Authors: Carlton Frederick
A stochastic model is presented for the Planck-scale nature of space-time. From it, many features of quantum mechanics and relativity are derived. As mathematical points have no extent, the stochastic manifold cannot be tessellated with points and so a granular model is required. A constant grain size is not Lorentz invariant but, since volume is a Lorentz invariant, we posit grains with constant volumes. We treat both space and time stochastically and thus require a new interpretation of time to prevent an object being in multiple places at the same time. As the grains do have a definite volume, a mechanism is required to create and annihilate grains (without leaving gaps in space-time) as the universe, or parts thereof, expands or contracts. Making the time coordinate complex provides a mechanism. As this is a 'root' model, it attempts to explicate phenomena usually taken for granted, such as gravity and the nature of time. Both the General Relativity field equations (the master equations of Relativity) and the Schrödinger equation (the master equation of quantum mechanics) are produced.
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