At 10:00 AM 12/8/4, Stephen A. Lawrence wrote: >I had three comments on this analysis (which I snipped -- hope that's OK).
Not only OK, but such snipping is mandated (or at least strongly encouraged) by the vortex rules. IMHO, the list could use more good snippers like you! 8^) > >First, watch out for Shadowitz -- I've seen an instance where he messed >up an analysis by using the "motion" of the EM field relative to a >particle, which has no role in relativistic EM. Rindler, Jackson, and >Griffiths seem more reliable, to name some I'm aware of. I don't know >any reason to doubt Shadowitz's formula for pancaking, but you should >definitely double check any general assertions he makes about how fields >transform. I've seen it various other places too. No refs handy at the moment. > >Second, pancaking of the field for a point charge is derived from >evaluating the 4-vector potential for the charge using the retarded >integral. Pancaking isn't really "fundamental"; the representation in >terms of retarded integrals is. So, to see what's really going on in a >complex situation involving accelerated charges, it's probably safer to >use the retarded integrals directly. Yes, I was wondering what effect acceleration might have. The approach I used for that I even felt was bogus at the time. > >Finally, let's do just that. For simplicity, assume a rotating ring of >uniform negative charge density, with a fixed positive charge in the >middle of the ring. Let's look at the axial field. > >Since the ring is uniform, the 4-current density is not varying in time, >and we can forget about the "retarded" part. This analysis bothers me. It says the whole is not the sum of the parts. I showed that if pancaking is valid for an individual particle, then the sum of such individual pancaking effects does not cancel at all points. However, I must admit I had the nagging feeling I probably left other important effects out of my analysis, like abberation, which might negate field pancaking. I have the impression that aberration applies to photons though, and pancaking to fields. There should be a simple way to visualize this situation. (Beign a rank amateur, I don't consider tensor analysis simple.) [snip conclusions] >This field is well understood and it's certainly conservative. I am curious as to just why it is thought the huge polar jets of material fly out of black holes and neutron stars. An analagous (and additional) polar gravitational field should develop in the vicinity of black holes, if the analysis is done according to the gravimagnetic isomorphism I proposed on this list anyway. > >It's got a nonzero dipole moment but the far field on axis goes rapidly >to zero (1/r^3, I think?). Yes, and thus aligned dipoles have a mutual 1/r^4 force. Regards, Horace Heffner
