Recent content by pervect

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...

I'm not all that familiar with fiber bundles, but I keep running into them, so this might be a good example of how to think and talk about them. This isn't an answer to any question, but me trying to interpret your answer. I'm considering the Langevian congruence and how we can interpret it...

I had to look this up, possibly there is some confusion over wording. What I wrote was in the thread on Born rigidity, and what the spatial projector operator ##h_{ab}## was in that context. The spatial projection operator ##h_{ab}## in general coordinates is a 4 dimensional linear operator...

My recollection is that there is a simple exponential relationship between mass ratio and maximum rapidity, regardless of the thrust profile. Something like w = ln(M), with a perfectly efficient photon rocket, where w is the rapidity and M is the mass ratio of the rocket. However, I haven't...

Possibly of interest. https://arxiv.org/abs/1409.4648 "Fermi-Normal, optical, and wave-syncrhonus coordinates for spaceetime with a plane gravitational wave". Why it might be of interest- Fermi Normal coordinates are generally the closest one can come to an inertial frame of reference. There...

Because of the interferometer design, the beam bounces back and forth multiple times, making the effective length (and the storage time) much longer. The web is suggesting the actual storage time is in the 1-3 millisecond range, due to what they call the "Finesse" of the Fabry-Perot interferometer.

My gut reaction is that it's unrealistic to believe one can maintain such a high acceleration for such a long time. But that's not your question. I did notice that you didn't have the mass ratio equation in your set of equations...

My understanding is that the test masses in Ligo essentially follow space-time geodesics (aka are in free fall), ignoring some of the complexities regarding the fact that they need to be suspended against the Earth's gravity. This is done with multiple isolating pendulums. Of course there is...