Stathis Papaioannou writes:
> There has been some discussion in recent posts about Tipler's Omega Point
> theory, which postulates that an infinite amount of subjective time can
> be squeezed into the last few moments of a collapsing universe. This
> is straightforward mathematically using infinite series, but if time
> is quantised, it would not work in reality; and it seems to be widely
> accepted that time is indeed quantised. Is there a way around this
> difficulty?

John Baez, a widely respected physicist, responds to the question,
is time quantized:

"The brief answer to this question is, 'Nobody knows.' Certainly there
is no experimental evidence in favor of such a minimal unit. On the
other hand, there is no evidence against it, except that we have not yet
found it. There are no well-worked-out physics theories incorporating
a fundamental unit of time, and there are substantial obstacles to
doing so in a way that is compatible with the principles of General
Relativity. Recent work on a theory of quantum gravity in which gravity is
represented using loops in space suggests that there might be a way to do
something roughly along these lines--not involving a minimum unit of time
but rather a minimum amount of area for any two-dimensional surface, a
minimum volume for any three-dimensional region in space and perhaps also
a minimum 'hypervolume' for any four-dimensional region of space-time."

So I think it is an oversimplification to say that it is widely accepted
that time is quantized.  It is pretty clear that something strange
must happen as we go to smaller and smaller time and distance scales,
but nobody knows what.

Tipler's Omega Point theory is basically a theory of general relativity
and I don't think it incorporates quantum mechanics.  So it has to
be viewed as extremely speculative on that basis, although the same
thing might be said of the Big Bang, or of discussion of black hole
singularities, both of which involve infinities much like the Omega
Point theory does.

I'll tell you something else about the OP that most people don't know.
Many people may think of the universal collapse as providing an energy
source and/or effective time speedup which leads to this prediction
that an infinity of calculating can be done.  But this is not the case.
With overwhelming probability, a natural Big Crunch will not allow
for infinite calculations, rather only a finite amount of computation
is possible.

The only way to get an infinite amount of calculation is for the collapse
to take a very special and peculiar form, in which the universe oscillates
unstably from one extreme shape to another.  Instead of collapsing as
a nice little ball getting smaller and smaller, the universe has to
stretch in first one direction, then another, ever more extensively.

Such wild gyrations will not occur naturally, yet they are the only way
for infinite calculations to occur.  Only this will create the ever more
extreme temperature variations that can drive ever-faster calculations.

Tipler's idea is that life itself will take over control of the
universe's collapse.  Just as we may some day control the weather by
predicting its course with extreme accuracy and modifying inputs to
make it do what we want, so, Tipler theorizes, life could control the
very shape of the universal collapse by measuring it, making short
and long term predictions, and then making small modifications to the
energy and matter under life's control in order to shape the path.
Since the universal collapse is a chaotic system, as is the weather,
it might theoretically be possible.

Life's task will become ever more difficult as each oscillation of the
collapse occurs.  With each gyration, life must move more quickly and
accurately to keep the universe on its path.  A single slip-up anywhere
along the line and the potential for infinite calculation is lost.
And meanwhile the temperature is rising exponentially, threatening the
physical stability of whatever substrate of mass and energy life has
adopted to provide for continuity of existence.

Oh, and I forgot to mention that life at one side of the universe can't
communicate with life at the other side.  Infinite computation may be
possible but not infinite communication.  The photons won't get there
before the collapse occurs.  So all of this delicate balancing act must be
accomplished without any global communication, each part of the universe
must act on faith that every other part is going to perform exactly those
steps required to make the whole thing come together and work perfectly.
All this is without any pre-arrangment beyond what we can accomplish in
this era.  We better get our acts together before we head out colonizing.

Given these immense challenges, which increase in difficulty
and complexity literally without limit, improbability piled upon
impossibility, we can throw in the still-unknown difficulties implied
by quantum theory, and a wildly unlikely theory becomes that much less

Then of course there is the new problem that the Big Crunch no longer
is a plausible outcome, tossing Tipler's theories into the trash.

In short, while the Omega Point theory was an interesting speculation
on how infinite computation might be possible in a universe based on
General Relativity, it was never very plausible and is much less so now.

Hal Finney

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