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arXiv · 1308.3691

Surprisingly Long Length Scales for Semiclassical Loop Quantum Gravity and Their Physical Consequences

Paul G. N. de Vegvar
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Abstract

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 $μ$m 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 $ξ$.

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Paul G. N. de Vegvar. 2014-02-19. Surprisingly Long Length Scales for Semiclassical Loop Quantum Gravity and Their Physical Consequences. https://arxiv.org/abs/1308.3691

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