Hal Finney wrote:
Sometimes we consider here the nature of consciousness, whether observer
moments need to be linked to one another, the role of causality in
consciousness, etc. I thought of an interesting puzzle about Boltzmann
Brains which offers a new twist to these questions.

As most readers are aware, Boltzmann Brains relate to an idea of Boltzmann
on how to explain the arrow of time. The laws of physics seem to be time
symmetric, yet the universe is grossly asymmetric in time.  Boltzmann
proposed that if you had a universe in a maximum entropy state, say a
uniform gas, then given enough time, the gas would undergo fluctuations
to regions of lower entropy.  Sometimes, purely at random, clumps of
molecules would happen to form. Even more rarely, these clumps might be
large and ordered. Given infinite time, one could even have an entire
visible-universe worth of matter clump together in an ordered fashion,
from which state it would then decay into higher entropy conditions. Life
could evolve during this decay, observe the universe around it, and find
itself in conditions much like our own.

The Boltzmann Brain is a counter-argument, suggesting that the universe
and everything else is redundant; all you need is a brain to form via
a spontaneous random fluctuation, and to hold together long enough to
engage in a few moments of conscious thought. Such a Boltzmann Brain is
far more likely to form than an entire universe, hence the vast majority
of conscious thoughts in such a model will be in Boltzmann Brains and not
in brains in large universes. If we were tempted to explain the arrow of
time in this way, we must accept that the universe is an illusion and
that we are actually Boltzmann Brains, a conclusion which most people
don't like.

Now this scenario can be criticized in many ways, but I want to emphasize
a couple of points which aren't always appreciated. The first is that the
Boltzmann scenario, whether a whole universe or just a Brain is forming,
is basically time symmetric. That means that if you saw a movie of a
Boltzmann universe forming and then decaying back to random entropy,
you would not be able to tell which way the movie was running, if it
were to be reversed. (This is an unavoidable consequence of the time
symmetry of the underlying physics.) It follows that while the universe
is moving into the low-entropy state, it must be evolving backwards. That
is, an observer from outside would see time appearing to run backwards.
Eggs would un-scramble themselves, objects would fall upwards from the
ground, ripples would converge on spots in lakes from which rocks would
then leap from the water, and so on.

At some point this time reversal effect would stop, and the universe
would then proceed to evolve back into a high entropy state, now with time
going "forwards". Now, the forward phase will not in general be an exact
mirror image of the reverse, because of slight random fluctuations and
the like, but it will be an alternate path that essentially starts with
the same initial conditions. So we will see one path backwards into the
minimum-entropy state, and another path forwards from that state. Both
paths are fully plausible histories and neither is distinguishable from
the other as far as which was reversed and which was forward, if you
ran a recording of the whole process backwards.

One might ask, what causes time to run backwards during the first half of
the Boltzmann scenario? The answer is, nothing but very, very odd luck.
Time is no more likely to continue to run backwards, or to run backwards
the same everywhere in the local fluctuation-area, than it is to start
running backwards right now in the universe around you. Nothing stops
eggs from unscrambling themselves except the unlikelihood, and the same
principle is at work during the Boltzmann time-reversal phase. It is
merely that we select, out of the infinity of time, those rare occasions
where time does in fact "happen to happen" like this, that allows us to
discuss it.

I want to emphasize that this picture of how Boltzmann fluctuations would
work is a consquence of the laws of thermodynamics, and time symmetry.
Sometimes people imagine that the fluctuation into the Boltzmann
low-entropy state is fundamentally different from the fluctuation out
of it. They accept that the fluctuation out will be similar to our own
existence, with complex events happening. But they imagine that the
fluctuation into low entropy might be much simpler, molecules simply
aggregating together into some convenient state from which the complex
fluctuation out and back to chaos can begin. While this is not impossible
and hence will happen occasionally among the infinity of fluctuations in
the Boltzmann universe, it will be rare. It will be no more common for a
"simple" fluctation-in process to occur than for a simple fluctuation-out
process. In our universe, knowing it will evolve to a chaotic heat
death, we might imagine that molecules would just fly apart into chaos,
but we know that is highly unlikely. Instead, by far the most likely
path is a complex one, full of turbulence and reactions and similar
activity. By time symmetry, exactly the same arguments apply during
the fluctation-in phase. The vast majority of Boltzmann fluctuations
that achieve a particular degree of low entropy will do so via complex,
turbulent paths which if viewed in reverse will appear to be perfectly
plausible sequences of events for a universe which is decaying from
order to disorder, like our own.

Following on to this, let us consider the nature of consciousness during
these Boltzmann excursions. Again let us focus on larger scale ones than
just Boltzmann Brains, although the same principles apply there. During
the time reversal phase, if conscious entities are present, their brains
are running backwards. They are talking backwards, walking backwards,
doing everything in reverse. They remember things that are coming in
the future, and forget everything as soon as it has happened.

The question is, is there any difference in consciousness during the
reverse and forward phases? Consider that during the forward phase, we
started with a low entropy state, and now the laws of physics are playing
out just as they do in our own universe. Everything is happening for a
reason, depending on what has happened before. Events cause memories to
appear in brains by virtue of the same causal effects which give rise
to our own memories. Hence I imagine that most would agree that brains
during the forward phase are conscious.

However, during the reverse phase, things are quite different. Brains
have memories of things that haven't happened yet. Again, one might
ask how this can be. The reason is because we stop paying attention
to fluctuations where this doesn't happen. We only focus on Boltzmann
fluctuations which take the universe into a plausible and consistent
low-entropy state, one from which things can evolve in a way that is
similar to what we see. When a brain remembers something, if that doesn't
happen, the fluctuation is inconsistent. We skip over that one and look
for one that is consistent.

In the consistent fluctuations, brain memories turn out to be correct,
purely by luck. Similarly, every internal function of the brain which
we might attribute to macroscopic-type causality, like neuron A firing
because neuron B fired, will happen instead by luck, with neuron A firing
as though neuron B is going to fire, and then neuron B just happening
to fire in precisely the anticipated way.

The point is that during the time-reversal phase, causality as we
normally think of it is absent. Subjectively-past events do not cause
subjectively-future ones; rather, subjectively-future events take place
before subjectively-past events, and it is merely through luck that things
happen in a consistent pattern. Again, if we hadn't gotten lucky so that
things work out, we wouldn't have called this a Boltzmann fluctuation of
the kind we are interested in (Boltzmann Brain or Boltzmann Universe).
By paying selective attention to only those fluctuations where things
work, we will only observe cases where luck, rather than causality,
makes things happen.

But things do happen, in the same pattern they would if causality were
active.  So the question is, are brains conscious during this time? Do
the thoughts that occur during the time reversal (which recall is not
exactly the same as what happens during the forward-time phase) have
the same level of subjective reality as thoughts which occur when time
runs forward?

We can argue it either way. In favor of consciousness, the main
argument is that time is fundamentally symmetric (we assume). Hence
there is no fundamental or inherent difference between the forward and
reverse phases.  The only differences are relative, with the arrow of
time pointing in opposite directions in the two phases. But within each
phase, we see events which can both be equally well described as leading
to consciousness, and therefore conscious experiences will occur in
both phases.

On the other side, many people see a role for causality in the creation
or manifestation of consciousness. And arguably, causality is different
in the two phases. In the forward phase (the part where we are returning
from a low-entropy excursion to the high-entropy static state), events
follow one another for the usual reasons, and it is correct to attribute
a role for causality just as we do in our own experience. But in the
reverse phase, it is purely by luck that things happen in a consistent
way, and only because we have an infinity of time to work with that we
are able to find sequences of events that look consistent even they arose
by simple happenstance. There is no true causality in this phase, just a
random sequence of events where we have selected a sequence that mimics
causality. And to the extent that consciousness depends on causality,
we should not say that brains during this reverse phase are conscious.

I lean towards the first interpretation, for the following reason. If
consciousness really was able to somehow distinguish the forward from
reverse phases in a Boltzmann fluctuation, it would be quite remarkable.
Given that the fundamental laws of physics are time symmetric, nothing
should be able to do that, to deduce a true "implicit" arrow of time that
goes beyond the superficial arrow of time caused by entropy differences.
  
Symmetry in the fundamental equations of physics doesn't imply that the solutions of those equations have the same symmetry.  Lee Smolin has made some very cogent criticisms of the idea that we can dispense with time as a fundamental variable. See

The present moment in quantum cosmology: challenges to the arguments for the elimination of time
Authors: Lee Smolin
Abstract: Barbour, Hawking, Misner and others have argued that time cannot play an essential role in the formulation of a quantum theory of cosmology. Here we present three challenges to their arguments, taken from works and remarks by Kauffman, Markopoulou and Newman. These can be seen to be based on two principles: that every observable in a theory of cosmology should be measurable by some observer inside the universe, and all mathematical constructions necessary to the formulation of the theory should be realizable in a finite time by a computer that fits inside the universe. We also briefly discuss how a cosmological theory could be formulated so it is in agreement with these principles.
Comments: This is a slightly revised version of an essay published in Time and the Instant, Robin Durie (ed.) Manchester: Clinamen Press, 2000
Subjects: General Relativity and Quantum Cosmology (gr-qc)
Cite as: arXiv:gr-qc/0104097v1

Brent Meeker

The whole point of time symmetry, the very definition, is that there
should be no such implicit arrow of time.  This suggestion would seem
to give consciousness a power that it should not have, allow it to do
something that is impossible.

And if the first interpretation is correct, it seems to call into question
the very nature of causality, and its posible role in consciousness. If
we are forced to attribute consciousness to sequences of events which
occur purely by luck, then causality can't play a significant role. This
is the rather surprising conclusion which I reached from these musings
on Boltzmann Brains.

Hal Finney



  


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