We set up an essential model to describe quanto-gravitational
fluctuations: the model is heuristic but gives a picture of
quantum fluctuations of the gravitational field that respect:
-
the uncertainty principle (fundamental principle
of quantum theory);
- a causal propagation that mimics the light-cone structure
of relativity.
The gravitational effects of these fluctuations of the energy
density are then considered: in this sense, and together with
1. and 2. above,our description of the fluctuations is quantum
and gravitational. In particular we picture spacetime
as a foam constituted of fluctuations of the energy density
that expand as spherical bubbles: during the expansion, the
energy density of the bubbles decreases, so that the Energy-Time
uncertainty principle is not violated. Moreover in computing
the total energy density due to the fluctuations at a given
point in space, we assume that randomly distributed fluctuations
propagate at most at the speed of light c.
The foamy picture of spacetime obtained in this way is certainly
not continuous, since discontinuities in the energy density
arise at the boundary of each expanding fluctuation. We give
a statistical analysis of the gravitational potential associated
to the above energy density, by computing the correlation functions
for the fluctuations.
In the above described framework, the non-continuity of the
foamy spacetime structure could, in principle, be detected by
its effects on the propagation of light signals. In this context
we show how it could be possible to estimate these effects in
a two arm interferometer.
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