Authors: Stephen H. Jarvis
Physics employs a variety of models constrained by how mathematical objects are used to label physical phenomena, primarily momentum being the mathematical object of choice. These models range from Newtonian mechanics to special and general relativity, to then quantum mechanics, and then to the standard model of particles. A clear issue that has arisen between these models is the dimensional mismatch between Einstein’s theory of gravitation and quantum mechanics (and thence the standard model) despite the idea of momentum being employed as a common mathematical object of choice for each of the models. Identified also with each of the models are three distinct and overlooked principles which remain as principles for each of the models without any further definition or derivation thereof, namely Fermat’s principle, the stationary-action principle, and the principle of inertia. In noting that these three principles are understood as assumptions for each of the models by the application of momentum as a mathematical descriptor base alone, the dimensional lack of cohesion between general relativity and quantum mechanics (and thence the standard model of particles) is brought to question with such. To rectify the dimensional mismatch, these three principles shall be derived from a zero-dimensional mathematical approach for the dimensions of time and space, specifically space as a point and time as a moment. By this derivation, the mathematical object approach of momentum shall be discussed and compared to the zero-dimensional mathematical approach.
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