Unifying relativity and classical dynamics
Relativity and classical dynamics, as defined so far, form distinct parts of classical physics and are formulated based on independent principles. We propose that the formalism of classical dynamics can be considered as the theoretical foundation of the current theory of relativity and may be employed for exploring possibilities beyond the current theory. We show that special-relativistic kinematics, including universality of the speed of massless particles relative to inertial frames, is a consequence of the formalism of classical dynamics, with no assumptions other than spacetime point transformations and Euclidean geometry of space in inertial frames. We discuss that energy-independent velocity is a general concept in classical dynamics, applicable even to massive objects, in appropriate canonical coordinates. The derivation of Lorentz symmetry is inherently local and allows the speed of massless particles (relative to local inertial frames) to vary with space and time globally, which may provide a theoretical foundation for variable speed of light cosmology. We obtain no kinematical scales other than the light-speed, specially no scale of energy or momentum as has been suggested in some quantum gravity investigations. We argue that this is a consequence of spacetime point transformations making the momentum space linear, and a possible second scale must require non-point transformations as a necessary condition, which seems compatible with the notion of relative locality in curved momentum space.