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

Abstract

Abstract.I briefly argue for logical necessity to incorporate, besides c,h, 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.

Exotic Statistics for Ordinary Particles in Quantum Gravity

“…The most convincing general arguments for changes to the basic commutators are perhaps those of Ahluwalia-Khalilova [13] based on the work of Mendes, Chryssomalakos and…”

The Stabilized Poincare–heisenberg Algebra: A Clifford Algebra Viewpoint

“…On top of this, spacetime in SPHA requires two new length scales, one in the extreme short distance range, the other on the cosmological scale. We denote these new length scales ℓ p and ℓ c respectively (following the notation used in [7]). …”

“…However, in the work presented here such resulting modifications to the quantum and spacetime structure arise not as an ad hoc speculation but from the Principle of Lie Algebraic stability. The reader is referred to [21,22,23,5,7,24] for additional discussion of these and related issues.…”

“…The algebra is given below in a similar form to that of Chryssomalakos and Okon [5] (which in turn is a somewhat more abstract and mathematical version than the one given by Ahluwalia-Khalilova [7] which focuses more on the physical aspects of the algebra).…”

Soft Singularity and the Fundamental Length

“…In Ref's [10], [11] (resting on the principles of the deformation idea) it is shown that the Lie algebra for the interface of the gravitational and quantum realms is the stabilized form of the Poincaré-Heisenberg algebra which carries three additional parameters and one from them is the fundamental length. It is shown that the stable Snyder-Yang-Mendes Lie algebra is a serious candidate for the symmetries underlying freely falling frames at the interface of quantum and gravitational ideas.…”