Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
2009-04-13
Annalen Phys.18:206-230,2009
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
25 pages, 1 figure
Scientific paper
10.1002/andp.200810343
The mechanics of wave motion in a medium are founded in conservation laws for the physical quantities that the waves carry, combined with the constitutive laws of the medium, and define Lorentzian structures only in degenerate cases of the dispersion laws that follow from the field equations. It is suggested that the transition from wave motion to point motion is best factored into an intermediate step of extended matter motion, which then makes the dimension-codimension duality of waves and trajectories a natural consequence of the bicharacteristic (geodesic) foliation associated with the dispersion law. This process is illustrated in the conventional case of quadratic dispersion, as well as quartic ones, which include the Heisenberg-Euler dispersion law. It is suggested that the contributions to geodesic motion from the non-quadratic nature of a dispersion law might represent another source of quantum fluctuations about classical extremals, in addition to the diffraction effects that are left out by the geometrical optics approximation.
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