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Quantum of action in Entangled Relativity

by Olivier Minazzoli

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Authors (as registered SciPost users):

Olivier Minazzoli

Abstract

In this article, we demonstrate that the novel general theory of relativity, named `Entangled Relativity', is more economical than General Relativity in terms of universal dimensionful constants when both theories are considered through a path integral formulation. The sole parameter of Entangled Relativity is a quantum of energy squared. However, in order to recover standard Quantum Field Theory when gravity is neglected in the path integral, we show that this quantum of energy corresponds to the reduced Planck energy. But this result also implies that Planck's quantum of action $\hbar$ and Newton's constant $G$ are not fixed constants in this framework but vary proportionally to a gravitational scalar degree of freedom, akin to typical scalar-tensor and $f(R)$ theories. In particular, it is derived that $\hbar$ is proportional to $G$ in this framework. This establishes an explicit connection between the quantum and gravitational realms. Given the absence of a free parameter in the theory, we argue that this unique prediction can likely be probed observationally in the future. Furthermore, due to the deficit of dimensionful parameters in Entangled Relativity compared to standard physics, fundamental length or time scales cannot be defined within this framework. We argue that this aspect is expected to become significant in the non-perturbative quantum gravity regime of the theory.

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• Present a breakthrough on a previously-identified and long-standing research stumbling block