 2094 Damon Wai Kwan So
 Nondeterministic Quantum Mechanics, the TwoSlit Experiment, Measurement, Wave Particle Duality, Spin and Energy
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Oct 30, 20

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Abstract. A previous paper [1] proposed an alternative interpretation of quantum mechanics which is distinct from the Copenhagen Interpretation and the pilot wave theory. This alternative interpretation and its associated nondeterministic surfing velocity component on the S (phase) surface are applied here to give an explanation of the oneslit experiment and the twoslit experiment in terms of the ontology of pointlike entity (particle) and the function of wave field, without the need to invoke the notion of wave function collapse. The behaviour of the pointlike entity is only partly influenced by the wave field so that there is a real degree of nondeterminacy for the behaviour of the pointlike entity. The path from the source of the pointlike entity to the detecting screen of the oneslit experiment or the twoslit experiment cannot be predetermined. Yet, a large collection of these paths will follow the probability pattern which is derived from the solution to the quantum mechanical equations with the slit boundary condition. Three modes of behaviour of the pointlike entity in free space are identified the cylindrical mode, the spherical mode and the intermediate mode.
The pointlike entity can either be a particle or a photon as the equations and their solutions for describing their behaviour are identical in form except that for the photon case the mass parameter is set to zero. Hence, the close similarity in behaviour between particles and photons is traced to the near identity of their relativistic equations. The particle nature of both particles and photons is thus affirmed while maintaining the influence (not determination) of the wave function on the particles and photons. In this way, the question of waveparticle duality is dealt with for particles and photons.
The absence of interference pattern when observation is made of the particles of the twoslit experiment can be explained by an exchange of momentum between a particle and the measuring element such that the two interacting intermediate modes before the momentum exchange reduce to the single cylindrical mode whose probability pattern is much more localised. Measurement is thus defined as an event where an exchange of momentum between the measured particle and the measuring agent takes place, leading to a wholesale and sudden change, but not collapse, of the wave function.
Louis de Broglie s formula for momentum and wavelength, and the PlanckEinstein relation, are also clearly evident from the analysis of the quantum mechanical equations.
The integration of the particle s angular momentum on the S surface yields the particle s spin. The notions of rest mass, rest energy and massless particles are investigated and unpacked with reference to the particle s surfing momentum on the S surface. A new definition of energy is proposed which could shed some light on the puzzle of dark matter. The crucial nondeterministic root in quantum mechanics is identified and Heisenberg s Uncertainty Principle is critiqued. Finally, a possible relationship between a quantumpotentiallike term and dark energy is posed.
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