2013/08/16 by Paul G. N. de Vegvar, de Vegvar, Paul G. N.
Physics and Astronomy · #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #gr-qc
paper · pdf · doi:10.48550/arxiv.1308.3691
13 pgs, resubmitted 8/15&16/2013 to correct typos 22 pgs, resubmitted 2/18/2014: Re-titled paper, revised estimate for epsilon to be self-contained, added discussion of key assumptions & upper bound for xi, corrected typos
arxiv created 2014/02/19 · arxiv updated 2014/02/20
When gauge field theory coherent states for loop quantum gravity (LQG) were introduced, an optimized semiclassical proper length emerged, corresponding to the edge length ε of a graph embedded in a given classical geometry. Here ε is explored in more detail. ε at the Earth's surface is found to lie between 100 μm and 0.7 m. The implied quantum fluctuating space-time strain amplitude and noise spectrum are estimated to be 4 1/2 orders smaller than the current experimental detectability. However, such a macroscopic ε makes regularization of the semiclassical electromagnetic Hamiltonian problematic for photon wavelengths shorter than ε. The origin of a large ε is traced to an edge-wise tensor product of independent edge-based coherent states for the whole graph state. This provides physical grounds for recently proposed collective coherent states, where ε acquires the interpretation of a sliding scale. A new proper distance ξ emerges as the characteristic length of semiclassical LQG. ξ will affect the LQG photon vacuum dispersion relations, and is also accessible to current measurements of space-time strain. Matter interactions may also affect ξ.