A freely falling frame at the interface of gravitational and quantum realms

TL;DR

This paper argues for the necessity of incorporating two fundamental length scales into symmetries at the gravitational-quantum interface, proposing the Snyder-Yang-Mendes algebra as a candidate symmetry framework and suggesting experimental exploration with quantum systems.

Contribution

It introduces the Snyder-Yang-Mendes Lie algebra as a promising symmetry candidate for the gravitational-quantum interface and derives new uncertainty relations involving fundamental length scales.

Findings

Proposes the Snyder-Yang-Mendes algebra as a symmetry at the interface.

Derives new uncertainty relations with fundamental length scales.

Suggests experimental tests using superconducting quantum interference devices.

Abstract

I briefly argue for logical necessity to incorporate, besides c, hbar, two fundamental length scales in the symmetries associated with the interface of gravitational and quantum realms. Next, in order to clear the proverbial bush, I discuss the CPT and indistinguishability issue related to recent non-linear deformations of special relativity and suggest why algebraically well-defined extensions of special relativity do not require non-linear deformations. That done, I suggest why the stable Snyder-Yang-Mendes Lie algebra should be considered as a serious candidate for the symmetries underlying freely falling frames at the interface of gravitational and quantum realms; thus echoing, and complementing, arguments recently put forward by Chryssomalakos and Okon. In the process I obtain concrete form of uncertainty relations which involve above-indicated length scales and a new dimensionless constant. I draw attention to the fact that because superconducting quantum interference devices can carry roughly 10^{23} Cooper pairs in a single quantum state, Planck-mass quantum systems already exist in the laboratory. These may be used for possible exploration of the interface of the gravitational and quantum realms.