### Urban Myths in Contemporary Cosmology

#### Posted by Urs Schreiber

Here is something that disturbs me.

For the bulk of human history, cosmology has been myth telling. Serious progress towards a science of cosmology was made when Einstein’s differential geometric theory of gravity was matched with the observation of the cosmic microwave radiation and the observation of Hubble’s law. With the advent of modern sattelite based refinements of such measurements, such as notably WMAP, cosmology has become an exact science. People therefore often speak of the present as the golden age of cosmology.

In this golden age of exact science cosmology, having overcome the age of myths, are we wary of urban myths within the scientific community?

Among some cosmologists the story of the Boltzmann brain is being retold frequently. Influential proponents are Alexander Vilenkin and Andrei Linde.

Vilenkin calls “Boltzmann brains” *freak observers*:

Alexander Vilenkin
*Freak observers and the measure of the multiverse*

arXiv:hep-th/0611271

Andrei Linde,
*Sinks in the Landscape, Boltzmann Brains, and the Cosmological Constant Problem*

arXiv:hep-th/0611043

(“Boltzmann brains” are spelled “Boltzmann branes” on p. 3 of that. One finds the typo the other way around, too.)

Richard Gott III voices the opinion that Boltzmann Brains–I’d Rather See Than Be One.

According to Sean Carroll # the term has been introduced into the scientific literature by

Andreas Albrecht, Lorenzo Sorbo
*Can the universe afford inflation?*

arXiv:hep-th/0405270

In section C of this article the authors make the following claim:

The most likely fluctuation consistent with everything you know is simply your brain (complete with “memories” of the Hubble Deep fields,WMAP data, etc) fluctuating briefly out of chaos and then immediately equilibrating back into chaos again.

No further details are provided there, nor is a justification given. Is this statement self-evident? Is it even clear what the terms mean? Is no quantitative scientific scrutinization necessary? Is this statement supposed to qualify as a scientific statement?

The only proof given in the above article is a reference to the book

J. Barrow and F. Tipler,
*The anthropic cosmological principle*

Oxford University Press (1986)

F. Tipler has otherwise written books such as *The physics of immortality* and *The physics of Christianity*. According to Wikipedia #, George Ellis has actually read these books and found that the myths they tell are a “masterpiece in pseudoscience”.

A version of the argument which is usually cited is on the first two pages of section 6 of

Lisa Dyson, Matthew Kleban, Leonard Susskind
*Disturbing Implications of a Cosmological Constant*

arXiv:hep-th/0208013

Two numbers are mentioned there in support of the claim. The first number, $N_1$, is taken to be the entropy of a given macrostate. The second number, $N_2 \lt\lt N_1$ to be the entropy of the macrostate it evolved from under time evolution. It is pointed out that this means that there are more microstates for the macrostate which did not time evolve from a low entropy macrostate than vice versa.

As far as I can tell, this is a version of the elementary standard thermodynamic textbook observation which says that picking any given macrostate its entropy will with high probability increase *both* in the future *and* in the past.

I am not a professional cosmologist. I have looked around through the literature, followed public discussions and talked in person to (a small sample of) active professional cosmologists. In all these places those who accepted the above statement did so with no further justification than the ones given above.

I do not accept the Boltzmann brain story as a scientific truth. For two reasons: first because I do not accept it as a well-defined scientific statement. And second, I don’t even think as a vague plausibility argument it is sensible.

This is why I don’t think the statement makes sense as a scientific statement:

- We have only a very vague understanding of thermodynamics in general relativity There is no accepted well-formed framework which would allow one to make good scientific sense of entropy and probability “of the universe”. For instance it is unclear which level of coarse-graining is assumed for the definition of entropy here, while on the other hand this is conceivably very relavant for the argument.

- The implicit assumption that we, as inhabitants of this world, are bound to perceive around us the “most typical situation” is neither well defined nor supported by logic. Certainly not by published logic.

(But this principle of mediocracy is propagating through the community of contemporary “theoretical cosmology”. )

- There is no concept of what matter configuration counts as an “observer” and which does not.

This is why I think the statement is wrong even as a plausibility argument:

A well-established scientific theory from two centuries ago explained well which complex structures can be expected to arise in an abundance much higher than suggested by their proportion among all equally weighted configurations: this theory is Darwinian evolution and it refers to self-replicating systems.

Based on this theory I would tend to say that I expect, if I were forced to do so, that the “typical observer in a universe” is a self-replicating system which is a descendant of a very small self-replicating system which arose from some local equilibrium through a comparatively small fluctuation.

And I even have circumstancial experimental support for this statement: by all what we know, the observers that we observe all arose from what must have been a coincidence (=”fluctuation”) by which a bunch of nucleotides suddenly came into an arrangement which lead to self-replication (possibly as described by the RNA world hypothesis).

I find it self-evident that the probability that an observer (a “brain” if you insist) evolves from such a comparatively tiny fluctionation by Darwinian evolution is orders of orders of orders of magnitudes higher than that the observer arises directly by a fluctuation.

But I promise I will not write a scientific article about this argument. My problem is rather: if I am wrong and Boltzmann-brainiology is right: can you prove it to me?

Is there more of an argument than I have summarized above (Albrecht-Sorbo and Dyson-Kleban-Susskind)?

Is the question in reach of exact science?

I find this comparison useful:

When Zeno formulated Zeno’s paradox of Achilles and the tortoise he was not doing exact science. Still, there was some value to the argument. It was finally resolved as a non-paradox many hundred years later in an exact way by the conception of differential calculus, which made the notions appearing in the argument precise and thereby amenable to rational discourse.

## Re: Urban Myths in Contemporary Cosmology

“My problem is rather: if I am wrong and Boltzmann-brainiology is right: can you prove it to me?”

This is like asking if a religion is wrong an other right. According to their own arguments, no one can, since it comes down to just waiting too long for one to show up. It’s like waiting the second coming of Jesus.