Abstract
The goal of this paper is to introduce the notion of a four-dimensional time in classical mechanics and in quantum mechanics as a natural concept related with the angular momentum. The four-dimensional time is a consequence of the geometrical relation in the particle in a given plane defined by the angular momentum. A quaternion is the mathematical entity that gives the correct direction to the four-dimensional time.
Taking into account the four-dimensional time as a vectorial quaternionic idea, we develop a set of generalizations and conclusions over the mechanics.
In quantum mechanics, the four-dimensional time appears as an observable.
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Reluz Machicote, J.E. Time as a Geometric Concept Involving Angular Relations in Classical Mechanics and Quantum Mechanics. Found Phys 40, 1744–1778 (2010). https://doi.org/10.1007/s10701-010-9479-2
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DOI: https://doi.org/10.1007/s10701-010-9479-2