The reader will be aware that Boltzmann argues that the universe is mostly in a state of equilibrium, with only rare instances of imbalance:
Man kann sich die Welt als ein mechanisches System von einer enorm großen Anzahl von Bestandteilen und von enorm langer Dauer denken, so dass die Dimensionen unseres Fixsternhimmels winzig gegen die Ausdehnung des Universums und Zeiten, die wir Äonen nennen, winzig gegen dessen Dauer sind. Es müssen dann im Universum, das sonst überall im Wärmegleichgewichte, also todt ist, hier und da solche verhältnismässig kleine Bezirke von der Ausdehnung unseres Sternenraumes (nennen wir sie Einzelwelten) vorkommen, die während der verhältnismässig kurzen Zeit von Äonen erheblich vom Wärmegleichgewichte abweichen, und zwar ebenso häufig solche, in denen die Zustandswahrscheinlichkeit gerade zu- als abnimmt.
Even more significant is his claim that in these rare pockets of disequilibrium, change is as likely to increase entropy as decrease it. This amounts to saying that time is as likely to move forward as backward, because, for Boltzmann, the motion toward entropy is time. For him, motion toward entropy does not happen within time, but rather that motion is time. The source of our observable universe is an anomaly, development away from equilibrium: our observable universe is a pocket within a larger universe.
Describing Boltzmann’s views, Craig Callender writes:
Boltzmann, however, explained this low-entropy condition by treating the observable universe as a natural statistical fluctuation away from equilibrium in a vastly larger universe.
Surveying Boltzmann’s conclusions, then, many questions might arise. Among them are these three:
First, Boltzmann’s hypotheses about the universe are based on, or prompted by, his investigation in gas theory. To which extent is it a valid methodological move, to apply the principles of gas theory to the entire universe? Aside from the observation that the universe includes solids and liquids, and is not composed of gas alone, it seems in other ways, too, that it is a great leap to assume that the principles which govern and explain the behavior of a gas inside a glass container sitting on Boltzmann’s laboratory table are sufficient to explain and govern the entire universe. Can Boltzmann validly generalize to the entire cosmos from a sealed beaker filled with nitrogen, oxygen, carbon dioxide?
Second, to which extent is Boltzmann’s assumption justified, that the universe is largely, almost entirely, in a state of equilibrium? And that any disequilibrium is a small, relatively microscopic, anomalous pocket within this larger universe? The glass container, filled with a gas, on Boltzmann’s laboratory table may well be largely, even entirely, in a state of equilibrium, but to assume the same of the entire universe seems again like an unwarranted generalization. Unlike the glass container in the laboratory, the universe contains near-perfect vacuums between galaxies, contrasted with the most dense possible compressions of matter elsewhere in the same universe. It contains the coldest possible and the hottest possible points. It seems that these would be pieces of evidence that perhaps disequilibrium is more pervasive in the universe than Boltzmann seems to indicate.
Third, do Boltzmann’s results contain a hidden assumption or requirement that there be some type of “meta-time” within which time operates? In order for Boltzmann to indicate that there would simultaneously be pockets within the larger universe, and that time in these different pockets could be going in different directions, there needs to be a larger meta-time in order for these to be happening “simultaneously.”
In addition to the above three questions, there are doubtless many more questions which can, and should, be posed both in order to understand and in order to evaluate Boltzmann’s work.
