Hal Finney wrote:
Jesse Mazer writes:
> Hal Finney wrote:
> >I imagine that multiple universes could exist, a la Schmidhuber's
> >or Tegmark's level 4 multiverse. Time does not play a special role in
> >the descriptions of these universes.
> Doesn't Schmidhuber consider only universes that are the results of
> computations? Can't we consider any computation as having an intrinsic
> "causal structure"? How would it be possible to write an algorithm that
> describes a "Life" universe where there's no time, where the t-axis is
> replaced by a z-axis, for example?
Well, you could just replace the letter t with the letter z, but of course
that wouldn't change the underlying nature of things. You might well
say that there was still a time axis, just that it had a different name.
But the bigger question is whether the order in which a universe is
computed must match the concept of "time" within that universe.
True, it isn't always necessary to compute things in the same order--if
you're simulating a system that obeys time-symmetric laws you can always
reverse all the time-dependent quantities (like the momentum of each
particle) in the final state and use that as an initial state for a new
simulation, and the new simulation will behave like a backwards movie of the
original simulation. But since I don't have a well-defined mathematical
theory of what it means for two computations to have the same "causal
structure", I'm not sure whether the causal structure would actually be any
different if you computed a universe in reverse order. When I think of
"causal structure", I'm not really presupposing any asymmetry between
"cause" and "effect", I'm just imagining a collection of events which are
linked to each other in some way like in a graph, but the links need not
have any built-in direction--if two events are linked, that doesn't mean one
event is the cause and the other is the effect, so the pattern of links
could still be the same even if you did compute things in reverse order.
From what I've read about loop quantum gravity, it's a theory in which space
and time emerge from a more primitive notion of linked events, but I'm
pretty sure it's not a time-asymmetric theory.
Further, in our own universe there appears to be quite a bit of ambiguity
about time ordering, and many different computational strategies will
work equally well. Relativity theory shows that events either have a
timelike separation, in which case it is clear which one is in the past,
or a spacelike separation, which makes it ambiguous which one is farther
in the past.
True, but the only way for two events to be causally linked in relativity is
if there is a timelike separation between them, and in that case all
reference frames will agree about the order of the events.
It was suggested here a while back that a Life universe could be
computed using an algorithm which ran around somewhat randomly and made
localized changes to cells in order to make them match the Life rules.
Eventually this would converge to a stable and consistent Life universe.
Any observers living in that universe would have a perceived direction
of time that was very different from the actual order in which it was
Another way to do this might just be to have a computer generate *all*
possible sequences of cell-changes over some finite number of steps and
using a finite-sized board, and then check each one to see if it is obeying
the rules of "Life" at each step, and throw out all those that don't. Is it
possible that the "causal structure" of a program checking every cell at
every step of a valid Life sequence is the same as the causal structure of
actually computing that sequence from its initial conditions? Or that even
if they're different, one causal structure "contains" the other, like a
graph that contains another one as a subset? Again, without a well-defined
notion of the causal structure of a given computation it's hard to be sure.