June 23, 2020
finiteness of distances, finiteness of times, actual infinity, digital spacetime, Pythagoras digital theorem, Lorentz relativistic factor, digital relativity
This paper uses transfinite ordinals to prove the distance between any two given points and the interval of time between any two given instants can only be finite, and that, under certain conditions, the number of events between any two events is always finite. It also proves a contradiction involving the actual infinity hypothesis on which the spacetime continuum is grounded. The alternative of a discrete spacetime is then considered, and the consideration leads, via Pythagoras digital theorem, to the conclusion that the factor for converting between continuous and digital geometries is the relativistic Lorentz factor if length is replaced with the product of speed and time in a isotropic space. These finitist results suggest the convenience to consider the possibility of a digital interpretation of special relativity.