The indeterministic character of physical laws is generally considered to be the most important consequence of quantum physics. A deterministic point of view, however, together with the possibility of well defined Hamiltonian trajectories, emerges as the most natural one from the analysis of the timeindependent Helmholtz-like equations encountered both in Classical Electromagnetism and in Wave Mechanics. In the former case the rays of a beam are described, for any set of boundary conditions, by an exact approach avoiding the geometrical optics approximation; in the latter case the same pattern of lines is shown to provide the trajectories of a quantum particle beam, and to correspond to a set of deterministic dynamical laws containing the classical ones as a simple limiting case. Paper available at: http://arxiv.org/ftp/arxiv/papers/0706/0706.3102.pdf
The indeterministic character of physical laws is generally considered to be the most important consequence of quantum physics. A deterministic point of view, however, together with the possibility of well defined Hamiltonian trajectories, emerges as the most natural one from the analysis of the timeindependent Helmholtz-like equations encountered both in Classical Electromagnetism and in Wave Mechanics. In the former case the rays of a beam are described, for any set of boundary conditions, by an exact approach avoiding the geometrical optics approximation; in the latter case the same pattern of lines is shown to provide the trajectories of a quantum particle beam, and to correspond to a set of deterministic dynamical laws containing the classical ones as a simple limiting case. Paper available at: http://arxiv.org/ftp/arxiv/papers/0706/0706.3102.pdf
The indeterministic character of physical laws is generally considered to be the most important consequence of quantum physics. A deterministic point of view, however, together with the possibility of well defined Hamiltonian trajectories, emerges as the most natural one from the analysis of the time-independent Helmholtz-like equations encountered both in Classical Electromagnetism and in Wave Mechanics. In the case of particle beams a suitable pattern of trajectories is provided (for any set of boundary conditions) by a set of dynamical laws containing the classical ones as a simple limiting case.
The behavior of classical and quantum wave beams in stationary media is shown to be ruled by a "Wave Potential" function encoded in Helmholtz-like equations, determined by the structure itself of the beam and taking, in the quantum case, the form of Bohm's "Quantum Potential", which is therefore not so much a "quantum" as a "wave" property. Exact, deterministic motion laws, mutually coupled by this term and describing wave-like features such as diffraction and interference, are obtained in terms of well defined Hamiltonian trajectories, and shown to reduce to the laws of usual geometrical optics and/or classical dynamics when this coupling term is neglected. As far as the quantum case is concerned, the approach proposed in the present paper, suggested by the direct extension of the treatment holding for classical waves, describes the motion of classical-looking, point-like particles, without resorting to the use of travelling wave-packets.
The behavior of classical and beams in stationary media is shown to be ruled by a Wave Potential function encoded in Helmholtz-like equations, determined by the structure itself of the beam and taking, in the case, the form of Bohm's Quantum Potential, which is therefore not so much a quantum as a wave property. Exact, deterministic motion laws, mutually coupled by this term and describing wave-like features such as diffraction and interference, are obtained in terms of well defined Hamiltonian trajectories, and shown to reduce to the laws of usual geometrical optics and/or classical dynamics when this coupling term is neglected. As far as the case is concerned, the approach proposed in the present paper, suggested by the direct extension of the treatment holding for classical waves, describes the motion of classical-looking, point-like particles, without resorting to the use of travelling wave-packets.
The time-independent Schroedinger and Klein-Gordon equations - as well as any other Helmholtz-like equation - were recently shown to be associated with exact sets of ray-trajectories (coupled by a "Wave Potential" function encoded in their structure itself) describing any kind of wave-like features, such as diffraction and interference. This property suggests to view Wave Mechanics as a direct, causal and realistic, extension of Classical Mechanics, based on exact trajectories and motion laws of point-like particles "piloted" by de Broglie's matter waves and avoiding the probabilistic content and the wave-packets both of the standard Copenhagen interpretation and of Bohm's theory.
The behavior of monochromatic electromagnetic in stationary media is shown to be ruled by a frequency dependent function, which we call Wave Potential, encoded in the structure of the Helmholtz equation. Contrary to the common belief that the very concept of ray trajectory is reserved to the eikonal approximation, a general and exact ray-based Hamiltonian treatment, reducing to the eikonal approximation in the absence of Wave Potential, shows that its presence induces a mutual, perpendicular ray-coupling, which is the one and only cause of any typically wave-like phenomenon, such as diffraction and interference. Recalling, then, that the time-independent Schroedinger and Klein-Gordon equations (associating stationary matter waves to mono-energetic particles) are themselves Helmholtz-like equations, the exact, ray-based treatment developed for classical electromagnetic is extended - without resorting to statistical concepts - to the exact, trajectory-based Hamiltonian dynamics of mono-energetic point-like particles, both in the non-relativistic and in the relativistic case. The trajectories turn out to be perpendicularly coupled, once more, by an exact, stationary, energy-dependent Wave Potential, coinciding in the form, but not in the physical meaning, with the statistical, time-varying, energy-independent Quantum of Bohm's theory, which views particles, just like the standard Copenhagen interpretation, as traveling wave-packets. These results, together with the connection which is shown to exist between Wave Potential and Uncertainty Principle, suggest a novel, non-probabilistic interpretation of Wave Mechanics.
The behavior of monochromatic electromagnetic waves in stationary media is shown to be ruled by a frequency dependent function, which we call Wave Potential, encoded in the structure of the Helmholtz equation. Contrary to the common belief that the very concept of "ray trajectory" is reserved to the eikonal approximation, a general and exact ray-based Hamiltonian treatment, reducing to the eikonal approximation in the absence of Wave Potential, shows that its presence induces a mutual, perpendicular ray-coupling, which is the one and only cause of any typically wave-like phenomenon, such as diffraction and interference. Recalling, then, that the time-independent Schroedinger and Klein-Gordon equations (associating stationary "matter waves" to mono-energetic particles) are themselves Helmholtz-like equations, the exact, ray-based treatment developed for classical electromagnetic waves is extended - without resorting to statistical concepts - to the exact, trajectory-based Hamiltonian dynamics of mono-energetic point-like particles, both in the non-relativistic and in the relativistic case. The trajectories turn out to be perpendicularly coupled, once more, by an exact, stationary, energy-dependent Wave Potential, coinciding in the form, but not in the physical meaning, with the statistical, time-varying, energy-independent "Quantum Potential" of Bohm's theory, which views particles, just like the standard Copenhagen interpretation, as traveling wave-packets. These results, together with the connection which is shown to exist between Wave Potential and Uncertainty Principle, suggest a novel, non-probabilistic interpretation of Wave Mechanics.