[ExI] Aharonov-Bohm Effect (was Precognition on TV)

Lee Corbin lcorbin at rawbw.com
Sun Jul 15 18:30:28 UTC 2007

Serafino writes (and thanks for correcting my spelling error in the subject line!)

> Lee [wrote]:
>> 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.

Well, doesn't this imply that we were wrong all the
time about the potential being "merely" a mathematical
construct?  (I would throw in the fact that quarks were
at first thought to be only a mathematical construct,
but that would not really be relevant enough to mention.)

Oops.  But I see you've addressed this below.

> 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;

Or, in simpler language, other, completely innocent
electrons drift by who're supposed to be unaware
of what's going on inside the shielded area.

> 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.

Oh!  I had forgotten about that. By an application of 
Stokes theorem here, you mean simply Gauss's Law
that states that the surface integral of an electrical field
equals the total charge contained therein?  I was 
thinking that the shielding interfered with that effect.
Just dead wrong, eh?

> 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.


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