[ExI] Aharonov-Bohm Effect (was Precognition on TV)
scerir
scerir at libero.it
Sun Jul 15 15:24:39 UTC 2007
Lee:
> As I understand it, this "Aharonov-Bohm" effect
> that you mention really depends on electromagnetic
> *potential*. Heretofore, was not this potential
> merely a mathematical convenience? (I mean that as
> a serious question.)
In classical physics the 4-potential, A_mu, is regarded
as a 'mathematical' construct, devoided of any physical
significance in itself, but useful in computing the
'fields' which, in turn, generate physical observable
effects, by acting on the charges, accelerating them,
affecting their energies and momenta.
The A-B effect is interesting exactly because there
is a real, physical, observable effect on charged
particles, ascribable to the 4-potential A_mu,
even when the field, say the EM tensor F_mu nu,
is zero. The two important features of the A-B effect
in fact are: a) the magnetic field is confined in
a region completely inaccessible to electrons, and
electrons propagate in a region where EM fields are
zero; b) the vector potential A must instead be
nonvanishing in the region where electrons propagate,
and this last condition is not so difficult to reach,
since it follows from the well known Stokes theorem
- altough it ceases to be applicable in more complex
A-B effects, with 'switching' magnetic fluxes - and
from the Schroedinger equation.
But from what you wrote here below it seems you are
interested in a sort of ontology of the vector
potential. And you are right. This is a very
difficult, deep, subtle question. I'll write
something later.
> Why action at a distance?? Can't potential be looked
> upon as a field phenomenon? After all, look at
> gravitational potential, which is so much easier for
> us amateurs to think about. Sure, preRelativity folks
> would say that *everything* about the trajectory
> of an object in a grav field followed Newton's Laws
> to a T. (No pun intended.) But now we know that
> even if you magically had "gravitational shielding"
> the clock would run more slowly depending on
> gravitational *potential* nothing more nothing less.
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