Abstract. I briefly argue for logical necessity to incorporate, besides c, , 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 nonlinear deformations of special relativity and suggest why algebraically well-defined extensions of special relativity do not require nonlinear 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 10²³ 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.

PACS numbers: 03.30.+p, 04.50.+h, 04.60.−m

Print publication: Issue 7 (7 April 2005)
Received 4 August 2004, in final form 4 February 2005
Published 17 March 2005