isn't a good quantum number? From the above answer, it seems like the particle can take any (or almost any) momentum value.
May
30
comment Momentum of particle in a box
That makes sense, however if the right side is $\psi(p)$, then I should be able to write $\psi(x)=\int_{-\infty}^{\infty} dp\,\psi(p)e^{-ipx}$, but this doesn't seem to be the case, which makes me suspicious.
May
30
revised Momentum of particle in a box
added 470 characters in body
May
30
asked Momentum of particle in a box
May
29
answered Gauss's Law understanding
May
28
answered Gauss's Law - Electric Field outside a Shell?