Stephen A. Lawrence wrote: > > > Harry Veeder wrote: >> Following up my last reply... >> >> >> Stephen A. Lawrence wrote: >>> Consider a pure B field (no E field) in inertial frame S. Consider >>> two identical particles, particle P1, at rest in S, and particle >>> P2, moving in S. P1 feels no force, and is not accelerating. >> >> >> A devout relativist (which I am not) would say there is no magnetic >> field for observer in P1's frame because that frame is at rest w.r.t. >> to a given charge distribution. > > C'mon Harry, your "devout relativist" is a strawman. If the spacelike > cross terms in the Faraday tensor are nonzero then there's a B field > present. If there's an inertial frame in which the timelike terms in > Faraday are all zero and at least one spacelike cross term is nonzero, > then there are nonzero spacelike cross terms in Faraday in _all_ > inertial frames, and any "relativist" I know would certainly would say > there's a B field present. > > The field of a solenoid (or a bar magnet) is one example of such a > field. The B field around a long, uncharged wire is another example. > > If you disagree, then I think you'd better define "B field" and "devout > relativist" because we're obviously talking past each other.
ok. Let me divide B-fields into two types. Those that depend on relative motion and those that do not. A "devout relativist" would say the existence of a B-field is relative to one's motion . Let us call the other relativist an "instrumental relativist". They would say every B-field is real and independent of motion. Both relativists agree that a B-force is relative to motion. > >>> P2 feels a force, and _is_ accelerating. The (Boolean-valued) >>> existence of an acceleration is absolute (at least as long as we >>> stick with inertial frames) -- a particle which is accelerating, is >>> accelerating in all frames; a particle which is "inertial" is >>> inertial in all frames. >> >> Likewise, a devout relativist would say the relative motion of P2 >> w.r.t. to a given charge distribution generates a magnetic field. > > You detect a B field by observing a charged particle in motion in your > frame of reference. If there's a velocity-dependent force on them in > your frame of reference, then there's a B field in your frame of reference. > > This use of test particles is discussed in reasonable detail in, for > example, "Gravitation" by Misner Thorne and Wheeler, who are certainly > all "devout relativists" according to most people. Philosophically, I would classify them as instrumental relativists. I don't know if this classification is novel or not, but I think it is helpful. >> >>> So, in all inertial frames, P1 will feel no net force, while P2 >>> will feel a net force. Since the only difference between the >>> particles is their velocity, yet they feel difference forces, they >>> are clearly subject to a velocity-dependent force. The E field >>> isn't velocity dependent, so it can't account for the difference. >>> Ergo, there's a B field in every frame. >> >> >> For a devout relativist there is no a-priori magnetic field in every >> frame. >> >> Harry >> Harry
