N. 3 - 21 aprile 2001 - Giano Bifronte

case of the AC effect which involves the interaction between a moving
neutral magnetic dipole and the external electric field , the approach of
Boyer, has been criticized by Aharonov, Pearle and Vaidman [7] (APV)
for not taking into account the hidden momentum of the magnetic
dipole.
As already mentioned, the intriguing aspect of these nonlocal effects
is that there is an observable displacement of the interference pattern
even though there are no forces acting locally on the beam of particles.
Here, the expression of the forces (for example, the Lorentz force) is the
one given by the relativistic interpretation of electrodynamics. If the
relativistic expression of the force is correct, then these effects are
surely nonlocal because the force is zero in the experimental conditions
that lead to these effects.
However, if the nature of these effects were not nonlocal and were
instead due to a local interaction, then it would imply that the
relativistic expression for the force is incorrect so that the actual force
on the beam of particles could turn out to be non-null.
In the next sections we consider in detail how, within a nonrelativistic
interpretation of classical electrodynamics, the em force on elementary
particles may differ from the relativistic expression.
3 - A modified expression of the Lorentz force
We consider here two cases: modification of the Lorentz force due to
the hypothetical existence of longitudinal forces in agreement with the
integral form of the Faraday Law; test of the validity of the Lorentz
force for the differential form of Faraday's Law.
3.1 - longitudinal forces
Making use of the connective derivative d/dt = ∂t + v.∇ , from
Faraday's Law for a moving loop, the electromotive force (emf) ΔV
may be expressed by means of the effective field Eeff as
ΔV = ∫ Eeff.dl = -(1/c) d
dt ∫ B.ds = -(1/c) ∫ (∂tA+v×B).dl . (2)
Using vector identities we may write
-(1/c) ∫ (v.∇)A.dl = -(1/c) ∫ [∇(v.A)+v×B].dl = (1/c) ∫ (v×B).dl , (3)
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