April 13, 2023
axiom of infinity, spacetime continuum, discrete space-time, discrete sum of velocities, Pythagoras' Discrete Theorem, Lorentz Transformation, preinertia, absolute motion, discrete mechanics.
The discrete nature of space and time is introduced here as a formal consequence of the more than probable inconsistency of the Hypothesis of the Actual Infinity. This space-time discreteness leads immediately to the existence of an insurmountable maximum velocity. From this universal maximum velocity, the formula for the sum of velocities in discrete space-times is deduced, a sum that coincides with the relativistic sum of velocities. Finally, the discrete sum of velocities and the discrete version of Pythagoras Theorem make it possible to deduce the relativistic Lorentz Transformation, which in this case converts between discrete and continuous spacetimes magnitudes. Consequently, and being special relativity incompatible with discrete space-times, its experimental confirmations would actually be empirically proving the discrete nature of space and time, i.e. the existence of atomic units of space and time, which are extensive, minimal, and indivisible, maybe of a Planck volume (space) and of Planck time duration. It is then reminded preinertia, an attribute of all physical objects (including photons) for which there is the maximum empirical evidence, and which makes the detection of absolute motion impossible, which in turn explains the negative results of all experiments a la Michelson-Morley, although we warn here of a possible exception that is currently being analyzed in experimental terms.