Open AccessA new approach to the evolving 4+1 spacetime metric
Author(s) -
Martin Land
Publication year - 2021
Publication title -
journal of physics. conference series
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.21
H-Index - 85
eISSN - 1742-6596
pISSN - 1742-6588
DOI - 10.1088/1742-6596/1956/1/012010
Subject(s) - spacetime , formalism (music) , mathematical physics , field equation , physics , minkowski space , metric (unit) , lorentz transformation , spacetime symmetries , manifold (fluid mechanics) , parameterized complexity , gravitation , lorentz group , classical mechanics , theoretical physics , mathematics , quantum , quantum field theory in curved spacetime , quantum gravity , quantum mechanics , mechanical engineering , art , musical , operations management , combinatorics , engineering , economics , visual arts
We recently proposed [1, 2] field equations that prescribe a metric g αβ ( x , τ ) that is local in the spacetime coordinates x and evolves with the external “worldtime” τ of the Stueckelberg Horwitz Piron (SHP) framework. As in SHP electrodynamics, these field equations exhibit a formal 5D symmetry ( α,β = 0, 1, 2, 3, 5), that is strategically broken to 4+1 representations of the Lorentz group. The resulting canonical formalism for this metric embodies a natural foliation of a 5D pseudo-manifold (encompassing both geometry and dynamics) into the τ -parameterized 4D spacetime posed in SHP theory. In this paper, we consider the linearized equations for weak gravitation in this 4+1 formalism, leading to a more straightforward and intuitive derivation of the coupled first-order evolution equations for the metric.