Abstract
The Laws of Classical and Quantum Mechanics are well known. However, their origin remains mysterious and their interpretation controversial. It has been argued that this situation will continue until one manages to derive the Laws of Physics from some very first principles. In this paper, we use basic concepts of Differential Geometry to yield the Klein-Gordon equation and the Lagrange equations of Relativistic Mechanics without using the standard postulates of Quantum Mechanics, Special Relativity or even General Relativity.
Highlights
Quantum Mechanics plays an important role in Science and Technology today
In the following we show that the scalar field ψ ( x) will obey the Klein Gordon equation that the path x ( s) will obey at the same time the geodesic equation, further we will try to find the meaning of the classical trajectory x (s) for the wave function ψ ( x)
We have tried to find the origin of Quantum Mechanics in the mathematical properties of scalar functions defined over a spacetime endowed with a metric tensor g that allows us to define the proper time τ
Summary
Quantum Mechanics plays an important role in Science and Technology today. Its predictions have been always confirmed and steadily improved. It can be related to the Dirac equation and to some extent to higher spin theories as well as to the non-relativistic Schrödinger. Quantum Mechanics occupies a very unusual place among physical theories: it contains Classical Mechanics as a limiting case, yet it requires this limiting case for its own formulation The results of this paper should help answer questions raised by the unexpected coexistence of Classical and Quantum Mechanics in some macroscopic topological insulators [11].
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