This is a keystone talk in my understanding of cosmology, precisely the understanding of the arrow of time and its relationship to the origin(s) of the universe. I will have to listen to this talk a few more times before I feel comfortable with the concepts.
Over a century ago, Boltzmann and others provided a microscopic understanding for the tendency of entropy to increase. But this understanding relies ultimately on an empirical fact about cosmology: the early universe had a very low entropy. Why was it like that? Cosmologists aspire to provide a dynamical explanation for the observed state of the universe, but have had very little to say about the dramatic asymmetry between early times and late times. I will argue that the search for a natural explanation for the observed breakdown of time-reversal symmetry in cosmology leads us directly to interesting conclusions about inflation, quantum gravity, and the multiverse.
Entropy is a measure of how evenly energy is distributed in a system. In a physical system entropy provides a measure of the amount of energy that cannot be used to do work.
When heat flows from a hot region to a cold region entropy increases, as heat is distributed throughout the system.[1] The concept of entropy is central to the second law of thermodynamics. The second law determines which physical processes can occur. For example, it predicts that heat flows from high temperature to low temperature in spontaneous processes. The second law of thermodynamics can be stated as saying that the entropy of an isolated system always increases, and processes which increase entropy can occur spontaneously. Since entropy increases as uniformity increases, the second law says qualitatively that uniformity increases.
Boltzmann brains are often referred to in the context of the "Boltzmann brain paradox" or "problem". They have also been referred to as "Boltzmann babies." [1]
The concept arises from the need to explain why we observe such a large degree of organization in the universe. The second law of thermodynamics states that the entropy in the universe will always increase. We may think of the most likely state of the universe as one of high entropy, closer to uniform and without order. So why is the observed entropy so low?
Boltzmann proposed that we and our observed low-entropy world are a random fluctuation in a higher-entropy universe. Even in a near-equilibrium state, there will be stochastic fluctuations in the level of entropy. The most common fluctuations will be relatively small, resulting in only small amounts of organization, while larger fluctuations and their resulting greater levels of organization will be comparatively more rare. Large fluctuations would be almost inconceivably rare, but this can be explained by the enormous size of the universe and by the idea that if we are the results of a fluctuation, there is a "selection bias": We observe this very unlikely universe because the unlikely conditions are necessary for us to be here, an expression of the anthropic principle. This leads to the Boltzmann brain concept: If our current level of organization, having many self-aware entities, is a result of a random fluctuation, it is much less likely than a level of organization which is only just able to create a single self-aware entity. For every universe with the level of organization we see, there should be an enormous number of lone Boltzmann brains floating around in unorganized environments. This refutes the observer argument above: the organization I see is vastly more than what is required to explain my consciousness, and therefore it is highly unlikely that I am the result of a stochastic fluctuation.
The Boltzmann brain paradox is that it is more likely that a brain randomly forms out of the chaos with false memories of its life than that the universe around us would have billions of self-aware brains. The rationale behind this being paradoxical is that, out of chaos, it is more likely for one instance of a complex structure to arise than for many instances of that thing to arise.
This ignores the possibility that the probability of a universe in which a brain pops into existence, without any prior mechanism driving towards its creation, may be dwarfed by the probability of a universe in which there are active mechanisms which lead to processes of development which (given a starting state that is unlikely but not as unlikely as the spontaneous appearance of a brain with no precursor) offer a reasonable probability of producing a species such as ourselves.
In a universe of the latter kind, the scenarios in which a brain can arise are naturally prone to produce many such brains, so the large number of such brains is an incidental detail.
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