ABSTRACT
The Einstein theory of relativistic gravity encoded in the General Relativity Theory (GRT) is
investigated from a holographic statistical geometrophysical viewpoint done so here for the first time.
In so doing, the arguments are carried out systematically and the four laws of geometrodynamics are
enunciated with a proper reasonable development. To do so, new objects characterizing the quantum
geometry christened “geomets” are proposed to exist and it is also proposed that there exist
geometrodynamic states that these geomets occupy. The geometrodynamic states are statistical states
of different curvature and when occupied determine the geometry of the spacetime domain under
scrutiny and thereby tell energy-momentum how to behave and distribute. This is a different take and
the theory is developed further by developing the idea that the quantities appearing in the Einstein
field equations are in fact physically realistic and measurable quantities called the geometrodynamic
state functions. A complete covariant geometrodynamic potential theory is then developed thereafter.
Finally a new quantity called the “collapse index” is defined and how the spacetime geometry curves
is shown as a first order geometrodynamic phase transition using information bit saturation instead of
the concept of temperature. Relationship between purely and only geometry and information is
stressed throughout. The statistical formula relating curvature and probability is inverted and
interpretation is provided. This is followed by a key application in the form of a correspondence
between the Euler-Poincaré formula and the proposed “extended Gibbs formula”. In an appendix the
nub of the proof of the Maldacena conjecture is provided.
References
[1] ‘tHooft, G. Dimensional Reduction in Quantum Gravity, Utrecht Preprint THU-93/26,
gr-qc/9310026; Susskind, L. The World as a Hologram, hep-th/9409089; ‘tHooft, G.
The Holographic Principle,hep-th/0003004.
[2] Bousso, R. The Holographic Principle, hep-th/0203101.
[3] Flanagan, E. E., D. Marolf and R. M. Wald, Proof of Classical Versions of the Bousso
Entropy Bound and of the Generalized Second Law, Phys. Rev. D62, 084035.hepth/9908070.
[4] Verlinde, E. On the Origin of Gravity and the Laws of Newton, hep-th/1001.0785.
[5] Caticha, A. Towards a Statistical Geometrodynamics, in Decoherence and Entropy in
Complex Systems ed. By H.-T. Elze (Springer Verlag, 2004). gr-qc/0301061. ibid., The
Information Geometry of Space and Time, gr-qc/0508108.
[6] Merali, Z. The Origins of Space and Time, Nature 500, 516, 29 Aug 2013.
[7] A. Sen, J. Math. Phys. 22(8) (1981) 1781; ibid., Int. J. Theor. Phys. 21 (1981) 1; ibid.,
Phys. Lett. 119B (1982) 89.
[8] A. Ashtekar, Phys. Rev. Lett. 57 (1986) 2244; ibid., Phys. Rev. D36 (1987) 1587
Download all article in PDF
Support the magazine and subscribe to the content
This is premium stuff. Subscribe to read the entire article.
