On Wed, Jan 08, 2003 at 04:07:47PM -0800, Hal Finney wrote:
> How could we go about modelling a universe like this?
A mathematical model should be straightforward. For a computational model,
consider a program that takes an infinitely long string as input, which it
interprets as the description of a 3d slice of such an infinite 4d
universe. The description starts at an arbitrary "center of the universe"
and continues in concentric shells. The program computes the future of the
universe from the center, reading its input as needed to obtain
information about the past lightcone.
Now to avoid an actual input that is infinitely long, use a pseudorandom
number generator to produce the input to the above program.
While the computational model has a fixed beginning and a center, the
observers living inside it have no way to tell that. Still it seems a lot
less elegant than a mathematical model that has no center or fixed
beginning. I think it's another reason to prefer a theory of everything
based on all mathematical structures rather than all computations.
> Can we rule out
> Steinhardt's cosmology on fundamental principles?
No, I don't think so.
> Are infinite-time
> universes of zero measure compared to ones with a fixed beginning?
It seems that all computational models must have fixed beginnings, but
maybe you can always find one that can't be distinguished from an
infinite-time universe from the inside.
> It would be interesting if the everything-exists model could be used to
> constrain cosmological theorizing in this way.
It may be possible, but not in this case, I don't think.