Quantum Gravity 149.9: A Probability-Induced Change in the Holographic Principle

From Osher Doctorow

We have derived the equation:

1) P(A-->V ' ) = 2 - [P(A) + P(A-->V)]

in recent Sections of this thread. Here A is interpreted as the
boundary of the volume V which is the "inside" contents of an
object. The outside is V ' .

The Holographic Principle of 't Hooft roughly says that A Causes V or
that P(A-->V) = 1 provided that the boundary A is fixed. In that
case, (1) becomes:

2) P(A-->V ' ) = 1 - P(A)

However, in 3-space, the boundary of a bounded volume V is a surface
area in the absence of holes, and surfaces have Lebesgue Measure 0
which leads us to suspect that P(A) = 0.

Since a bounded surface A is "infinitely thin" in 3 dimensional
Euclidean Space or an approximation thereof, it "makes sense" for P(A)
to be 0. But in that case, (2) would yield:

3) P(A-->V ' ) = 1

which means that the surface A also Causes V ' , which in our context
is the "outer part of the Universe", that is to say not only is P(A--
V) = 1 from before (2) above, i.e., A is Causing Contraction/
Gravitation, but also P(A--> V ' ) = 1 from (3), i.e., A is Causing
Expansion/Acceleration.

The answer must lie in A itself and in the assumption that P(A) = 0,
which in turn is the assumption that the surface A is an "infinitely
thin" boundary of V.

The equation (2) leads to the following:

4) P(A --> V ' ) = 0 if P(A) = 1
5) P(A --> V ' ) = 1 if P(A) = 0

The first case represents contraction, the second expansion/
acceleration of the Universe, and the Holographic Principle's
assumption that the boundary A is fixed is false. The boundary of a
bounded object when gravitation is dominant is arguably regarded by
the Universe as a finite-thickness shell rather than an infinitely
thin surface as in (4), while the boundary is regarded as an
infinitely thin surface when expansion-acceleration is dominant as in
(5).

Osher Doctorow

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