[ExI] Aharonov-Bohm Effect

[Lee Corbin]

Serafino writes

----- Original Message ----- 
From: "scerir" <scerir at libero.it>
To: "Lee Corbin" <lcorbin at rawbw.com>; "ExI chat list" <extropy-chat at lists.extropy.org>
Sent: Sunday, July 15, 2007 11:27 AM

Actually, let me quote from your slightly earlier email again
this passage which was so well-written and clear:

> 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,

The more I understand about this, indeed the more
outrageous it is. But I have one more question, below.

> As you remember the famous psi-wavefunction of QM has 
> its roots in Einstein's conception of 'Gespensterfelder'
> (a ghost field, *devoid of momentum and energy*, guiding
> the particles)....
> ...
> In the A-B example the action of the 'Gespensterfelder'
> on each individual electron changes its trajectory, due
> to the presence of the quantum potential (vector potential)
> and results in the overall shift of the interference
> pattern, even if the 'Gespensterfelder' is devoid of
> momentum and energy, and even if the EM tensor (F_mu nu)
> is zero.

The shielding restricts the EM tensor (EM field, that is) 
to a region where it cannot affect the electron's path.
The magnetic field in particular cannot affect the electron's
path, nor can any electric field!  But the *potential* can!

I had thought that I had a glimmer of an understanding
by comparing this to the situation with gravitational fields.
But the problem is this:  consider the effect of the
gravitational potention (concretely, say, on the rate at which
clocks advance). Indeed, at the center of a (fictional)
hollow Earth, there is no gravitational force (and, so
I might suppose, no gravitational field?). But of course
the potential is still there, and the clocks obediently
---along with all other physical processes---proceed
more slowly. 

But that is related to the fact that the potential is not
changing in this (fictional) case at the center! Outside
the Earth, however, the potential must be changing
with the radial distance, and this is exactly because
there *is* a gravitational field.

So in the A-B effect, is the vector potential outside
the (shielded) solenoid different along the path that
the electron takes? That is, if X and Y are two points
of the path, is there or isn't there a difference in the
strength of the vector potential?   Surely the answer
must be that there is *no* change!  (Else we would
have to say that the EM field itself was there, right?)

So how, in the electron's journey, as it comes in from
very, very far away, can it begin to be affected by
some potential that is not changing over distance?

(I hope that I am not so thoroughly confused that none
of the above makes sense!)

> (This is the reason why sometimes people say that
> in the A-B effect the momentum and energy
> conservation principles do not hold).

Sheer heresy, of course!  Below, I have the rest of
your post for reference.

Lee

>  Even Bohr conceded that Einstein's
> use of such picturesque phrases as Gespensterfelder
> 'implied no tendency to mysticism, but illuminated
> rather a profound humor behind his piercing remarks.'
> As you also remember the very concept of ghost field
> (ghost waves) has been developed by deBroglie and, 
> later, by Bohm (with his Bohmian mechanics).
> 
> In Bohmian mechanics a solution of the Schroedinger
> eq. is regarded as an objectively existing real field - 
> not so so different from the 'Gespensterfelder' 
> (though in general it does propagate in a 3n-dimensional
> configuration space) - which guides the particle trough
> its trajectory. Moreover the action of this real field 
> on a particle is non-classical (since the particle is 
> assumed not to react *dynamically* on the real field acting 
> on it) and is represented by a suitably defined 'quantum
> potential Q', whose features are different from the
> classical potentials, and whose exact mathematical
> expression can be deduced from the solution of the
> Schroedinger eq., written in a specific form.
> 
> For sure you have already realized it is a logically
> compelling requirement of any theory using test-particles
> and (ghost or real) field concepts that there is a
> 'dialectical' interplay between particles and fields.
> 
> In the A-B effect the situation is somewhat conceptually 
> analogous to that in classical electrodynamics (and maybe 
> in gravitation, as you pointed out) where the abstract
> notion of fields has a physical manifestation only by 
> the action (non classical though) on charged particles. 
> 
> ...
> Summing up, what can we say? It is a rather messy
> situation. Ghost fields, invented by Einstein
> (around 1909/1912 I think) are still there. Like
> any other ghost they appear, from time to time.