Recent content by SiennaTheGr8

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...

I also wanted to thank you for leaving this comment. I'm guessing that you simply weren't aware that the camera could be controlled. I've just made some changes to make it more apparent to the user that the visualization is 3D and comes with camera controls. Previously the instructions for...

If you rotate the camera in the visualization, I think you'll see that it's correct (only looks like 2 from that angle). Maybe I should consider an option to display grid-lines!

A few updates: Dark mode. Sliders (originally suggested by @robphy), though the input-boxes are still there for "custom" values. On desktop, the options and controls now go side-by-side with the visualization, so that it's easier to adjust the parameters while viewing the results...

7 days is a lot longer than I'd realized is feasible. I wonder how much time you'd have (in this scenario) before the tidal forces became uncomfortable; I have a summer vacation to plan...

And the ultrarelativistic approximation in terms of rapidity: $$1 - \beta \approx \dfrac{1}{2} \textrm{sech}^2 \, \theta$$ or just as good: $$1 - \beta \approx \textrm{sech} \, (2 \theta)$$

This "ultrarelativistic" approximation can even be done without a binomial expansion (in case OP or other lurkers aren't familiar with that technique). Using ##\beta = v/c##: $$ \begin{align*} \gamma^{-2} &= 1 - \beta^2 \\ & = 1 - \left( 1 - \left( 1 - \beta \right) \right)^{2} \\ & = 1 -...

I just meant that they're serious physics textbooks, not pop-sci. Whether they use it in their research I don't know.

There are still exceptions, though. Hobson/Efstathiou/Lasenby used it in their GR book (2006), and more recently d'Inverno/Vickers continued using it in the 2nd edition of theirs (2022). John Kogut (2018) uses it in deriving the relativistic momentum, but then tells the reader that he'll always...

I don't interpret Einstein's original paper as using relativistic mass. Or I'm at least unsure. The thought experiment involves a body that gives off equally energetic radiation in opposite directions, such that its velocity is unaffected by the emission. That's the context that precedes the key...

Nobody's perfect.

If I'm not mistaken, it's a little more subtle than that, since both the time and the energy transform. In general, the "coordinate power" is given by ##P = \gamma^3(\vec v \cdot \vec a)m + \gamma \dot{m}##, and by time dilation and the chain rule we have ##\gamma \dot{m} = dm/d\tau ## (i.e...