origin of order in the universe

[Metric]

One problem with cosmology is the fact that the universe appears so ordered. One of the main postulates of statistical mechanics is that there are no a-priori "preferred" or "special" states. This leads to the prediction that a closed system without any external constraints, should almost always be expected to be in the highest entropy state (thermodynamic equilibrium). But the universe is dramatically NOT in one of these states -- we are alive because the universe apparently started from a supremely "special" state at the big bang, blatantly contradicting the standard assumption of stat mech (invoking anthropic arguments here does not help -- there are a HUGE number of "vastly more probable" ways the universe could support life than the way it was apparently done).

So, what's the explanation? The fact is, "because God did it that way" is nearly as good as anything we have so far. (I'm exaggerating a bit, but not very much)

However, I think there may be another way to look at this. There is a concept computer scientists should be aware of called "computational complexity." Basically, the computational complexity of a bit string is the length of the shortest program that produces that bit string. So, for example:

111111111111111111111111111111

has a very low complexity, since it can be described as "30 1s". On the other hand:

0010011010110010101110101110110

is much more complex -- the shortest description of this string is much longer. An "algorithmically random" bit string is such that no program shorter than the string itself exists -- i.e. their complexity is a maximum.

Now, 20 years ago there was an interesting paper published. Basically, the upshot was that if you want to simulate a physical system on a computer, the amount of information needed to specify the state of the system basically scaled like the entropy. So highly entropic states are much more difficult to specify than low-entropy states. This makes some sense -- try specifying the exact state of every atom of gas in a large chamber, vs. specifying the exact state of those same atoms in a perfect crystal lattice at absolute zero. One is very simple -- the other, mind bogglingly complex.

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.

So, if you envision a kind of "cosmic Turing machine" outputting an ensemble of universes with "random rules of physics and initial conditions" -- then the universal probability distribution predicts that we should expect to find ourselves in a universe evolving from a low-entropy (and thus algorithmically simple) initial state.

So we get to keep the Copernican principle, and at the same time live with the fact that we find ourselves in a "thermodynamically special" state of the universe -- since those are by far the most common!

(this argument has already been used as an explanation of the fact that the rules of physics tend to be "unreasonably simple" -- but I've not seen the connection to the entropy problem of universe drawn before)

[Phil153]

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This leads to the prediction that a closed system without any external constraints should almost always be expected to be in the highest entropy state (thermodynamic equilibrium).

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This is where the argument falls flat. The universe contains billions of heat sources and matter sinks - as well as forces which create these when sufficient matter clumps together. These invalidate the statistical laws of thermodynamics by effectively making it a non closed system.

Hence, sunshine and plants.

[Metric]

[ QUOTE ]
[ QUOTE ]
This leads to the prediction that a closed system without any external constraints should almost always be expected to be in the highest entropy state (thermodynamic equilibrium).

[/ QUOTE ]
This is where the argument falls flat. The universe contains billions of heat sources and matter sinks - as well as forces which create these when sufficient matter clumps together. These invalidate the statistical laws of thermodynamics by effectively making it a non closed system.

Hence, sunshine and plants.

[/ QUOTE ]

I'm afraid you can't get away from thermodynamics that easily. The stars shine because they're moving from a state of low entropy to one of high entropy. If you pick a random point of the universe's phase space, it is almost certainly one dominated by black holes and low-temperature radiation, incapable of supporting life. Penrose has estimated that the state of our universe occupies a volume of phase space roughly 10^10^123 times smaller (and thus 10^10^123 times less probable according to stat mech) than these high-entropy states -- hence the problem.

[RayBornert]

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

[Borodog]

Metric,

Can you expound on the problem a bit more here? I recall running afoul of this subject before in a discussion. I hated stat mech and never had a course in cosmology, so I'm completely adrift in this subject.

For example, what is the roll of the expansion of the early universe? Even if the early universe was in a very high entropy state, as it expanded and cooled the entropy per unit volume would drop tremendously. Does that not get you anywhere?

Also, can you expand on what kind of universe is vastly more likely than ours that could still support life? What would it be like? What is so unlikely about ours?

[FortunaMaximus]

Interesting.

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The universe contains billions of heat sources and matter sinks - as well as forces which create these when sufficient matter clumps together. These invalidate the statistical laws of thermodynamics by effectively making it a non closed system.

[/ QUOTE ]

Not if you consider those processes as smaller states within a system of larger states.

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we are alive because the universe apparently started from a supremely "special" state at the big bang, blatantly contradicting the standard assumption of stat mech (invoking anthropic arguments here does not help -- there are a HUGE number of "vastly more probable" ways the universe could support life than the way it was apparently done).

So, what's the explanation? The fact is, "because God did it that way" is nearly as good as anything we have so far. (I'm exaggerating a bit, but not very much)

[/ QUOTE ]

Observer censorship, perhaps? We know of one Universe because we have no proof, either theortical or practical of others. That doesn't prevent these other probable Universes from existing. I think there's a gap between statistical probability and statistical provability.

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If you pick a random point of the universe's phase space, it is almost certainly one dominated by black holes and low-temperature radiation, incapable of supporting life.

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Does this really have any significance? Take Terra. If you pick a point at random, you're more likely to have a sample of salt water rather than anything else. The various parameters of a system may be co-dependent, rather than independent factors.

[Skidoo]

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One of the main postulates of statistical mechanics is that there are no a-priori "preferred" or "special" states. This leads to the prediction that a closed system without any external constraints, should almost always be expected to be in the highest entropy state (thermodynamic equilibrium).

...

There is a concept computer scientists should be aware of called "computational complexity."

...

Basically, the upshot was that if you want to simulate a physical system on a computer, the amount of information needed to specify the state of the system basically scaled like the entropy.

[/ QUOTE ]

Excellent article. Thanks for the effort.

A next question could concern the requirement of relative computational complexity, or the equivalent in terms of physical information, for any representational means and the physical system it represents.

The obvious answer would imply that it's impossible for anything to contain a (complete) representation of itself, which, if true, means the ordered state of every physical system has an external contributing cause.

[Metric]

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For example, what is the roll of the expansion of the early universe? Even if the early universe was in a very high entropy state, as it expanded and cooled the entropy per unit volume would drop tremendously. Does that not get you anywhere?

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This was originally thought to be part of an explanation, but the problem is that you have to take into account gravitational degrees of freedom as well as matter degrees of freedom -- so the universe isn't just an expanding chamber in which things happen. The state of spacetime itself has to be thought of as part of the system. When you do this, you are back to the problem of a much-too-orderly universe.

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Also, can you expand on what kind of universe is vastly more likely than ours that could still support life? What would it be like? What is so unlikely about ours?

[/ QUOTE ]
You could, for example, have only one galaxy (ours) and the rest be dominated by high-entropy objects (e.g. black holes). States such as these are tremendously more likely from the stat-mech point of view, as they occupy more phase space than a universe like ours (with shining galaxies as far as the eye can see) by a factor of some massive double exponential.

You could argue that a universe like ours would produce more life than one of these, due to the fact that we have more galaxies, but that still doesn't help -- in a statistical ensemble of universes, isolated galaxies still outnumber galaxies in universes like ours by a massive double exponential.

For a truly excellent and entertaining talk on this subject by Penrose, see: http://www.princeton.edu/WebMedia/le...roseVN300K.asx

He discusses both of your questions in much more detail.

[Metric]

[ QUOTE ]
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

[/ QUOTE ]
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")

[thylacine]

Metric, could you post some references to the appropriate papers.

One thing that strikes me immediately is that on the one hand there is the unitary evolution in quantum theory (although I'm sure some theorists are willing to let this go). On the other hand, the processes in a Turing machine are very much not unitary. What kind of processes are supposed to be happening in the picture you describe?

Also, you said "If you pick a random point of the universe's phase space, it is almost certainly one dominated by black holes and low-temperature radiation." Wouldn't a state after the black holes have evaporated be even higher entropy (and hence dominate the phase space)? Of course that may take 2^hundreds of years to get to, which is another point.

Is there a well-defined state-space, (with unitary evolution) anyway?

By the way what do you think of Penrose's chapter "Gravity's role in quantum state reduction" which is Chapter 30 from his book "The Road to Reality"?

I personally believe that black holes spawn new universes with low entropy. Is there any reason to believe this or to doubt this? Is there any theory on how exactly this could happen?