From: goldenfieldquaternions@gmail.com
On Monday, June 19, 2017 at 7:19:01 AM UTC-5, Gerry Quinn wrote:
> In article <7e938fae-5abf-481e-9f00-fe9cef4b9168@googlegroups.com>,
> goldenfieldquaternions@gmail.com says...
>>
>> On Thursday, June 15, 2017 at 9:14:49 AM UTC-5, Gerry Quinn wrote:
>>> In article ,
>>> goldenfieldquaternions@gmail.com says...
>>>>
>>
>>>>
>>>> Poincare recurrence in general relativity is a bit hard to put a finger
>>>> on. It is a phase space concept, which is not always easy to quantify. =
>
> [--]
>
>>> If we believe in Poincare recurrence, don't we have to believe in
>>> Boltzmann brains?
>
>> With Boltzmann brains there is a bit of a problem that the time for
>> the assembly of such by random events should be shorter than the
>> time it would take a universe to appear, or maybe equivalently the
>> Poincare recurrence time. Sean Carroll sees this as a problem, for
>> we are left with the uncertainty we might be Boltzmann brains. I
>> see this as more of an annoyance than a problem. If we were Boltzmann
>> brains it would then be questioned how the level of complexity we
>> observe in the exterior universe also came about. This is also
>> connected in some ways to the quirky question over whether we are
>> a simulation. I think these things are unlikely, for it would imply
>> some tight limitation on the level of complexity in the outside
>> world, and so far at least that has not been found.
>
> Well, that was essentially the point I was making. I think we can
> discount the possibility that we are Boltzmann brains, because there
> seems to be no logical reason why the universe visible to a Boltzmann
> brain needs to be ordered nearly so well as the universe we observe.
> Obviously there must be some sort of order and logic in such a brain's
> perceptions so that it can zctually think, but there is no reason why
> there should be - for example - astronomical phenomena that can be
> reasoned about. A permanently foggy sky would do as well for the
> environment of such a brain.
>
> And if Boltzmann brains do not occur, how can we expect that an entire
> universe will recur?
>
> It might be argued that the path to the recurrence of the Big Bang (or
> some later epoch) is the reverse of the path away from it, i.e. the
> history of later events. This might solve the Boltzmann brain problem,
> but at the cost of making Poincare recurrence meaningless. Because if
> we say that events are proceeding in reverse order towards the Big Bang,
> we are appealing to an invented time coordinate carrying on sequentially
> from ordinary time. But the arrow of time itself is a function of
> entropy, so such a universe is not really going backwards in time - the
> only sensible time coordinate for it is that corresponding to increasing
> entropy, i.e. the coordinate moving away from the Poincare recurrence
> event.
>
> So a universe with a Poincare recurrence of that kind would not actually
> have a future recurrence. Instead, it would have a time of maximum
> entropy in which there would be no future but multiple pasts.
>
> - Gerry Quinn
As I said the classical Poincare recurrence may not be defined in
cosmology. In fact for the de Sitter cosmology with accelerated
expansion there does not seem to be much way that an equilibrium based
Poincare recurrence can happen. A quantum recurrence might happen, and
if we think the universe is ultimately unitary then we might demand
that. As I stated a few days ago there is no conveniently defined
concept of equilibrium in general relativity or the thermodynamics and
quantum mechanics of fields in spacetime. So there may simply be no
classical recurrence of cosmology. This does not of course prevent
Boltzmann brains. but it does suggest the two issues are independent of
each other.
LC
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