Re: Doomsday-like argument in cosmology

From: Hal Finney <>
Date: Sat, 17 Aug 2002 13:57:06 -0700

> Dyson, L., Kleban, M. & Susskind, L. Disturbing implications of a
> cosmological constant. Preprint <>,
> (2002).

Most of this paper is way over my head. I need to read the ending much
more carefully in order to understand its conclusions. But I wanted to
make one point which IMO is really amazing and not often appreciated.
I'm not 100% sure that it applies to the specific model considered in
this paper, but it does apply in general. I think I got this idea from
the Huw Price book on The Arrow of Time.

The authors use the example of a box containing a gas, which starts in
a low-entropy state with all the molecules in a small region. Then as
time moves forward the molecules spread out and we get entropy increase,
allowing for dissipating structures to form such as vortices, and in
the general case even life.

Then the gas reaches equilibrium, and all the dissipative states die out.
All structure and order is lost, and in a sense, time is no longer
passing, as far as causality is concerned. Causal time is something
that only happens when there is entropy increase.

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.

The authors suggest, applying this concept to cosmology, "In the
recurrent view of cosmology the second law of thermodynamics and the
arrow of time would have an unusual significance. In fact they are not
laws at all. What is true is that interesting events, such as life,
can only occur during the brief out-of-equilibrium periods while the
system is returning to equilibrium."

The amazing thing is that this is wrong. Life and other dissipating
events are not restricted to the period when the system is returning to
equilibrium. Here is the surprise: these events also occur, to exactly
the same extent, while the system is *departing* from equilibrium.

That is, if we wait long enough for a Poincare recurrence of the kind
described here, where the gas goes into a low entropy state and then
goes through some kind of complex evolution back to equilibrium, we must
pay attention to how exactly the gas goes into the low entropy state.
And given the microscopic reversibility of the system, the most likely
path into the low entropy state is a mirror of the most likely path out
of it.

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. Life would un-evolve back to a
primordial state, and eventually to simpler dissipative structures and
chemical reactions. The whole clock of the universe would continue
to turn back until it reached the peak of the Poincare recurrence, the
point of minimal entropy, and then it would start to run forward again.

Now, this does not mean that we would see exactly the same path out
of the low entropy state as in; but rather, that both paths would be
governed by the same statistical constraints. The path out of the
recurrence shows constant increases in entropy which guide its path.
The path into the recurrence shows constant decreases in entropy which
guide it in exactly the corresponding manner.

I know this is pretty amazing; so amazing that I can hardly believe it
myself. But it follows immediately from the time-symmetry of the laws
of physics. If Poincare recurrences did not occur in this way, it would
mean that physics had an absolute arrow of time. We could watch a movie
of a low-entropy state forming and then dissipating, and the two phases
would look different, showing that physics is not symmetric in time.

One more point: during the entropy-decrease phase of the Poincare
recurrence, what force pushes us backwards in time? Why does entropy
continue to decrease? The answer is, there is no such force. At every
point during the recurrence, it is *overwhelmingly* more likely to turn
around and start heading towards higher entropy than to continue towards
further decreases in entropy. It is no more likely for time to continue
to run backwards during the first half of a Poincare recurrence than it
is for time to turn around and begin running backwards today.

So how come it happens, then? It is not a physical phenomenon, rather it
is a selection effect. We choose to pay attention only to those Poincare
recurrences which are interesting, that is, those which go back to what
we consider a "beginning of the universe" state. Given enough time,
enormous time, some recurrences will go back that far. So if we restrict
our attention to that minute subset of events, and we ask what path did
the universe follow in getting to this amazing low-entropy state, then
what I have said above is true. The most likely path into the low entropy
state runs along the same constraints as the most likely path out of it.
Time runs backwards into the low-entropy state.

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.)

Hal Finney
Received on Sat Aug 17 2002 - 14:12:48 PDT

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