Our interpretation is based on a line of research [1-4] starting from the demonstration that any kind of wave-like features may be treated by means of an exact ray-based treatment: a property which was thought to be reserved to the geometrical optics approximation. A property which, when applied to the currently accepted wave-mechanical equations, directly leads to an exact ray-based dynamical description.
It is shown in fact that, contrary to a common belief (ultimately due, as we shall see, to an excessively rigid application of the Uncertainty Principle), a classical-looking, wave-mechanical dynamics is possible, in terms of the exact trajectories of point-like particles moving, along well defined trajectories, under the soft piloting action - free from any wave-particle energy exchange - of de Broglie's monochromatic matter waves.
The so-called "Quantum Potential" is only a particular case of a much more general Wave Potential, acting on any kind of waves and determining any typically wave-like behavior.
It's therefore the simple and direct manifestation of the pilot waves associated by de Broglie to material particles.

We synthetize our own approach [4] and Bohm's one in the following Tables I and II, comparing the respective (non-relativistic) sets of equations for the motion of single particles in an external potential V(r).

The equations of TAB.I are structurally encoded in Schrödinger's (Helmholtz-like) time-independent equation, and provide the exact trajectories of a point-particle of assigned energy E, piloted by a monochromatic de Broglie matter wave whose objective physical reality is undeniably certified by its observed diffractive properties.
The equations of TAB.II, on the other hand, provide the probability flux-lines of a wave-packet (resulting from the entire set of stationary eigen-solutions) built up as a whole by the simultaneous solution of Schrödinger's time-dependent equation, declaredly giving an equivalent version of the (intrinsically probabilistic) Copenhagen vision, including most "quantum paradoxes".

The comparison between our merely geometrical Helmholtz coupling of monochromatic trajectories (along which point-particles are simply driven by de Broglie's stationary waves) and the inextricably non-local coupling of any part of the physical system involved by the "guidance equations" leads us to conclude that Bohmian theory is far from the spirit of our approach, aiming to start a non-probabilistic approach (based on the currently accepted equations of Wave Mechanics) running as close as possible to Classical Dynamics.

The full paper in PDF format, may be downloaded here

1. A. Orefice, R. Giovanelli and D. Ditto, Found. Phys. 39, 256 (2009)
2. A. Orefice, R. Giovanelli and D. Ditto, Ref.[23], Chapter 7, pg.425-453 (2012)
3. A. Orefice, R. Giovanelli and D. Ditto, Annales de la Fondation Louis de Broglie, 38, 7 (2013)
4. A. Orefice, R. Giovanelli and D. Ditto, (2015) arXiv:1406.4968v3 [quant-ph]
5. R. E. Wyatt, pg.28 of the Conf. Proc. Quantum Trajectories, ed. by K. H. Hughes and G. Parlant, CCP6, Daresbury, (2011)
6. J. Mompart, X. Oriols, Ref.[23], Introduction, pg.1-14
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23. AA.VV., Applied Bohmian Mechanics: from Nanoscale Systems to Cosmology, ed. by X. Oriols and J. Mompart, Pan Stanford Publishing (2012)

The following papers may be download from: ArXiv.org
(Cornell University Library)





ArXiv Publications [link]

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arXiv:1406.4968
From Classical to Wave-Mechanical Dynamics
A.Orefice, R.Giovanelli, D.Ditto
[v3] wed, 14 Jan. 2015

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arXiv:1310.8077
Objective Reality of de Broglie's Waves
A.Orefice, R.Giovanelli, D.Ditto
[v7] Sat, 22 Mar 2014

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arXiv:1302.4247
Wave Mechanics without Probability
A.Orefice, R.Giovanelli, D.Ditto
[v7] Thu, 22 Aug 2013

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arXiv:1207.0130
The Helmholtz Wave Potential: a non-probabilistic insight into Wave Mechanics
A.Orefice, R.Giovanelli, D.Ditto
[v8] Tue, 16 Apr 2013

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arXiv:1202.6225
Quantum trajectories and Cushing's historical contingency
A.Orefice, R.Giovanelli, D.Ditto
[v2] Tue, 16 Oct 2012

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arXiv:1105.4973
Helmholtz wave trajectories in classical and quantum physics
A.Orefice, R.Giovanelli, D.Ditto
[v3] Sat, 29 Oct 2011

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arXiv:0706.3102
Complete Hamiltonian description of wave-like features in classical and quantum physics
A.Orefice, R.Giovanelli, D.Ditto
[v5] Tue, 16 Sep 2008

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arXiv:0705.4049
Beyond Geometrical Optics and Bohmian Physics: A New Exact and Deterministic Hamiltonian Approach to Wave-Like Features in Classical and Quantum Physics
A.Orefice, R.Giovanelli, D.Ditto
[v1] Mon, 28 May 2007

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