Minkowski Spacetime and QED from Ontology of Time

TL;DR

This paper proposes a unified symplectic Hamiltonian framework for classical mechanics, relativity, electrodynamics, and quantum mechanics based on an ontology of time, offering new insights into spacetime, measurement, and fundamental laws.

Contribution

It introduces a common formalism linking various physics domains through an ontology of time, deriving spacetime structure and fundamental laws from symplectic dynamics.

Findings

Derives spacetime dimensionality and Lorentz transformations from symplectic structure.

Provides a geometric interpretation of quantum mechanics and relativity.

Reveals the non-fundamental nature of spacetime in physics.

Abstract

Classical mechanics, relativity, electrodynamics and quantum mechanics are often depicted as separate realms of physics, each with its own formalism and notion. This remains unsatisfactory with respect to the unity of nature and to the necessary number of postulates. We uncover the intrinsic connection of these areas of physics and describe them using a common symplectic Hamiltonian formalism. Our approach is based on a proper distinction between variables and constants, i.e. on a basic but rigorous ontology of time. We link these concept with the obvious conditions for the possibility of measurements. The derived consequences put the measurement problem of quantum mechanics and the Copenhagen interpretation of the quantum mechanical wavefunction into perspective. According to our (onto-) logic we find that spacetime can not be fundamental. We argue that a geometric interpretation of symplectic dynamics emerges from the isomorphism between the corresponding Lie algebra and the representation of a Clifford algebra. Within this conceptional framework we derive the dimensionality of spacetime, the form of Lorentz transformations and of the Lorentz force and fundamental laws of physics as the Planck-Einstein relation, the Maxwell equations and finally the Dirac equation.