Abstract
An information-theoretic approach is shown to derive both the classical weak-field equations and the quantum phenomenon of metric fluctuation within the Planck length. A key result is that the weak-field metric\(\bar h_{\mu \nu } \) is proportional to a probability amplitude φuv, on quantum fluctuations in four-position. Also derived is the correct form for the Planck quantum length, and the prediction that the cosmological constant is zero. The overall approach utilizes the concept of the Fisher information I acquired in a measurement of the weak-field metric. An associated physical information K is defined as K=I−J, where J is the information that is intrinsic to the physics (stress-energy tensor Tμv) of the measurement scenario. A posited conservation of information change δI=ΔJ implies a variational principle δK=0. The solution is the weak-field equations in the metric\(\bar h_{\mu \nu } \) and associated equations in the probability amplitudes φuv. The gauge condition φ uvv =0 (Lorentz condition) and conservation of energy and momentum Tv μv=0 are used. A well-known “bootstrapping” argument allows the weak-field assumption to be lifted, resulting in the usual Einstein field equations. A special solution of these is well known to be the geodesic equations of motion of a particle. Thus, the information approach derives the classical field equations and equations of motion, as well as the quantum nature of the probability amplitudes φuv.
Similar content being viewed by others
References
I. D. Lawrie,A Unified Grand Tour of Theoretical Physics (Hilger, New York, 1990), pp. 27, 167, 297.
L. D. Landau and E. M. Lifshitz,Classical theory of Fields (Addison-Wesley, Reading, Mass., 1951), p. 258.
B. R. Frieden and B. H. Soffer,Phys. Rev. E 52, 2274 (1995).
L. Brillouin,Science and Information Theory (Academic, New York, 1962), pp. 168, 232.
C. W. Misner, K. S. Thorne, and J. A. Wheeler,Gravitation (Freeman, New York, 1973), p. 480.
Ref. 5, p. 417.
B. R. Frieden,Am. J. Phys. 57, 1007 (1989).
B. R. Frieden, inAdvances in Imaging and Electron Physics, P. W. Hawkes, ed. (Academic, Orlando, 1994), Vol. 90, pp. 123–204.
B. R. Frieden, “Quantum gravitational wave equations from an information viewpoint,” unpublished.
B. R. Frieden,Phys. Rev. A 41, 4265 (1990).
B. R. Frieden,Physica A 198, 262 (1993).
B. R. Frieden,Physica A 180, 359 (1992).
B. R. Frieden and R. J. Hughes,Phys. Rev. E 49, 2644 (1994).
B. R. Frieden,Probability, Statistical Optics and Data Testing, 2nd edn. (Springer, New York, 1991), pp. 15, 202.
M. K. Murray and J. W. Rice,Differential Geometry and Statistics (Chapman & Hall, New York, 1993), pp. 158, 163, 181–182.
B. R. Frieden and W. J. Cocke,Phys. Rev. E 53, 257 (1996).
H. L. Van Trees,Detection, Estimation, and Modulation Theory, Part I (Wiley, New York, 1968).
A. J. Stam,Information Control 2, 101 (1959).
A. R. Plastino and A. Plastino,Phys. Rev. E 54, 4423 (1996).
We are indebted to B. H. Soffer for a valuable discussion of this effect.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Cocke, W.J., Frieden, B.R. Information and gravitation. Found Phys 27, 1397–1412 (1997). https://doi.org/10.1007/BF02551519
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02551519