[ExI] Boltzmann brains

Rafal Smigrodzki rafal.smigrodzki at gmail.com
Mon May 11 05:00:01 UTC 2020

On Tue, May 5, 2020 at 4:21 AM Stathis Papaioannou <stathisp at gmail.com>

> On Tue, 5 May 2020 at 16:47, Rafal Smigrodzki via extropy-chat <
> extropy-chat at lists.extropy.org> wrote:
>>> ### 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
> space.
> 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.
> https://arxiv.org/pdf/0808.3778.pdf
> 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.
### The theories assume that the quantum vacuum fluctuations sample the
space of all possible arrangements of matter in an inverse-size dependent
manner. All structures are created by fluctuations but the larger the
structure the lower the density of such structures in the De Sitter space.
Since De Sitter space is infinitely growing, Boltzmann brains at some point
outnumber evolved brains, for some choices of measurement basis. I agree
that this assumption is not enough to dismiss those theories.

As I mentioned before, Wolfram's approach dispenses with randomness and
imposes structure on vacuum, thus allowing (but not necessarily forcing)
universes without Boltzmann brains. This is of course not a sufficient
reason to choose his approach over conventional ones. However, if his
research program generates theories that have an equal explanatory power to
conventional theories, then the potential absence of Boltzmann brains might
be a factor in his favor, for Occam's razor reasons.

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