Publications
Special Relativity 2.0: Hamiltonian Relativity
Foundations of E-Theory (Part I)
ABSTRACT
Although the mathematical framework for Special Relativity has proven phenomenally successful for over a century, it is predicated on an assumption that time and space are the independent properties of physics - an assumption which is then fundamental to its mathematical foundation. By defining the energy associated with relative motion as the fundamental, independent property, not space and time, this paper challenges that assumption. In doing so, we find that a single unified spacetime, covariant with changes in energy, emerges. A spacetime that is not an independent set of coordinates between which we must transform, but a single adaptive spacetime responsive to relative energy.
In this paper we will show how, when we define energy as intrinsic and independent, momentum, space and time adapt algebraically to relative motion with covariance embedded in their relationships with energy. We demonstrate how this covariance is assured in every inertial frame, not by coordinate transformations but by simple algebraic scaling of time and spatial elements. Further, when momentum, time and space are defined in terms of covariant relationships, time and length are understood as intervals that scale in an adaptable space time, not as coordinates in a fixed spacetime. Where proper time and proper length emerge naturally as rest frame representations of these relationships. This ultimately allows us to define relativity not just as energy-responsive scaling, but as eigenstates of a system's Hamiltonian. This formulation then allows us to define special relativity through the lens of Hamiltonian mechanics and quantum operators, not just scaled Newtonian laws of motion-- the Hamiltonian Relativity identified in the title. This energy-responsive and naturally quantum structure then becomes the initial step on the path to the unification of quantum theory with general relativity.