Classical Gravity as an Eikonal Approximation to a Manifestly Lorentz Covariant Quantum Theory with Brownian Interpretation

Details Classical Gravity as an Eikonal Approximation to a Manifestly Lorentz Covariant Quantum Theory with Brownian Interpretation Classical Gravity as an Eikonal Approximation to a Manifestly Lorentz Covariant Quantum Theory with Brownian Interpretation

2004-07-20

arxiv.org/abs/gr-qc/0407076v1

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

46 pages, PLain TeX. To be published in "Progress in General Relativity and Quantum Cosmology Research". Hauppage (2004)

Scientific paper

We discuss in this Chapter a series of theoretical developments which motivate the introduction of a quantum evolution equation for which the eikonal approximation results in the geodesics of a four dimensional manifold. This geodesic motion can be put into correspondence with general relativity. One obtains in this way a quantum theory on a flat spacetime, obeying the rules of the standard quantum theory in Lorentz covariant form, with a spacetime dependent Lorentz tensor $g_{\mu\nu}$, somewhat analogous to a gauge field, coupling to the kinetic terms. Since the geodesics predicted by the eikonal approximation, with appropriate choice of $g_{\mu\nu}$, can be those of general relativity, this theory provides a quantum theory which could be underlying to classical gravitation, and coincides with it in this classical ray approximation. In order to understand the possible origin of the structure of this equation, we appeal to the approach of Nelson in constructing a Schroedinger equation from the properties of Brownian motion. Extending the notion of Browninan motion to spacetime in a covariant way, we show that such an equation follows from correlations between spacetime dimensions in the stochastic process.

Affiliated with

Also associated with

No associations

Rating

Classical Gravity as an Eikonal Approximation to a Manifestly Lorentz Covariant Quantum Theory with Brownian Interpretation does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Classical Gravity as an Eikonal Approximation to a Manifestly Lorentz Covariant Quantum Theory with Brownian Interpretation, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Classical Gravity as an Eikonal Approximation to a Manifestly Lorentz Covariant Quantum Theory with Brownian Interpretation will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-143143