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Presentation: An "intuitive" origin of Zitterbewegung
- (or rather of spin) and (in an "orthodox" way,
incidentally) of the Bohm potential [following some
Hestenes-Campolattaro-Barut-Zanghi's ideas]; a series of
quantum consequences from such hydrodynamical (or, more
generally, classical-like) approach; etc.
The most recent work in this field has
been performed however by my younger collaborator
G.Salesi [I was too busy with the "superluminal" work,
that (after our pioneering work, following Sudarshan's,
of the early seventies) has come into fashion since 15
years or so]: Salesi has formalized the previous results
of ours only on the basis of the ordinary conservation
principles, has found the Bohm potential for
Klein-Gordon and Dirac eqs., gas written down the
extra-terms to be added to Newton's F=ma when spin is
taken into account, and so on... Without him, my
panoramic presentation will be limited but I don't trust
too much he'll be able to come]. Here, let me only refer
to the papers:
E. Recami & G. Salesi: "Hydrodynamics and kinematics of
spinning particles", Phys. Rev. A, vol. 57, p. 98
(1998).
G. Salesi & E. Recami: "Hydrodynamical reformulation and
quantum limit of the Barut--Zanghi theory", Found. Phys.
Lett. 10, p. 533 (1997).
G. Salesi & E. Recami, "Spin effects on the cyclotron
frequency for a Dirac electron", Phys. Lett. A, vol.
267, p. 219 (2000).
G. Salesi: "Non-Newtonian mechanics", Int. J. Mod. Phys.
A, vol. 17, p. 347 (2002).
G. Salesi, "Non relativistic classical mechanics for
spinning particles", Int. J. Mod. Phys., vol. 20, p.
2027 (2005).
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Presentation: "Super-luminal" motions
After
Sudarshan et al.'s (and Recami et al.'s) papers of the
sixties and seventies, positive experiments and
mathematical work became a reality, increasing more and
more after 1992. The main topics to which my group and I
contributed are:
(a) Construction of solutions to the
wave equations (and of Maxwell's eqs.) with superluminal
[or super-sonic,...] group-velocities: such solutions,
as predicted by Recami & Mignani's 1974 "extended
relativity", travel without practical deformation along
a wide field-depth; they are called "localized
(non-dispersive) waves"; particularly known are the
so-called "X-shaped waves" [predicted by Recami and
Barut in 1980]; many experiments confirmed their
existence.
For short reviews (also of the
experimental side), one might be willing to check, e.g.,
E. Recami: "Superluminal motions? A bird's-eye view of
the experimental status-of-the-art" [e-print
physics/0101108], Found. Phys., vol. 31, p. 1119 (2001),
and refs. therein (a simple, preliminary review, but of
an electronic small size), or rather
E. Recami et al.: "On the localized superluminal
solutions to the Maxwell equations" [report
NSF-ITF-02-93 (I.T.P., UCSB; 2002], IEEE Journal of
Selected Topics in Quantum Electronics, vol. 9, no. 1,
p. 59 (2003), (a larger review, but of a bigger
electronic size).
For more details, one could check, e.g.,
E. Recami, "On localized `X-shaped' Superluminal
solutions to Maxwell equations", Physica A, vol. 252, p.
586 (1998), and refs. therein;
M.Z. Rached, E. Recami, et al.: "New localized
Superluminal solutions to the wave equations with finite
total energies and arbitrary frequencies" [e-print
physics/0109062], European Physical Journal D, vol. 21,
p. 217 (2002);
Zamboni-Rached, et al., "Superluminal X-shaped beams
propagating without distortion along a co-axial guide",
Physical Review E, vol. 66, no.046617 (2002);
"The X-shaped, localized field generated by a
superluminal electric charge", Phys. Rev. E, vol. 69,
no.027602 (2004);
(b) Prediction and experimental
verification that QM implies even infinite
group-velocities during tunneling (e.g., through 2 or
more successive barriers): which is confirmed also by
mathematical calculations, numerical simulations and
experiments performed at the level of CLASSICAL barriers
[since the Schrödinger eq. is mathematically identical
to the Helmholtz equation, everything can be developed
on the basis of Maxwell eqs. only]; let us here limit
ourselves to quoting, e.g.,
V.S. Olkhovsky, E. Recami & G. Salesi, "Tunneling
through two successive barriers and the Hartman
(Superluminal) effect" [e-print quant-ph/0002022],
Europhysics Letters, vol. 57, p. 879 (2002);
Y. Aharaonov et al., "Superoscillations and tunneling
times," Phys. Rev. A, vol. 65, no. 052124 (2002)
(which constitutes a theoretical confirmation within
QM);
S. Longhi et al.: "Measurement of Superluminal optical
tunneling times in double-barrier photonic bandgaps",
Phys. Rev. E, vol. 65, no. 046610 (2002)
(which contains a clear experimental verification, at
the level of classical barriers). |
