Is the 2nd Law of Thermodynamics invariant?

[madnak]

What if there are infinite universes? Or just a really really really big number?

[Metric]

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What if there are infinite universes? Or just a really really really big number?

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It is possible -- in fact, one often imagines this to be true in formulating the problem. But it certainly does not get rid of the problem: Why do we find ourselves in such a special one, when the vast, vast, vast majority of intelligent beings in this "multiverse" should find themselves sitting in a little localized "oasis" of low entropy, surrounded by black holes? So the problem is effectively the same -- what makes us so fantastically special to be in a universe like this?

[madnak]

Well, with an infinite number of universes, there is certain to be one with the configuration of our universe. And of course, the people in such a universe are likely to consider themselves special in any case.

I don't mean to suggest that there is no reason to question. In that scenario the evidence we have isn't representative. So of course the likelihood of something "strange" behind the scenes is more likely. But our universe isn't inconsistent with the infinite universe idea, either.

Think about this. Maybe within infinite universes, most universes are unique in some way. Maybe a perfectly normal universe is quite rare. Maybe every universe is a bit quirky, so it's no surprise ours is. After all, if we are trying to evaluate our universe as "special," we have to take the full range of variation into account. Who knows what kinds of variables are very "normal" in our universe? We focus on that which stands out, but maybe only a few of a very large number of elements are out of place.

Wouldn't we need to know the range and extent of variability between universes in order to evaluate the likelihood of ours?

[Metric]

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Well, with an infinite number of universes, there is certain to be one with the configuration of our universe. And of course, the people in such a universe are likely to consider themselves special in any case.

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No doubt. However, in cosmology, one is typically guided by the "copernican principle" -- that we don't occupy any particularly special place in the universe (or universe of universes). It's always possible that we really ARE the richest beings (entropy-wise) in 10^10^123 universes and we are simply destined to marvel forever at our extreme luck, but that's not a terribly satisfying answer from a scientific point of view...

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Think about this. Maybe within infinite universes, most universes are unique in some way. Maybe a perfectly normal universe is quite rare. Maybe every universe is a bit quirky, so it's no surprise ours is. After all, if we are trying to evaluate our universe as "special," we have to take the full range of variation into account. Who knows what kinds of variables are very "normal" in our universe? We focus on that which stands out, but maybe only a few of a very large number of elements are out of place.

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But quantifying the kind of strangeness or "specialness" we see is what stat-mech was designed to do. Maybe (in fact, most probably) it just is not up to the task without some subtle revision to take into account general relativity.

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Wouldn't we need to know the range and extent of variability between universes in order to evaluate the likelihood of ours?

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If we're considering universes that have the same raw materials as ours, and we simply look at the number of ways those materials can be ordered -- this is what stat mech is for. If the other universes are just completely different with utterly different physical laws, etc. then there really isn't much one can say statistically at all -- all bets are off.

[madnak]

Well, I don't see any reason to believe that all universes have the <i>same</i> materials or laws. Maybe most of our physical laws are similar with the laws of most other universes. But 100%? I don't know, that actually seems far-fetched to me considering other universes.

Maybe the laws of thermodynamics don't apply at all in some universes, and we aren't really very "lucky" in terms of entropy at all.

But even if we are special, I'm not sure how we would go about drawing conclusions from that.

[Metric]

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Well, I don't see any reason to believe that all universes have the <i>same</i> materials or laws. Maybe most of our physical laws are similar with the laws of most other universes. But 100%? I don't know, that actually seems far-fetched to me considering other universes.

Maybe the laws of thermodynamics don't apply at all in some universes, and we aren't really very "lucky" in terms of entropy at all.

But even if we are special, I'm not sure how we would go about drawing conclusions from that.

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This is the danger of taking the "other universes" too literally. Usually, multiple copies of a system are simply used as a mathematical tool (called a "statistical ensemble") to make probabilistic predictions about a single, given system. For example, you can make correct thermodynamic predictions about a single cylinder of gas by considering a large collection of identical systems (without actually having to consult billions of identical cylinders of gas).

[madnak]

So when you say all "possible" universes, you mean all universes that might have been derived from the same big bang? Are you trying to suggest that the current configuration of the universe doesn't follow from the big bang?

[Metric]

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So when you say all "possible" universes, you mean all universes that might have been derived from the same big bang? Are you trying to suggest that the current configuration of the universe doesn't follow from the big bang?

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Yes, I'm using "all possible universes" and "all possible configurations of our universe" more or less interchangably (see wikipedia's entry on "statistical ensemble" for details). As for the big bang, I'm simply saying that it implies something very puzzling about thermodynamics and statistical mechanics.

[maurile]

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It is true over the long run, but there are local, temporary exceptions.

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Are you sure? What would these be and what do you mean by local? Inside the event horizon of a black hole entrophy decreases but the entrophy of the universe as a whole increases.

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When it was new, in the 1800's, the law was believed to be absolute and fundamental. Philosophers agonized over the "inevitable heat-death" of the universe, when it would have a uniform temperature and everything interesting would be over forever. This cultural fad has carried over to a lot of people's attitudes today, even though it's obsolete. Heat-death is never going to happen.

The 2nd Law is now recognized as an artifact of the way we describe the world, and it only applies probabilistically. That is, violations of the law are unlikely, not impossible, but the bigger the violation, the more unlikely it is. Imagine an evacuated box with a permeable partition and only four gas molecules in it.
<font class="small">Code:</font><hr /><pre>
--------------- ---------------
| mmmm : | | m m : m m |
--------------- ---------------
Low Entropy High Entropy
</pre><hr />
The reason entropy tends to increase is simply that if the molecules are bouncing around at random, the high entropy state is more probable. But it's perfectly possible for the system to spontaneously change from the high entropy state to the low entropy state, and if you wait long enough it will happen. It's just that the more molecules there are, the longer you'd have to wait on average.

You can watch the 2nd Law being violated any time you like with a microscope and a drop of water. According to the 2nd Law, an object moving through a viscous fluid should slow down and stop and stay stopped. But if you watch tiny dust particles in the water, they jump around erratically. Stopped particles start moving. It's perpetual motion. The particles are just getting shoved around by random water molecules.

[Metric]

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You can watch the 2nd Law being violated any time you like with a microscope and a drop of water.

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Whoa -- that is a huge statement!
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According to the 2nd Law, an object moving through a viscous fluid should slow down and stop and stay stopped.

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Actually, the 2nd law says that the entropy of the combined system can only increase. What is breaking down here is the concept of a "viscous fluid" -- we are seeing that the fluid is actually made of individual molecules.

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But if you watch tiny dust particles in the water, they jump around erratically. Stopped particles start moving. It's perpetual motion. The particles are just getting shoved around by random water molecules.

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Yes, but this is actually a prediction of the 2nd law -- not a violation of it! One can see this as follows: The 2nd law predicts that if two systems are in thermal contact, their temperatures will tend to become equal -- i.e. the combined system will move toward a state of equilibrium. Let's model the "dust particle" as a simplified, two state system. It can either be "at rest" (and have no kinetic energy) or it can be "moving" (with some kinetic energy E). Let's say we start the dust particle out "at rest". This represents the energy probability distribution if the dust was at absolute zero. However -- now the 2nd law says that it will move into equilibrium with the "fluid" system and end up at temperature T. The Boltzmann distribution (which maximizes the entropy of a given system), then tells us that the probability to find the dust "moving" will be proportional to exp(-E/kT) where k is Boltzmann's constant and T is the equilibrium temperature. Thus, the probability to find the dust "moving" is now non-zero! (similarly, if you started out in a state of "moving" you would find that the particle moves to the same distribuition with non-zero probability to find the particle "at rest" -- effectively "slowing down" in the fluid as your intuition tells you)

Thus, the 2nd law holds up -- in fact, the 2nd law would have been in deep trouble if the opposite had happened -- if we had started the dust particle out in the "moving" state and then it ended up with 100% probability in the "at rest" state!