Recurrence in the universe

From: Tim May <tcmay.domain.name.hidden>
Date: Sat, 17 Aug 2002 21:29:24 -0700

On Saturday, August 17, 2002, at 01:57 PM, Hal Finney wrote:
>
> After an extremely long interval, we may get a Poincare recurrence.
> (Actually, I'm not sure this is the right term for this; I think a
> Poincare recurrence is a more general thermodynamic effect. But I will
> use the phrase here to specifically talk about a low-entropy fluctuation
> out of a high-energy equilibrium state.) The gas will randomly happen
> to
> move back into a low-energy state, perhaps even the same state we
> started
> with, all the molecules in one corner. At that point we once again get
> dissipation, structures, the passage of time, and the possibility of
> life.
> This cycle can and will repeat indefinitely.

As usual, I am intensely skeptical. From the magnitudes of the
calculations, not from a "gut feel."

The gedankenexperiment of all the molecules in a box being found in one
small volume/corner of the box is a classic textbook calculation. I
haven't done the calcs in a long, long time, but it's fairly clear that
even a mole-magnitude quantity of molecules might "easily" take some
incredibly huge amount of time, something like 10^500 years, to
"randomly" end up in a volume 1% as large as the box. (It might just as
easily be 10^2000 years or more....6 x10^23 molecules bouncing around
is hard to find in one region of the phase space.)

How long before 10 moles find their way to a small part of the phase
space? Or galactic-cloud-sized quantities?

And biological structures with chemical reactions driven by
concentration gradients on lipid layers...whew.

I guarantee that the "time for gas molecule-type recurrence" is
something like 10^10^10^10^10^10.....10 years.

Now I realize that "infinity" is a much larger number than
"10^10^10^10^.....10 years," and so a Cantorian correspondence might
suggest that "it could happen."

But in any finite chunk of time, no matter how large, my hunch is that
the "divergence" issues utterly dominate. That is, in the first 100
billion years of the universe's life after the stars all burn out (say,
200 billion years from now), there still will not be a single instance
anywhere in the universe where a mole of hydrogen in some reasonable
volume (a thousand cubic kilometers, maybe) has "fluctuated" into an
ordered state where the hydrogen is at much higher concentration.

(This doesn't preclude bounces which reset to very dense states.)

> That is, if we really assume that somehow this gas in the corner evolved
> life which then died out in the heat death of the universe, then the
> most likely path back into the corner is to evolve life backwards.
> We would see the formless void of space begin to cluster together to
> form
> structure. That structure would include the pattern of dead life-forms.
> These life-forms would come to life, and they would live their lives
> backwards. They would grow young and be un-born. Each generation
> would be replaced by its ancestors.

I don't claim to understand the physics of time asymmetry (despite the
books I have read, including starting Huw Price's book recently, based
on recommendations here), but this extension of billiard ball
gedankenexperiments to "living lives backwards" is just too bizarre.

So many chemical reactions, so many biological "objects," so many issues
of functional causality (as but one example, the heart pumping blood,
enabling cell growth, etc.). To hypothesis that "if we wait long enough,
cells will randomly get smaller, will ungrow, causing reverse fluid flow
to then cause the heart to beat backwards...." (as but one of a vast
number of examples...and this effect has to happen across all organisms
in all places, else the Universe has not really "unaged."

If a mole quantity of hydrogen may take "10^10^10^...10" years just to
get to a "low entropy state, but not necessarily the same structure as
before," then how long .... well, it ain't something I'll lose sleep
over.

> I believe it follows, then, that if we are living in such a Poincare
> recurrence, it is overwhelmingly likely that the universe did not really
> go all the way back to the Big Bang. Rather, our past is an illusion.
> Time ran backwards far enough to form us; but among those recurrences
> where we formed, the overwhelming majority of them don't have time go
> back much farther than that. (My son is reading the Price book now and
> says that this idea goes back to Boltzmann, that our past is false and
> the universe no older than us, if our experience are explained by such
> a recurrence.)


Nietzsche had similar ideas of the "eternal recurrence," circa 1870.



--Tim May
(.sig for Everything list background)
Corralitos, CA. Born in 1951. Retired from Intel in 1986.
Current main interest: category and topos theory, math, quantum reality,
cosmology.
Background: physics, Intel, crypto, Cypherpunks
Received on Sat Aug 17 2002 - 21:36:31 PDT