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.
> 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.
> 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
