On 8/25/2014 12:46 AM, Russell Standish wrote:
On Mon, Aug 25, 2014 at 12:10:49AM -0700, meekerdb wrote:
On 8/24/2014 9:18 PM, Russell Standish wrote:
On Sun, Aug 24, 2014 at 08:56:03PM -0700, meekerdb wrote:
I think the idea is that quantum randomness is just
first-person-indeterminancy relative to the universes of the
multiverse. The holographic principle would imply that the
information content of any universe is always finite. If there are
infinitely many universes (per eternal inflation) then there would
be infinitely many copies of distinct universe. Or invoking
Leibniz's identity of indiscernibles there would be finitely many
distinct universes, but the number of those that are expanding would
increase without bound. So that would all be consistent with
"comp".
Why finitely many distinct universes? The number of things of finite
information content will be \aleph_0, not finite.
You would only get finitely many distinct universes if the information
content is bounded for some reason, but I don't see any theory giving
that - even the Lloyd limit only refers to this universe, not any
others that might be out there.
The holographic theory implies that any volume enclosed by an event
horizon can contain at most a number of bits of information equal to
it's surface area in Planck units. Since in an expanding universe
the Hubble sphere defines an event horizon, that would imply finite
information in each Hubble sphere volume.
Of course this is a speculative application of the Beckenstein
bound, but it does give right order of magnitude value for the
cosmological constant if the degrees of freedom of quantum fields
are constrained this way.
Brent
My point was that even though each bubble universe had finite
information content, there was no upper bound to the amount of
information a bubble universe could contain. If I specify a certain
ginormous number of bits, then somewhere in the level 2 multiverse,
one will find a bubble universe whose information content exceeds that value.
Cheers
I think the original question was whether this was consistent with comp (or the UD). So
long as every universe is finite at every epoch, I think it is. And since there can be an
infinite number of universes there will be infinitely many copies of each one - which will
diverge in to the future and hence provide FPI for their residents.
Brent
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