Minkowski Spacetime and QED from Ontology of Time

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 concepts 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. 9 In other words: "The wave function does not describe matter, it describes how matter behaves" [34].

Old Game, New Rules: Rethinking the Form of Physics

“…It is easy to prove and has been shown in Reference [16] that the elements γ 0 , γ 10 and γ 14 represent parity, time reversal and charge conjugation. The combination of these operators to form a multispinor, may lead (with normalization) to the construction of symplectic matrices M. Some examples are:…”

“…But it is known that this type of matrix is closely connected to symplectic matrices as every symplectic matrix is a matrix exponential of a matrix F [12]. We consider the matrices as defined by Equations (15) and (16) as too important and fundamental to have no meaningful and unique names: Therefore we speak of a symplex (plural symplices), if a matrix holds Equation (15) and of a cosymplex if it holds Equation (16).…”

“…Note furthermore that all skew-symmetric unit vectors square to −1 while the symmetric ones square to 1 [16].…”

“…The reason is quite simple: If 2 n > N as for all higher-dimensional state vectors, there are less generators of the algebra than independent variables. This discrepancy increases with n. Hence the described objects can not be pure vectors anymore, but must contain tensor-type components (k-vectors) (For a deeper discussion of the dimensionality of space-time, see Reference [16] and references therein).…”

“…But there are different ways to argue this. In Reference [16] we argued that Maxwell's equations can be derived within our framework by (a) the postulate that space-time emerges from interaction, i.e., that the fields E and B have to be constructed from the 4-vectors. X = t γ 0 + x · γ, J = ρ γ 0 + j · γ and A = Φ γ 0 + A · γ with (b) the requirement that no co-symplices emerge.…”