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

*From*: "Jim Black" <tramspap@xxxxxxxxx>*Date*: 8 Dec 2006 00:32:22 -0800

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

.

**References**:**Physical System as Finite, Discrete-State Machine?***From:*da5id65536@xxxxxxxxx

**Re: Physical System as Finite, Discrete-State Machine?***From:*Jim Black

**Re: Physical System as Finite, Discrete-State Machine?***From:*da5id65536@xxxxxxxxx

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