Authors: Jean Louis Van Belle
The geometry of the elementary quantum-mechanical wavefunction and a linearly polarized electromagnetic wave consist of two plane waves that are perpendicular to the direction of propagation: their components only differ in magnitude and – more importantly – in their relative phase (0 and 90° respectively). The physical dimension of the electric field vector is force per unit charge (N/C). It is, therefore, tempting to associate the real and imaginary component of the wavefunction with a similar physical dimension: force per unit mass (N/kg). This is, of course, the dimension of the gravitational field, which reduces to the dimension of acceleration (1 N/kg = 1 m/s2). The results and implications are remarkably elegant and intuitive: - Schrödinger’s wave equation, for example, can now be interpreted as an energy diffusion equation, and the wavefunction itself can be interpreted as a propagating gravitational wave. - The energy conservation principle then gives us a physical normalization condition, as probabilities (P = |ψ|2) are then, effectively, proportional to energy densities (u). - We also get a more intuitive explanation of spin angular momentum, the boson-fermion dichotomy, and the Compton scattering radius for a particle. - Finally, this physical interpretation of the wavefunction may also give us some clues in regard to the mechanism of relativistic length contraction. The interpretation does not challenge the Copenhagen interpretation of quantum mechanics: interpreting probability amplitudes as traveling field disturbances does not explain why a particle hits a detector as a particle (not as a wave). As such, this interpretation respects the complementarity principle.
Comments: 35 Pages.
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