2005/06/06 by Varqa Abyaneh, Abyaneh, Varqa, Bernard S. Kay +1 · 1 citation
Physics and Astronomy · #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #Optical and Acousto-Optic Technologies #Quantum Mechanics and Applications #Quantum Physics (quant-ph) #Statistical Mechanics and Entropy #gr-qc #quant-ph
paper · pdf · doi:10.48550/arxiv.gr-qc/0506039
Now 12 pages, no figures. LaTeX (includes iopart class/style files, uses amsthm.sty). Submitted to Class. Quantum Grav. Proof simplified and shortened (at expense of only slight weakening of theorem). Some more discussion and two further acknowledgments added
openalex publication_date 2005/06/06 · arxiv created 2006/01/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In ``Decoherence of macroscopic closed systems within Newtonian quantum gravity'' (Kay B S 1998 Class. Quantum Grav. 15 L89-L98) it was argued that, given a many-body Schroedinger wave function ψ(x1,...,xN) for the centre-of-mass degrees of freedom of a closed system of N identical uniform-mass balls of mass M and radius R, taking account of quantum gravitational effects and then tracing over the gravitational field amounts to multiplying the position-space density matrix ρ(x1,...,xN; x1',...,xN')= ψ(x1,...,xN)ψ*(x1',...,xN') by a multiplicative factor, which, if the positions x1,...,xN; x1',...,xN' are all much further away from one another than R, is well-approximated by the product from 1 to N over I, J, K (I<J) of ((|xK-xK'|/R)(|xI'-xJ||xI-xJ'|/|xI-xJ||xI'-xJ'|))-24M2. Here we show that if each uniform-mass ball is replaced by a grainy ball or more general-shaped lump of similar size consisting of a number, n, of well-spaced small balls of mass m and radius r and, in the above formula, R is replaced by r, M by m and the products are taken over all Nn positions of all the small balls, then the result is well-approximated by replacing R in the original formula by a new value Reff. This suggests that the original formula will apply in general to physically realistic lumps -- be they macroscopic lumps of ordinary matter with the grains atomic nuclei etc. or be they atomic nuclei themselves with their own (quantum) grainy substructure -- provided R is chosen suitably. In the case of a cubical lump consisting of n=(2L+1)3 small balls (L > 0) of radius r with centres at the vertices of a cubic lattice of spacing a (assumed to be very much bigger than 2r) and side 2La we establish the bound e-1/3(r/a)1/nLa < Reff < 2√ 3(r/a)1/n La.