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Yes. Also, any four-velocity is a 4D tangent vector to a worldline. So that vector is the same vector in different frames, although its...

Which, incidentally, means that "locally flat" is a bit of a misnomer. The analogue in spherical geometry is that you can lay your...

Playing around with this a little more, it looks like this only works for ##r<R## inside the horizon. For outside the horizon with...

As @PeterDonis mentioned also the coordinate two way speed of light can vary in non-inertial charts. Although that does also depend on...

No, he doesn't. For example, if you transform to Rindler coordinates, the round trip speed of light is not always ##c## in those...

For that, you'd have to do the experiment.

Yes. Whatever diffraction pattern you manage to produce with your source (and you can design a source to produce any pattern you want -...

Excellent, thanks @renormalize. It was just not occurring to me to eliminate one of the variables algebraically before integrating.

Yes you can! Inspired by https://en.wikipedia.org/wiki/Lema%C3%AEtre_coordinates, note that your two...

Ok, so the Jacobian would be $$ \left( \begin{array}{cc} \frac{\partial \tau}{\partial t} & \frac{\partial \tau}{\partial r} \\...

I think the general approach is to use the differential transforms to write the Jacobian (or is it Jacobean?) and use that to write the...

It seems from this research that there is very little benefit to underlining in addition to blue color. The effects seem small and the...

Most color-blind users are not achromatic and would be effectively served by different color schemes. For example, the various viridis...

I've been teaching physics since 2008, and I've spent 5 hard years becoming a physicist. We all here thought about these questions...

What goes into standards is based on the judgement and agreement of the members of the standards committee. Often they agree because...