From: Larry (email@example.com)
Date: Wed Jan 23 2008 - 09:24:42 MST
While you can't prove a negative, the universe certainly could be a
simulation, I'd say the following:
The universe behaves like a finite state machine because it has state and
its finite. The fun thing about finite state machines, there are certain
rules that hold irregardless of the program being executed. The simple
fact that your operating on a finite number of bits in progress time
slices by itself ends up implying quite a bit. For example unless bits
are added (from where?), the universal state machine will eventually
repeat in 2^N steps or less where N is the number of bits the universe
I tend to think what we see as randomness and probability in quantum
mechanics is due to the fact that we cannot possible know the
entanglements a particle has. The universe at the lowest
level is deterministic, but only on the scale of the entire universe.
Any given quantum system is coupled to the outside world in ways we
cannot know due to its history, and thus appears random. A thought
experiment to prove that entanglement leads to uncertainty.
A and B independantly measure the spin directions of electrons of
unknown history. This means that A & Bs electrons (call them Ae & Be) may
be entangled in any possible way. It may be that Ae spin up implies Be
spin down, or it may be that Ae spin up implies Be spin up, or any other
possible entanglement. Observer A measures spin up, and because the
entanglement history is unknown and cannot be known, B cannot possibly
know in advance what the spin of direction of Be is. Unknown entanglement
histories force local non-determinism, however interestingly they do not
force global non-determinism.
The philosophical implications of a deterministic universe are
interesting. It might well be a fractal being executed which contains
essentially no information at all other than pseudo-random results.
On Wed, 23 Jan 2008, Matt Mahoney wrote:
> Evidence (not proof) that the universe is simulated by a finite state machine
> or Turing machine.
> 1. The universe lacks uncomputable phenomena, such as real-valued states or
> infinite memory computers such as Turing machines. We lack a non
> probabilistic model of physics (quantum mechanics). In a finite state machine
> simulation, a deterministic model would not be possible because the machine
> could not simulate itself.
> 2. The universe has finite entropy. It has finite age T, finite size limited
> by the speed of light c, finite mass limited by G, and finite resolution
> limited by Planck's constant h. Its quantum state can be described in roughly
> (c^5)(T^2)/hG ~ 2^404.6 ~ 10^122 bits. (By coincidence, if the universe is
> divided into 10^122 parts, then one bit is the size of the smallest stable
> particle, even though T, c, h, and G do not depend on the properties of any
> 3. Occam's Razor is observed in practice. It is predicted by AIXI if the
> universe has a computable probability distribution.
> 4. The simplest algorithm (and by AIXI, the most likely) for modeling the
> universe is to enumerate all Turing machines until a universe supporting
> intelligent life is found. The most efficient way to execute this algorithm
> is to run each machine with complexity n for 2^n steps. We observe that the
> complexity of physics (the free parameters in the Standard Model or most
> string theories, plus general relativity) is on the order of n = a few
> hundred bits, which is the log of its entropy.
> If any of these 4 facts did not hold, we would have proof that the universe is
> not simulated by a Turing machine. (It could still be simulated by a more
> powerful machine, such as a computer with real valued registers). However, we
> cannot prove the opposite.
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