Recent content by SiennaTheGr8

To clarify, what do you (and presumably other commenters in this thread) mean by "total" mass here? Do you mean the mass of the disc, or the sum of the masses of its constituents?

I wonder... what's the speed of sound in unobtainium?

Please report back with your test results!

Here is a demonstration:

If I'm correctly understanding what you're saying, I don't think the "first-order"/"second-order" business means there's a flaw. The "order" by itself doesn't tell you whether we can notice the effects of something when only "non-relativistic" speeds are involved. Consider, for example, that...

I think that would be the "proper charge density" (for the right kind of charge distribution, anyway).

Terme and conditions may apply.

As an interesting(?) aside, we can "pick out" the magnetic force for a particular observer in a manifestly covariant way (I know this isn't what you meant). With the field tensor ##F^{\mu \nu}## and the "projection tensor" ##P^{\mu}_{\nu} = \delta^{\mu}_{\nu} - u^{\mu} u_{\nu} ## for observer...

Notably, Zangwill uses the "Lorentz force = magnetic force" convention.

To be clear, the Kronecker delta is symmetric too.

You can also derive ##d \gamma = \gamma^3 (\vec \beta \cdot d \vec \beta)## fairly easily and use that to do a change of variables (where ##\vec \beta = \vec u / c## and ##\gamma = (1 - \beta^2)^{-1/2}##)...

I think it's worth mentioning that this statement isn't true. The "electricity + length-contraction = magnetism" concept works for some special cases, and you can use it to show that magnetism must exist (as Purcell famously does in the textbook Electricity and Magnetism), but you can't use it...

Yes, I suppose all I've shown (if my math was right) is that the addition of a "4-curl" term to the electromagnetic stress-energy tensor can "make a difference" in general relativity in a way that it doesn't in special relativity. Interesting maybe, but I think you're right: not what Wald was...

Thinking about this a little more... For the laws of physics to be expressed covariantly, we'd have to add not just a curl-term to the Poynting 3-vector, but rather some "curl-like" 4-tensor term to the electromagnetic stress-energy that gives rise to that 3-curl term in the 3+1 split. In flat...

I briefly looked at some GR books for an explanation but didn't find anything. I had better luck with graduate-level E&M books; in addition to Jackson, there's at least Wald (Chapter 1), Garg (Section 25), and Zangwill (Section 15.4.3). Perhaps a satisfactory answer is in the paper that Zangwill...