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2013

Emergent General Relativity from Fisher Information Metric

Matsueda, Hiroaki

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We derive the Einstein tensor from the Fisher information metric that is defined by the probability distribution of a statistical mechanical system.

We find that the tensor naturally contains essential information of the energy-momentum tensor of a classical scalar field, when the entropy data or the spectrum data of the system are embedded into the classical field as the field strength.
Thus, we can regard the Einstein equation as the equation of coarse-grained states for the original microscopic system behind the classical field theory.
We make some remarks on quantization of gravity and various quantum-classical correspondences.

Emergent General Relativity from Fisher Information Metric · Around

Built on

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Similar

Shun-ichi Amari and Hiroshi Nagaoka, ”Methods of Information Geometry”, Oxford (2000)
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Hirohiko Shima, ”Hessian Goemetry”, Shokabo, Tokyo (2001)
2001
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T. Padmanabhan, Class. Quant. Grav. 19
2002
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P. Calabrese and J. Cardy, J. Stat. Mech. 0406 (2004) P002 [note added: arXiv:hep-th/0405152]
2004
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C. Eling, R. Guedens, and T. Jacobson, Phys. Rev. Lett. 96
2006
Cited alongside, same era.
H. Matsueda, arXiv:1112.5566
Original
Cited in the paper.
H. Matsueda, arXiv:1208.5103
Original
Cited in the paper.

Then

L. Tagliacozzo, Thiago. R. de Oliveira, S. Iblisdir, amd J. I. Latorre, Phys. Rev. B 78
2008
Later among the works it cites.
Frank Pollmann, Subroto Mukerjee, Ari M. Turner, and Joel E. Moore, Phys. Rev. Lett. 102
2009
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Ching-Yu Huang and Feng-Li Lin, Phys. Rev. A 81
2010
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Sergey N. Solodukhin, Living Rev. Relativity, 14
2011
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E. P. Verlinde, JHEP 1104
2011
Later among the works it cites.

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