[ExI] Boltzmann brains

Rafal Smigrodzki rafal.smigrodzki at gmail.com
Sat May 2 02:31:29 UTC 2020

It occurred to me today that Wolfram's hypergraph theory offers a solution
to the paradox of Boltzmann brains.

Boltzmann brains show up when you contemplate sufficiently large numbers of
fluctuating physical entities (atoms, molecules), where any physically
possible arrangement of molecules eventually happens by some random
aggregation of molecules. The theorists assume that the likelihood of a
particular arrangement of smaller entities coming "randomly" into existence
is a more or less simple function of the number of entities needed to form
that arrangement. Since it takes a lot fewer atoms to make a brain than
needed to make a galaxy, brains just randomly forming and miserably and
almost immediately expiring somewhere in the universe should outnumber
galaxies randomly forming in that universe by some hundreds of orders of
magnitude. Therefore, you should expect your existence to end just about
now, since you are more likely to be a Boltzmann brain than a brain in a
body on a planet. Since none of the Boltzmann brains survive to tell us
about their experiences, our life is not affected and the whole notion is
not excluded by available physical evidence.

The above assumes that the "random fluctuations" uniformly sample the
configuration space of molecular assemblies, without providing any clear
physical interpretation of how such a random process could work. It seems
to assume an idea of true randomness that given a bunch of swirling
physical thingies literally anything can happen if you wait long enough.
You notice how I use very non-sciency sounding words to refer to this idea,
which I find rather suspect.

Wolfram's hypergraph theory is deterministic and finite.The laws of his
universes are simple rules repeatedly applied to simple mathematical parent
structures that generate completely predictable progeny structures, without
any place for randomness. The structures so created are however
computationally irreducible - the only way of finding out which structures
will be created by the process is to run the process, there are no exact
and general shortcuts.

It follows that if our universe is created by one of these deterministic
and finite processes, then there is a structure to the seemingly random
movements of molecules we see. The law of our universe does not uniformly
sample the configuration space of molecular assemblies. The law imposes a
precise structure on all that happens, and most stuff we can vaguely
imagine cannot happen. There is no physical shortcut that leads from a
handful of atoms to a Boltzmann brain, you actually have to go through
making quarks, then atoms, then galaxies, then planets... etc. The initial
state of the graph and the rule applying to it, the moment zero of all
time, is the ultimate conceivable high-energy and low-entropy physical
state and at the same time a pure mathematical entity. It implies all the
theorems true of that entity but not any other theorems.

Of course, since we don't know our universe's rule we cannot begin to
calculate if there are Boltzmann brains out there, and even if we knew the
rule we would not be able to run the rule's calculation precisely enough to
get an answer. So we still cannot exclude the possibility of Boltzmann
brains - but we can say that if Wolfram is right, then they are not
necessarily implied by the physics of our universe, and may very well be

If we find a good candidate for the rule of our universe, the final TOE,
among Wolfram's hypergraphs, we might eventually be able to perform
approximate first-principle calculations of vacuum energy, the cosmological
constant, find a solution to the vacuum catastrophe and calculate the
density of Boltzmann brains in space.

My guess is Boltzmann brains are very few and far between, compared to us
normal folks.

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