Quantum of action in entangled relativity

Description

In this manuscript, I show that the quantum field theory treatment of entangled relativity requires the existence of a new quantum of action that is not the usual constant of Planck ($\hbar$). On the other hand, $\hbar$ can be thought to be an effective \textit{late times} and \textit{low energy limit} quantum of action -- which depends on the spacetime localisation. But in the end, the only dimensionful fundamental constant that appears in the quantum phase of theory actually is the Planck energy -- which, surprisingly, remains a fundamental constant in entangled relativity, although neither Newton's constant $G$ nor $\hbar$ are. Indeed, in the \textit{semiclassical} limit that corresponds to our present universe, $\hbar$ turns out to be proportional to $G$, such that their ratio remains a constant. This manifests an explicit connection between the quantum and the gravitational worlds in entangled relativity.

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