Ask a physics author

[tolbiny]

For xmass i got "Hiding in the mirror" by Lawrence Krauss- its a physics book, attempting to describe the best theories as to the properties and existance of the universe. He works at the same university as my Dad (different departments)- so i have his email and he is willing to answer any questions i have about the material. Not everyone has access to these types of situations so i fully intend to take advantage. If anyone wanted to pick up the book and had questions of their own i could pass them on- or if it was to be included into the book club that was suggested around here that could work to.

[Metric]

I'm not familiar with that specific book, but you might want to ask him the following question -- I'd be interested to hear his response...

Roger Penrose has pointed out the following interesting fact: The number of microstates of the universe compatable with the current macrostate of the universe occupies a tiny fraction of the total phase space compatable with life (an observer, i.e. us) -- the figure is something like one in 10^10^123. It then follows from the postulate of a priori equal probabilities that the observed macroscopic state of the universe is fantastically improbable. This is seperate from the arguments concering the apparent "fine tuning" of coupling constants, and follows from a simple counting of degrees of freedom... It's an interesting problem that I don't often see addressed.

[Borodog]

Unless I missed it, you didn't ask a question.

Besides, the situation you described smacks of:

I was driving today, and I pulled up behind a car with a license plate that read XJR-5836. What are the odds!

[Metric]

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Unless I missed it, you didn't ask a question.

[/ QUOTE ]
The question is implied, of course. Does he, or anyone else, have potential insights that could explain this paradoxical (but little known, apparently) situation?

[ QUOTE ]
Besides, the situation you described smacks of:

I was driving today, and I pulled up behind a car with a license plate that read XJR-5836. What are the odds!

[/ QUOTE ]
No, it is much closer to the following: I walked into the living room this morning and every gas molecule in the room just happened to be sitting for five minutes in a 1" by 1" cube in the far corner by the ceiling. (no mechanical laws forbid it -- those microstates as likely to occur as any other microstate, but seeing this macrostate is vastly improbable: the universe appears to be in a similarly odd situation)

[Borodog]

Actually, those microstate are not as likely to occur as any other microstates. Not by a practically incalculable factor. I think you have a very poor understanding of fluid dynamics.

Also, how does the universe appear to be in an odd situation?

[Borodog]

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those microstates as likely to occur as any other microstate, but seeing this macrostate is vastly improbable

[/ QUOTE ]

Clearly both clauses cannot be true. Do you see why?

[Metric]

The first clause is essentially a statement that "there is no preferred region of phase space" and the second is a restatement of the fact that "macrostates which occupy a relatively tiny region of the allowed phase space are relatively improbable." These are not contradictory statements, in fact they are foundational for statistical mechanics -- the fact that you're balking at them has me worried.

Now, obviously, if you constrain your system such that only a small region of phase space is allowed, you can achieve bizarre states -- but external constraints on the phase space are exactly the sort of thing that we would like to avoid in cosmology.

[Metric]

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Actually, those microstate are not as likely to occur as any other microstates. Not by a practically incalculable factor. I think you have a very poor understanding of fluid dynamics.

[/ QUOTE ]
You know, if you can prove your assertion that the ergodic hypothesis is wrong, there is probably a Nobel prize in it for you.

From wikipedia's entry:

"In physics and thermodynamics, the ergodic hypothesis says that, over long periods of time, the time spent in some region of the phase space of microstates with the same energy is proportional to the volume of this region, i.e., that all accessible microstates are equally probable over long period of time. Equivalently, it says that time average and average over the statistical ensemble are the same."

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Also, how does the universe appear to be in an odd situation?

[/ QUOTE ]
The entropy is very far from maximal, i.e. the current macrostate occupies a volume of phase space very much smaller than other macrostates whose phase space volume is easily calculable.

[gumpzilla]

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[ QUOTE ]
those microstates as likely to occur as any other microstate, but seeing this macrostate is vastly improbable

[/ QUOTE ]

Clearly both clauses cannot be true. Do you see why?

[/ QUOTE ]

There's nothing like "do you see why?" posts that are wrong.

If all the microstates are equally possible, then microstates where everything is in one corner are just as probable as those where they are more evenly spread out. However, the macrostate of evenly spread out across the room admits the presence of incredibly more microstates that can reproduce it. So the macrostate being improbable is a function of the paucity of microstates that can produce it, not the improbability of those microstates themselves.

For a simpler example, let's say I have an urn filled with 1000 black marbles and 1000 white marbles, and I pull out 200 marbles, one at a time. The odds that I pull out 200 black marbles is the same as the odds that I pull out the sequence BWBBBWWBWBWWW..., but the chances that I see 100 white and 100 black instead of 200 black is vastly greater than the chance of seeing 200 black. This is what Metric is talking about. (EDIT: Coin flipping would be a better example, or use an infinite number of marbles instead of 1000 of each, which can complicate things and makes what I've written here inexact. The general argument remains the same, and this one is correct in spirit.)

[Borodog]

I concede. I mispoke. I should have said that the probability of finding the air in the room in the macrostate of being contained within a 1" cube is vastly smaller than the probability of finding the air to be in the macrostate of being distributed throughout the room.

Now that I've taken my head from my ass, I'll have to think about the rest of the question (the bit about the Universe).

Edit: For the record, I didn't have to use any stat mech in my dissertation. /images/graemlins/wink.gif