Sagittarius A-Star's latest activity

I have some solemn news to report. Many in the community had been wondering where the prolific @Vanadium 50 has been. V50 hasn't posted...

PS note that it is the speed of light that is independent of the motion of the source. Not the velocity of light, which is a vector and...

The explanation of aberration in the light-clock scenario does not only work with classical particles, but also with EM waves. The...

Do you mean the case ##v=0##? You get ##2\arccos{} 0= \pi##, but not ##2\pi##. It seems that you want to describe the headlight effect...

I think the train actually distorts in its original rest frame, rather than tilting. Although it's a funny kind of stress-free...

In the restframe of the train, the bridge-length maybe even smaller than the train-length due to length contraction, if the bridge moves...

The crater depth will not be different.

A change in kinetic energy is ##\int \vec F \cdot d\vec s##. A force to decelerate the moving body by mechanical contact is in the end...

I think this must be multiplied with ##m## to get the four-momentum.

This means for proper time squared: ##(d\tau)^2 = (dT + \kappa dX)^2 - dX^2 - dY^2 - dZ^2\ \ \ \ \ (1)## Multiplying equation ##(1)##...

But I think it is correct: The reason is, that the term ##m ({dx \over d\tau}, {dy \over d\tau}, {dz \over d\tau})## does not contain...

Conserved energy is the time-component of the 4-momentum ##p_\mu=m {dx_\mu \over d\tau}##. ##E = m {dt \over d\tau}##. The conserved...

Please see A. Einstein: "The Meaning of Relativity"/Lecture 2, equations (39) and (42)...

Einstein modified Newton's definition ##p_x=mv_x## to ##p_x=m {dx \over d\tau}##. This does not depend on the clock-synchronization...

As @PeterDonis said in #22, the OP calculated in the Born coordinates (see the "edit" note at the end of #20). I just "tidied up" the...