The paradox of recurrence

In addition to the paradox of reversibility, there is another possibility allowed by the kinetic theory that leads to a situation that seems to unequivocally contradict the second law. What we will call the paradox of recurrence recovered an idea that appeared frequently in ancient philosophies and is also present in current Hindu philosophy: the myth of the "eternal return". According to this myth, the long-term history of the world is cyclical. All historical events are finally repeated, perhaps many times, perhaps infinitely. With enough time, even the stuff that people are made of will revert to a concrete form by chance. At that moment a dead person could be born again and, perhaps with even more time, live the same life already lived. The German philosopher Friedrich Nietzsche was convinced of the truth of this idea.

"Reptiles", by M.C. Escher. Lithography 33.4 cm × 38.5 cm (1943)

The recurrence paradox comes from the fact that the number of molecules in the world is finite, therefore, there is only a finite number of possible molecules dispositions. Therefore, if time continues infinitely, the same combination of molecules will re-emerge. At some point, all the molecules in the universe would again take exactly the same arrangement they had at some previous time. All events that follow this point would be exactly the same as the events that followed before. That is, if any single moment in the history of the Universe is repeated exactly, then the entire history of the Universe will be repeated from that moment. In fact, unless we reflect we will realize that it would repeat again and again to infinity. And this contradicts the second law, since the energy would not dissipate without end. Nietzsche affirmed that this vision of the eternal return refuted the theory of the "thermal death" of the universe.

Almost at the same time, in 1889, the French mathematician Henri Poincare published a theorem on the possibility of recurrence in mechanical systems. According to Poincaré, despite the fact that the universe could suffer a thermal death, finally it would end up being resurrected. In his words:

A limited world, governed only by the laws of mechanics, will always go through a state very close to its initial state. On the other hand, according to the accepted experimental laws (if one attributes absolute validity to them, and if one is willing to take its consequences to the extreme), the universe tends to a certain final state, which it will never abandon. In this final state, [...], all bodies will be at rest at the same temperature [...]. . . Kinetic theories can liberate themselves from this contradiction.

The world, according to these, tends at the beginning to a state in which it remains for a long time without apparent changes; and this is consistent with experience; but it does not remain that way forever; . . . it simply remains there for an enormously long time, a time that is longer the more numerous the molecules are. This state will not be the final death of the universe, but a kind of lethargy, from which it will awaken after millions of centuries.

According to this theory, to see the heat pass from a cold body to a warm one, it will not be necessary to have the sharp vision, intelligence and dexterity of Maxwell's demon; It will be enough to have a little patience.

Poincaré was willing to accept the possibility of a violation of the second law had always been a long enough time. Others refused to even admit this possibility.

The kinetic theory is almost correct

The result of the dispute between the defenders and the critics of the kinetic theory was that both sides were partly right. Mach and his followers were right in believing that Newton's mechanical laws can not fully describe molecular and atomic processes. For example, it is only approximately valid to describe gases in terms of collections of small balls that move at different speeds. But Boltzmann was right in defending the utility of the molecular model. The kinetic theory is almost correct, except for those properties of matter that involve the very structure of molecules. To advance in this way, all the development of quantum mechanics would be necessary.

The success of the kinetic theory with Einstein's explanation of the Brownian motion, together with the discoveries in radioactivity and atomic physics, convinced almost all critics that, in fact, atoms and molecules exist. But the problems of irreversibility and whether the laws of physics must distinguish between the past and the future are still latent. To make matters worse, the discoveries of the twentieth century led the studies of the dynamics of heat through increasingly subtle and fascinating territories.

About the author: César Tomé López is a scientific disseminator and editor of Mapping Ignorance