Three possible implications of spacetime discreteness
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We analyze the possible implications of the discreteness of spacetime, which is defined here as the existence of a minimum observable interval of spacetime. First, it is argued that the discreteness of spacetime may result in the existence of a finite invariant speed when combining with the principle of relativity. Next, it is argued that when combining with the uncertainty principle, the discreteness of space seems to require that spacetime is curved by matter, and the dynamical relationship between matter and spacetime holds true not only for macroscopic objects but also for microscopic particles. Moreover, the Einstein gravitational constant can also be determined in terms of the minimum size of discrete spacetime. Thirdly, it is argued that the discreteness of time may result in the dynamical collapse of the wave function, and the minimum size of discrete spacetime also yields a plausible collapse criterion consistent with experiments. These heuristic arguments might provide a deeper understanding of the special and general relativity and quantum theory, and also have implications for the solutions to the measurement problem and the problem of quantum gravity.