Recent content by djy

The Schwarzschild metric is the solution of spacetime around a spherical, uncharged, non-rotating mass. Yes, it does closely explain the difference in passage of time on GPS satellites compared to the Earth's surface. And, as you said, there are components of time dilation due both to velocity...

If you have a finite plane, then the current will continuously pile up as more and more net charge at the ends. I think a wire loop, in which the current is suddenly turned on, is a better example. Once the entire current loop is within the past light cone of an observer, there should be a...

I think I got this copied over properly (it is my own derivation). Incidentally, anyone know how to get del to show up? "\del" doesn't seem to work. Suppose an infinite sheet, in the y-z plane, goes from zero current before t = 0 to \vec{j} = (0, 0, j) current after t = 0. Assume the...

The key is that, even though vector potential drops off with 1/r, the circumference of points contributing to potential at any given time increases with r, thus there is no diminishing tail. Hopefully a bit later I can post a derivation.

Sorry -- 18-4, volume 2, in the chapter on Maxwell's equations.

Feynman confirms my thinking (from his Lectures, section 18-4): "In short, we turn on the current and the magnetic field immediately next to it turns on to a constant value B; then the turning on of B spreads out from the source region. After a certain time, there is a uniform magnetic field...

For an infinite current sheet whose current has always been on, it is well known that a purely magnetic field exists on each side, in all of space. For an infinite current sheet whose current is initially off, then suddenly turned on everywhere simultaneously, I think I have worked out that a...

To reword it even more precisely: the limit of acceleration required to keep an object at a constant distance from the event horizon is infinite as the distance approaches zero.

Whether spacetime is flat is frame-independent. It can't be "made flat" by different observers and coordinate systems.

DaleSpam's example with spherical coordinates is in flat spacetime. The coordinate system is curvilinear, which is why the Christoffel symbols don't vanish and why a geodesic is defined by the covariant derivative, not the ordinary derivative.

To get a distance, you need to divide up space and time. For some observer, the logical way to do this is to send out geodesics that are orthogonal to the observer's world line at a given time. Assuming one of these geodesics intersects the spaceship's world line, then its distance to the...

First, suppose the collection of particles is "dust", i.e. no intermolecular forces. Then each particle will be on its own free fall trajectory, and geodesic deviation ("tidal forces" in Newtonian parlance) will distort the dust field with time. If the collection of particles is being held...

I'm pretty sure this isn't right. For example, it's possible that A = (0, 0), and then v = 0/0, undefined. The velocity of the frame in which B and C are simultaneous is, I believe, v = c^2 \frac{t_C - t_B}{x_C - x_B}. Of course, if v \ge c, then the frame is not physically realistic.

No. Your premises are that A and B are spacelike separated, and A and C are spacelike separated. It is easy to come up with an A, B, and C such that B and C are timelike separated. This means there's no FOR in which they're simultaneous. For example, consider one FOR with (x, t)...

The result is the same except for one important difference. In the train's frame, the right end meets its lightning rod (fixed to the track) before the left end meets its rod. This is a consequence of Lorentz contraction. In the platform's frame, the train is Lorentz contracted and it's...