Recent content by pervect

Not exactly. II do recall reading about acoustic models that have mathematical analogies to black holes that have been investigated experimentally, but I don't know the details. Google finds a theoretical paper by Matt Visser, https://arxiv.org/abs/gr-qc/9712010. Wiki mentions a paper by...

Reading your post (and Demystifers) did encourage me to consider a different case than the ones I had considered in the past, a case where we choose our freedom of how to distribute the stress that is needed to hold the disk together in such a way that it ends up not contributing to the energy...

I've come to realizie that when we spin up the disk, we have a choice to determine what stresses hold it together. If we make all the stresses radial, and make the circumferential stresses zero (or negligible), the problem becomes a lot more intuititve, and better behaved to boot. This was...

I recall a bit more about that now. The vector u is just the 4-velocity of a point on the rotating hoop. w is a vector perpendicular to u, representing the direction of the stress. Then ##\rho u \otimes u## is just a coordinate independent way of writing the stress-energy tensor contribution...

The system with rockets isn't a closed system, so I don't think it would be a good model at all. I'd question whether a non-closed system even had a definite invariant mass or energy, due to the relativity of simultaneity. I wouldn't have any objection to a system where the rockets exhcanged...

Greg Egan did the non-zero extension case with a hyperelastic material model which he describes in detail. It was definitely involved, especially for a disk rather than a hoop. I believe he's revised his analysis since I looked at it a long time ago. At the time, there was some discussion...

I remember looking at relativistic hoops and disks a long time ago, but I no longer recall most of the details. I do recall Greg Egan had a treatment at https://www.gregegan.net/SCIENCE/Rings/Rings.html using a "hyper-elastic" material model. This may be significantly harder than what you want...

I'm trying to untangle the notation. I am assuming that the lab frame, S, is unprimed, so all unprimed quantites are measured in S. And I am assuming that the primed quanties are measured in frame S' moving with velocity v relative to S. Further, I am assuming ##v_0## is the drift velocity...

I went over the calculation from Purcell from the references that others have posted - thanks to all who responded, by the way - and I can see why his argument works in the special case when the drift velocity, which I'll call v_d, is equal to the observer velocity. When v_0 = v_d = v, the...

As far as having both change, that would just double the effect, not change the order. It might be related as to linearizing around v=0 or v not equal to zero when expanding gamma in a taylor series to argue changes in gamma, 1/gamma, and hence "length contraction" are second order, but I'm not...

As I dig into this a bit more, I am becoming a bit confused myself. Purcell famously explains magnetism as due to "length contraction" of the distance between charge, which is what the original poster's question is about. But - length contraction is a second order effect in (normalized)...

After thinking about this some, I think you have gotten some good advice when you suggested you wanted to learn more about transformation laws. Maxwell's equations are fully relativistic. If you know how to properly transform charges and currents (usually expressed as charge density and...

Your source got trimmed - but I do find the argument that the idea that the electromagnetic force should preserve the rest mass of a particle does imply that if we formulate the 4-force as a tensor, said tensor should be anitsymmetric. In terms of 4-forces and 4-vectors, it implies that the...

Indeed, yes. At this point I'm not sure how familiar the OP is with the concept of covariance and what we call the covariant fomulation of electromagnetism. In case they either were familiar with it or were potentially interested in learning about it, I thought I'd give them a nudge in that...

It seems to me that if you define the Lorentz force as being only due to the magnetic field, the Lorentz force is perpendicular to the magnetic field because you defined it that way. Perhaps there's some way to rephrase the question in a more covariant way that doesn't treat the electric and...