The time at the subplanckian scale

Abstract

With the theory of special relativity, time has been linked with space into a four-dimensional space-time from which a basic question must be asked: can space be really transformed into time and vice-versa? The response is affirmative if time has the same structural topological structure as space at the subplanckian quantum level in such a way that a discrete structural quantum time constitutes the time part of the space-time internal vacuum of every elementary particle. It has thus been shown that a quantum time, quantized algebraically according to a lattice of time quanta, really exists and is emergent in the sense that time quanta can be transformed into space quanta and vice-versa. Furthermore,this quantum time, only relevant at the subplanckian scale, is proved to be in one-to-one correspondence with the absolute and relative clock times.