[ExI] Aharonov-Bohm Effect (was Precognition on TV)
scerir at libero.it
Sun Jul 15 18:27:53 UTC 2007
> 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.
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). 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.
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. (This is the reason why sometimes people
say that in the A-B effect the momentum and energy
conservation principles do not hold).
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.
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