> 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.

One problem with this in practice is that it seems that the information
needed to specify the final state is far greater than the information
needed to specify the original state, at least with physics like ours.
In our universe, you could take a snapshot at some time that recorded all
the particle motions in a brain.  Then you could evolve it forward and
produce the successive subjective experiences.  However, I don't think the
snapshot has to be completely detailed.  Some sloppiness is acceptable.
The brain is robust and you could change the details of thermal motions
very considerably and the brain would still work fine.

If you took a snapshot at the end and evolved it backward it would
also work, in theory, but in practice it would not work unless every
detail of every motion was precise to an incredible degree.  (This is
ignoring issues of QM state reduction and such, I'm basically considering
a Newtonian clockwork here.)  It's like, it's easy to come up with
motions to scramble an egg; but to come up with motions to unscramble
one will require absolute precision in every respect.  The result is
that the information requirements for specifying a final-state based
simulation that includes an arrow of time are exponentially greater than
the information needed to create a plausible initial-state simulation.

If we then add the concept of measure based inversely on the size of
the information description, we find that almost all measure of such
simulations comes from initial-state based ones rather than final-state

> 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.

My feeling is that causality, like time, is in the eye of the beholder.
It's not an inherent or fundamental property.  Rather, it is a way that
we can interpret events in some kinds of universes.  Completely chaotic
universes (where every moment is random and uncorrelated with the next)
would not have causality in any meaningful sense.  Likewise for static

In fact I would suggest that causality only exists in our universe in
areas where there is an arrow of time; that is, in areas which are far
from equlibrium and where entropy is unusually low.  The problem in
equilibrium regions is that you can always look at things two ways.
Suppose particle A collides with B and changes its course so that B
collides with C.  We can express this as that A causes B to hit C.
But all the physics works just as well in the reverse direction, in
equilibrium, so we could just as easily say that C caused B to hit A.

Scerir has also posted some interesting paradoxes along these lines
relating to QM.  Suppose we have a photon that passes through a
polarizer oriented at 20 degrees from vertical, then through one
oriented at 40 degrees, and makes it through both.  At the end we would
say its polarization was 40 degrees.  But what was it between the two
polarizers?  Conventionally we would say that the first polarizer made its
polarization become 20 degrees and the second polarizer then changed the
polarization to 40 degrees.  But actually you can just as easily argue
that the photon polarization was 40 degrees between the two polarizers.
That interpretation works just as well, a sort of retroactive causality.

As with time, my guess is that if we restrict our attention to observers
like us, of a type we can comprehend, then automatically we are going to
pick out information systems that have a notion of time, an arrow of time,
and hence a sense of causality.  Not all systems have these properties,
but some do, and all the ones that we would identify as observers fall
into that category.

Hal Finney

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