Re: Physical System as Finite, Discrete-State Machine?

da5id65536@xxxxxxxxx wrote:
Wow! Thanks for the time.

I design and analyze pseudo-random bit generating algorithms. These
are all finite, discrete-state machines. While reading an article on
Collapse Theories in the Stanford Enclopedia of Philosophy,
(http://plato.stanford.edu/entries/qm-collapse/) it occrred to me to
wonder if what I already knew had anything to do with what I was
enjoying learning about.

I don't know much about the various collapse models it describes, so I
don't know if random bit-generating algorithms have any connection.
But I can say that the state vectors of quantum mechanics are elements
in a continuous vector space. But no one really knows if state vectors
are the right way to describe the universe at the fundamental level.

Chaotic vs. stable systems is a familiar concept. I can implement
next-state functions for my pseudo-random bit generators which cause
each successive state to be radically different from one before or
different in ways that are small and/or obvious. I can also implement
next-state functions in which a small difference in initial state
results in increasingly divergent states with each iteration, or
next-state functions where initial differences are gradually ironed
out. In all of these cases, however, the next-state function is
completely deterministic. A given state with a given next-state
function always progresses to the same next state. Of course,
next-state functions don't have to be bijective. A given next state
can correspond to more than one previous state. (This is how the
effect of differences in initial states can be eliminated.)

If the universe is some sort of state machine, I would guess that the
state function would be bijective, not because of chaotic systems, but
because a bijective state function implies that the second law of
thermodynamics holds. Of course, just because the second law does hold
doesn't prove that the state function would have to be bijective, so
your guess is as good as mine.

This is a good paper about the relationship between information and
thermodynamics:

http://arxiv.org/abs/quant-ph/0103108

When I was child (before extreme light pollution) I saw a universe that
looked in some respects chaotic and in some respects regular. What I
saw during the day also included bits that seemed ordered and bits that
seemed disordered. Nothing I saw, it seems to me, implies infinitely
many possible states or a next-state function with a huge (much less
infinite) Kolmogorov complexity. Of course, Kolmogorov complexity
isn't actually calculable.

If random mutations of the state occur, outside the control of the
next-state function, a non-bijective next-state function might still
eliminate them--as long as they're rare. On the other hand, a bjective
next-state function could accumulate the differences without
amplifiying them.

I'm not a physicist, but in information theory, "random" means
"unpredictable." Surely Schroedinger's equation at least allows for
precise probabilities!

If you know something is possible at all, Schroedinger's equation will
tell you its probability. It will also tell you the probability of
nonsense statements like the probability of the cat being (1/sqrt(2))
(|alive> + |dead>), provided sufficiently specific definitions of the
|alive> and |dead> states.

But wait--even if it does, that can never
guarantee a (completely) predictable next state, can it? Actually, I
think I like that. If every particle has some degree of freedom, and
I'm a collection of particles, maybe I have some freedom. Hmm.

I read a library book about a year ago on theories of quantum gravity.
It assumed I knew math and physics I didn't know. Do the quantum
gravity theories eliminate all the genuine unpredictablity?

I am merely a student, and I know next to nothing about quantum
gravity. But the answer is probably no, because the unpredicable
things include when a radioactive atom decays, which has no connection
to gravity that I'm aware of. Some interpretations of quantum
mechanics do not posit genuine unpredictability; for example, in
many-worlds, all possible outcomes happen, and in Bohmian mechanics,
the randomness is the result of unknown initial conditions.

I hadn't seen the implication that a "flat" universe implied infinitely
many particles for Schroedinger's equation to work on.

Thanks again, Jim.

Dave

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