origin of order in the universe

[thylacine]

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References:

Robert Wald: http://lanl.arxiv.org/abs/gr-qc/0507094
Roger Penrose also has a section in The Road to Reality, called "the thermodynamic legacy of the big bang" or something like that.

Gambini and Pullin:
http://lanl.arxiv.org/abs/gr-qc/0306095


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Ok I read these. The Penrose chapter is 27.

A summary of one aspect (of Penrose and Wald) FWIW: The big bang started in a LOW entropy state in which matter had a uniform density, temperature, and uniform also in all other macroscopic properties. This trips up a lot of people (including me) because, in the absence of gravity, uniform matter is often in a state of HIGH entropy (e.g. gas in a closed container). But when gravity is brought into it, uniform matter has LOW entropy, while clumped matter, especially black holes, and most especially just one giant black hole, has HIGH entropy. Furthermore, this gravitational contribution to entropy potentially swamps all other contributions, that is, the seemingly high entropy of uniform matter in the big bang is actually virtually infintessimally tiny compared the genuinely extremely HIGH entropy of a NON-uniform distribution of matter in the presence of gravity.

I was also going to say something about how a lot of people (including me) also get tripped up in the connection between entropy and things being simple or complex, as well as various other potential sources of confusion about entropy. But I'm getting baffled so I'll stop.

Anyway, the physicists who know what they're talking about make it clear that the big bang started in a LOW entropy state. So the big question is "WHY?" This was the theme of Metric's original post.

[m_the0ry]

Determinism has been disproven which makes this a very difficult question to answer.

The heisenberg uncertainty principle states that the product of the uncertainty in momentum and uncertainty in position must be equal to or greater than a constant (h-bar/2)

dX * dP >= hbar/2

where dX and dP are the uncertainties of the position and momentum, respectively. Simple algebra also governs that this statement is true:

dP >= h-bar/2dX

which is to say that the boundary for the uncertainty in momentum increases as the uncertainty in position decreases. Thus we picture a system in a crystal lattice at nanokelvin temperatures (or, 10^-9 degrees above absolute zero) the uncertainty in position is an incredibly miniscule number, raising the uncertainty in momentum dramatically. Momentum relativistically increases the energy of a system - this can be observed as particles gain mass exponentially as they approach the speed of light. When our nanokelvin crystal is cooled to a certain point the uncertainty in its momentum (corresponding to uncertainty in energy) is great enough that the particle is uncertain enough about its own energy that it can spontaneously create a particle/antiparticle pair.

This is just one example of how the uncertainty principle actually puts a limit on our bitstream represesntation of the universe. As complexity decreases, the effects of quantum mechanics are amplified - which is the antithesis of determinism in the essence that they are completely random. Then we return to representing the universe as a bitstream of a random sequence which, you said yourself, cannot be algorithmically simplified by any less than the length of its components.


my 2 cents.

[RayBornert]

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metric,

what is the general scientific opinion as to what was happening with the overall entropy of the system as the big bang occurred?

a) began with hi entropy which decreased to present levels with the bang.

b) began with lo entropy which increased to present levels with the bang.

c) entropy was selected constant and has never changed.

ray

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There are some attempts to make models that behave like situation (a), though they don't exactly say this in your terms, since it would amount to advertizing the fact that these models violate the 2nd law of thermodynamics (entropy can only increase or stay the same for an isolated system).

Situation (b) is demanded by the 2nd law, so people who think about cosmology in terms of entropy pretty much automatically agree with scenario (b), unless they are prepared to ditch the 2nd law.

I've never heard situation (c) discussed with respect to cosmology.

(btw, I assume your terminology "with the bang" is to be read the same as "after the bang")

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metric,

yes, my phrase "with the bang" refers to everyting from this point back to whatever limit is approached (i.e. singularity).

let me ask it this way,

if we begin here now with our present level of entropy (whatever science says that is) and we move back in time toward the bang event, what does science say about the level of entropy:

a) continuously increasing
b) continuously decreasing
c) constant
d) oscillating

ray

[Metric]

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CC topic 1: "the amount of information needed to specify the state of the system basically scaled like the entropy." This sounds totally reasonable (and uncontroversial) to me, so I guess I don't need to see a paper.

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Just for the record, I'm talking about the following paper by Zurek:
http://prola.aps.org/abstract/PRA/v40/i8/p4731_1
"Algorithmic randomness and physical entropy"

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CC topic 2: "Basically, the computational complexity of a bit string is the length of the shortest program that produces that bit string. ......... Now, one more thing: There is a thing called the "universal probability distribution," which basically says that with RANDOM input, the probability that bit string "x" is the output of a generic Turing machine is (to a good approximation) proportional to 2^-C (where "C" is the complexity of "x"). Thus, "algorithmically simple" outputs are vastly more probable." I guess I can see how this would go, but I'd definitely like to see the paper(s). I'm interested to see exactly what they say, and also to understand what you are saying. Then I think I will be able to form an opinion about this.

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The main paper on this concept of viewing the universe as one of an ensemble generated by random "input" is this:
http://arxiv.org/abs/quant-ph/0011122
"Algorithmic Theories of Everything" by Juergen Schmidhuber
It reviews the basic concepts of algorithmic complexity and the universal probability distribution. Basically, he explains why the universe should be expected to be described by simple laws of physics, using these tools. My only addition is that to specify a universe, in addition to the dynamical laws you must ALSO specify the "initial condtions" (or some generalization of these in a covariant picture), and so by the argument of Zurek in the first paper above means that universes with a simple algorithmic description (and thus low entropy), will come to dominate the "ensemble of universes."

So this is a very different way to think about the statistical mechanics of the early universe -- somehow the use of the "universal distribution" turns a low-probability situation into a high-probability one, while still allowing "randomness" to be the guide for the initial conditions.

[thylacine]

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....
Just for the record, I'm talking about the following paper by Zurek:
http://prola.aps.org/abstract/PRA/v40/i8/p4731_1
"Algorithmic randomness and physical entropy"

....
The main paper on this concept of viewing the universe as one of an ensemble generated by random "input" is this:
http://arxiv.org/abs/quant-ph/0011122
"Algorithmic Theories of Everything" by Juergen Schmidhuber
....

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I could not download the Zurek paper. I guess I'll get it from the library eventually.

I have the Schmidhuber paper on my screen and I plan to read it right now, modulo distractions.

Will I miss much by just reading the second paper?

[Metric]

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Will I miss much by just reading the second paper?

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Nah, not as long as you find it reasonable that high-entropy states require more information to specify precisely than low-entropy states.

[thylacine]

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....
Just for the record, I'm talking about the following paper by Zurek:
http://prola.aps.org/abstract/PRA/v40/i8/p4731_1
"Algorithmic randomness and physical entropy"

....
The main paper on this concept of viewing the universe as one of an ensemble generated by random "input" is this:
http://arxiv.org/abs/quant-ph/0011122
"Algorithmic Theories of Everything" by Juergen Schmidhuber
....

[/ QUOTE ]

I could not download the Zurek paper. I guess I'll get it from the library eventually.

I have the Schmidhuber paper on my screen and I plan to read it right now, modulo distractions.

Will I miss much by just reading the second paper?

[/ QUOTE ]

Okay I read the second paper. Actually I skimmed some parts, so I could easily have missed some important points.

Firstly, although the paper sets out to do various other things as well, there are probably lots of systems for setting things up so that simple laws and/or simple initial conditions are much more likely than complex ones. Probably all such systems are somewhat similar, (if not sometimes equivalent in a broad sense) but they could at least appear to be very different to what is in this paper. You could take Occam's binary-string distribution P(x)=2^{-2length(x)-1} and feed the strings into some process that outputs things (of various kinds) described by those strings (or instead by other finite objects).

I like the absence of the continuum, and the restriction to things being at most countably infinite. Also I like that none of the usual features of physics are taken for granted. (I understand the are diverse speculate models of physics with this characteristic.) On the downside, none of the usual features of physics are shown to (be likely to) emerge from the model, except that dynamical processes are like computations. (Of course causality and locality are built in from the outset, and strict determinism is imposed.) Worse, the author seems to make predictions that I bet most physicists don't believe.

And even when a Turing machine can simulate a `universe' I don't feel that it captures all the features manifestly. For example, say the `universe' has reality being John Conway's game of life in a two-dimensional grid, and it is simulated on a Turing machine which only has one-dimensional tapes. The simulation doesn't make manifest all the symmetries of the two-dimensional grid, for example, and this is a bit unsatisfying.

By the way, the paper is definitely using classical Turing machines, certainly not unitary processes. Presumably the author thinks of unitary processes as something that (seem to) occur in some universes.

I probably had more (and will have more) comments but my brain is full just now.

[Metric]

Keep in mind that the Turing machine example is talked about only because it's a concrete context studied extensively in computer science. I don't think anyone actually believes that there's a single-tape Turing machine running our universe. But the concept is that the univeral probability distribution should apply to anything with a similar structure -- an information input (the laws of physics and initial conditions), something that implements the input, and an information output which corresponds to what we percieve as reality. Then with random input, simpler universes are much more likely. Note that this isn't even a "model" by usual standards -- it's more of a logical principle which seems to justify a lot of things we already know but find a bit mystifying.

The fact that it also seems to go a long way toward making the entropy problem of the universe palatable definately makes me sit up and take notice -- this is a very serious (if underappreciated) problem that that has been sitting in the back of my mind for quite a while.

[thylacine]

As a piece of pure mathematics it's fine but I guess I don't see any deep consequences for physics that could not be obtained just as well, and perhaps more simply, in other ways, such as invoking Occam's binary-string distribution P(x)=2^{-2length(x)-1} and feeding the strings into your favorite process.

Are you saying that this paper makes Occam's razor type conclusions, without making any Occam's razor type asumptions?

Also Penrose estimates the big bang entropy as 10^{88} which is tiny compared to the maximal entropy of 10^{123}, but 10^{88} is nevertheless a huge number, so you need to explain both why it's so small and why it's so big. My gut unstinct (FWIW) is that the ideas in that paper are just not poweful enough to account for that magnitude.

Am I saying something ridiculous?

[Metric]

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Are you saying that this paper makes Occam's razor type conclusions, without making any Occam's razor type asumptions?

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The general concept of the paper is that it provides a kind of justification for Occam's razor in physics (i.e. the unmistakable trend over the centuries to more and more unified, simple theories). And my own observation is that rather than throwing a random dart at the phase space to pick the initial state (the standard stat-mech assumption), simple states (giving low entropy) are preferred if random information is used to actually give a description of the state.

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Also Penrose estimates the big bang entropy as 10^{88} which is tiny compared to the maximal entropy of 10^{123}, but 10^{88} is nevertheless a huge number, so you need to explain both why it's so small and why it's so big. My gut unstinct (FWIW) is that the ideas in that paper are just not poweful enough to account for that magnitude.

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Explaining why it's "that big" isn't too much of a problem -- you can always invoke thermalization. In fact, this is exactly what inflation is designed to do. You'll note that Penrose points out that inflation means that the initial state would have to be even more thermodynamically special, since thermalization means that entropy is increasing from some earlier even-lower-entropy state. While this only makes things worse for "inflation of a random state," it might be absolutely perfect for "inflation of an algorithmically simple state."

In fact, depending on whether I decide to write some of this up, I think spinning it as support for inflationary models (which are in vogue for other reasons right now) would probably be the best way to get attention.

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Am I saying something ridiculous?

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Not at all -- scientists are supposed to be reasonably conservative, and I value your skepticism.