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Re: simplier is more difficult



James Wheeler wrote:

I didn't think that a uniform magnetic field was possible (except as an
approximation).

This is true, but it is not a problem in principle. In physics we use
idealizations all the time to simplify the things when considering problems
of principle. It's also not possible to make a perfectly ideal gas, simple
harmonic oscillator, frictionless plane, or a host of other idealizations.
If a given region of arbitrary size is required to have a B field of a
specified degree of uniformity, then it is possible in principle to build an
appropriate coil external to that region such that it will produce the
required field to the uniformity specifications desired. The only problem in
practice is one of practicality, cost and technological prowess -- not
principle.

Three thoughts (not-coherent)
1. The assymetry is that electric charges exist, and magnetic monopoles
do not. (Cabrerra notwithstanding) This means that all
real electric and magnetic fields are the superposition of
relativistically transformed electric fields. (N.B. the superposition
of transformed fields need not be the transform of a single field.)

This is not true. Superposing separately transformed the static electric
fields from charged particles will never produce propagating electromagnetic
waves. E&M is *not* just electrostatics supplemented with the Lorentz
transformation rules for the sources and the E fields. The EM field is its
own dynamic entity and is not just a mathematical artifact left over from a
creative way (using a field description) of treating electrostatic coulomb
interactions between charges.

2. What about the intrinsic magnetic moments of elementary particles.
These are relativistic in origin, but need not represent moving
charge.

This statement contradicts the point 1. above. Clearly, the magnetic field
from the intrinsic magnetic moment of an elementary particle is *not* the
result of a relativistic transform of that particle's electric field (esp.
since it exists when that particle is at rest). Your example in point 2. is
a counterexample which invalidates your point 1. Whether or not an intrinsic
magnetic moment is relativistic in origin or not is a somewhat debatable
issue which depends to some extent on just how the term 'relativistic' is
used. What is more certain, however, is that intrinsic magnetic moments are
*quantum* effects.

3. Since charge cannot be created, perhaps we should believe that
current rather than charge is intrinsic. Maybe all electric fields
are transforms of magnetic fields! Isn't duality fun! Pick your
basis.

This is not true either. It simply is not possible to get along with just
E-fields or just B-fields and treat the other field type as a transform (or a
superposition of separate transforms over the separate sources) of the other
type of field.

David Bowman
dbowman@gtc.georgetown.ky.us