[ExI] Boltzmann brains

Stathis Papaioannou stathisp at gmail.com
Tue May 5 08:21:31 UTC 2020

On Tue, 5 May 2020 at 16:47, Rafal Smigrodzki via extropy-chat <
extropy-chat at lists.extropy.org> wrote:

> On Tue, May 5, 2020 at 2:21 AM Stathis Papaioannou <stathisp at gmail.com>
> wrote:
>> On Tue, 5 May 2020 at 15:55, Rafal Smigrodzki via extropy-chat <
>> extropy-chat at lists.extropy.org> wrote:
>>> On Sun, May 3, 2020 at 11:31 AM John Clark via extropy-chat <
>>> extropy-chat at lists.extropy.org> wrote:
>>>> We have infinity to work with if Hugh Everett's Many Worlds
>>>> interpretation of Quantum Mechanics is correct, or if Eternal Inflation is
>>>> right, and if the inflationary model of the Big Bang is right then Eternal
>>>> Inflation probably is too. And even if none of that is true and the
>>>> universe is finite in the past dimension it could still have a infinite
>>>> eternal future.
>>> ### For the Boltzmann brain idea to be a paradox you need to consider
>>> not so much the size of the universe (or multiverse), as the density of
>>> biological vs Boltzmann brains per unit of volume. Using a simplistic
>>> approach, biological brains that are a part of larger entities (such as
>>> galaxies) should be much less common per unit of volume, than Boltzmann
>>> brains, since the former require many more atoms to come together.
>>> As I mentioned elsewhere, the resolution of the paradox is that galaxies
>>> and biological brains (but not Boltzmann brains) are created by physical
>>> law, not randomly, so their density is dictated by physical law and cannot
>>> be easily simplistically deduced from the number of moving parts inside
>>> them.
>> It could be that, as you say, regular brains are more likely than
>> Boltzmann brains, but the problem is that in some cosmological models
>> Boltzmann brains are more likely. These cosmological models otherwise seem
>> reasonable; should they be rejected on the grounds that Boltzmann brains
>> are absurd?
>> ### Which cosmological models make Boltzmann brains more likely, and how?

Here is a paper co-authored by several eminent cosmologists:

“The simplest interpretation of the observed accelerating expansion of the
universe is that it is driven by a constant vacuum energy density ρΛ, which
is about three times greater than the present density of nonrelativistic
matter. While ordinary matter becomes more dilute as the universe expands,
the vacuum energy density remains the same, and in another ten billion
years or so the universe will be completely dominated by vacuum energy. The
subsequent evolution of the universe is accurately described as de Sitter
It was shown by Gibbons and Hawking [1] that an observer in de Sitter space
would detect thermal radiation with a characteristic temperature TdS =
HΛ/2π, where
HΛ =��8πGρΛ (1) 3
is the de Sitter Hubble expansion rate. For the observed value of ρΛ, the
de Sitter temperature is extremely low, TdS = 2.3 × 10−30 K. Nevertheless,
complex structures will occasionally emerge from the vacuum as quantum
fluctuations, at a small but nonzero rate per unit space-time volume. An
intelligent observer, like a human, could be one such structure. Or, short
of a complete observer, a disembodied brain may fluctuate into existence,
with a pattern of neuron firings creating a perception of be- ing on Earth
and, for example, observing the cosmic mi- crowave background radiation.
Such freak observers are collectively referred to as “Boltzmann brains” [2,
3]. Of course, the nucleation rate ΓBB of Boltzmann brains is extremely
small, its magnitude depending on how one defines a Boltzmann brain. The
important point, however, is that ΓBB is always nonzero.
De Sitter space is eternal to the future. Thus, if the accelerating
expansion of the universe is truly driven by the energy density of a stable
vacuum state, then Boltzmann brains will eventually outnumber normal
observers, no matter how small the value of ΓBB [4, 7, 5, 8, 9] might be.


There are other models, such as eternal inflation, where Boltzmann brains
may predominate.

Most physicists see it as a problem with their theories, but on its own it
doesn’t seem to be enough to dismiss a theory, unlike, say, an astronomical
prediction that turns out to be wrong.

Stathis Papaioannou
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