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Written by Sean Gryb and illustrated by Marc Ngui

Abstract

Is there a number for every bit of spacetime, or is spacetime smooth like the real line? The ultimate

fate of a quantum theory of gravity might depend on it. The troublesome infinities of quantum gravity

can be cured by assuming that spacetime comes in countable, discrete pieces which one could simulate

on a computer. But, perhaps there is another way? In this essay, we propose a picture where scale

is meaningless so that there can be no minimum length and, hence, no fundamental discreteness. In

this picture, Einstein’s Special Relativity, suitably modified to accommodate an expanding Universe,

can be reinterpreted as a theory where only the instantaneous shapes of configurations count.

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Scale invariance and shape dynamics for gravity are more appropriate Ansätze (approach) for a quasi Faster Than Light induced world view. Is Spacetime Countable?