Lee Corbin points to
Tipler's March 2005 paper "The Structure of the World From Pure Numbers":

I tried to read this paper, but it was 60 pages long and extremely
technical, mostly over my head.  The gist of it was an updating of
Tipler's Omega Point theory, advanced in his book, The Physics of
Immortality.  Basically the OP theory predicts, based on the assumption
that the laws of physics we know today are roughly correct, that the
universe must re-collapse in a special way that can't really happen
naturally, hence Tipler deduces that intelligent life will survive
through and guide the ultimate collapse, during which time the information
content of the universe will go to infinity.

The new paper proposes an updated cosmological model that includes a
number of new ideas.  One is that the fundamental laws of physics for the
universe are infinitely complex.  This is where his title comes from; he
assumes that the universe is based on the mathematics of the continuum,
i.e. the real numbers.  In fact Tipler argues that the universe must
have infinitely complex laws, basing this surprising conclusion on the
Lowenheim-Skolem paradox, which says that any set of finite axioms
can be fit to a mathematical object that is only countable in size.
Hence technically we can't really describe the real numbers without an
infinite number of axioms, and therefore if the universe is truly based
on the reals, it must have laws of infinite complexity.  (Otherwise the
laws would equally well describe a universe based only on the integers.)

Another idea Tipler proposes is that under the MWI, different universes
in the multiverse will expand to different maximum sizes R before
re-collapsing.  The probability measure however works out to be higher
with larger R, hence for any finite R the probability is 1 (i.e. certain)
that our universe will be bigger than that.  This is his solution to why
the universe appears to be flat - it's finite in size but very very big.

Although Tipler wants the laws to be infinitely complex, the physical
information content of the universe should be zero, he argues, at the
time of the Big Bang (this is due to the Beckenstein Bound).  That means
among other things there are no particles back then, and so he proposes
a special field called an SU(2) gauge field which creates particles
as the universe expands.  He is able to sort of show that it would
preferentially create matter instead of antimatter, and also that this
field would be responsible for the cosmological constant which is being
observed, aka negative energy.

In order for the universe to re-collapse as Tipler insists it must,
due to his Omega Point theory, the CC must reverse sign eventually.
Tipler suggests that this will happen because life will choose to do so,
and that somehow people will find a way to reverse the particle-creation
effect, catalyzing the destruction of particles in such a way as to
reverse the CC and cause the universe to begin to re-collapse.

Yes, he's definitely full of wild ideas here.  Another idea is that
particle masses should not have specific, arbitrary values as most
physicists believe, but rather they should take on a full range of values,
from 0 to positive infinity, over the history of the universe.  There is
some slight observational evidence for a time-based change in the fine
structure constant alpha, and Tipler points to that to buttress his theory
- however the actual measured value is inconsistent with other aspects,
so he has to assume that the measurements are mistaken!

Another testable idea is that the cosmic microwave background radiation
is not the cooled-down EM radiation from the big bang, but instead is the
remnants of that SU(2) field which was responsible for particle creation.
He shows that such a field would look superficially like cooled down
photons, but it really is not.  In particular, the photons in this special
field would only interact with left handed electrons, not right handed
ones.  This would cause the photons to have less interaction with matter
in a way which should be measurable.  He uses this to solve the current
puzzle of high energy cosmic rays: such rays should not exist due to
interaction with microwave background photons.  Tipler's alternative does
not interact so well and so it would at least help to explain the problem.

Overall it is quite a mixed bag of exotic ideas that I don't think
physicists are going to find very convincing.  The idea of infinitely
complex natural laws is going to be particularly off-putting, I would
imagine.  However the idea that the cosmic microwave background interacts
differently with matter than ordinary photons is an interesting one and
might be worth investigating.  It doesn't have that much connection to
the rest of his theory, though.

Hal Finney

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