From Osher Doctorow
From Probable Influence/Causation (PI), space and time reverse between
the Big Bang and the Big Crunch, and the Doctorow-Penrose Diagram
(which I have named in honor of Sir Roger Penrose's space-time-light
diagram, although Sir Roger wouldn't know me from Adam) illustrates
this.
We begin with:
1) P' (A-->B) = 1 + y - x, y = P(B), x = P(A), y < = x
Now use z for P' (A-->B), which yields:
2) z = 1 + y - x, y = P(B), x = P(A), y < = x
Let x = t (time normalized on [0, 1]) or the probability of time.
There are two cases two consider:
A. The Big Bang. Here x = 0, y = 0, so z = 1, and we have a point
singularity at (0, 0, 1). The Doctorow-Penrose Diagram is the graph of
(x, y, z) in (2), so it begins at the point singularity at (0, 0, 1),
at "time" t = x = 0. From there on until near the Big Crunch, time is
increasing toward infinity (coded as 1), that is to say x increases
toward 1.
B. The Big Crunch. In the PI interpretation as explained in the
previous Sections, over-massive stars undergo gravitational collapse
toward singularities, and this time x = t = 1 at the Big Crunch since t
has been asymptotically increasing toward infinity (coded as 1). The
equation (2) is now:
3) z = 1 + y - 1 = y
Time has vanished from the equation, and we are now in a 2-dimensional
surface/plane rather than a 3-dimensional representation in the
Doctorow-Penrose Diagram. Since y is a spatial variable or spatial
probability, we get y increasing toward 1 (for example, expansion of
the Universe) but time is "frozen", and so space and time have
reversed. When y = 1, then z = 1, and we reach the point (1, 1, 1)
which is the Big Crunch. We can arguably "reset the clock" there to
another Big Bang. Notice that Black Holes also reverse time and
space, further indication that the Singularity is actually a Black Hole
at least at the endpoints or near them.
Osher Doctorow
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