The paradox of reversibility

At the end of the 19th century, a small but influential group of scientists began to question the basic philosophical assumptions of Newtonian mechanics. They even questioned the very idea of ​​atom. The Austrian physicist Ernst Mach, a very influential figure, argued that scientific theories should not depend on assuming the existence of things (such as atoms) that could not be observed directly. It was a matter of time before these scientists devoted themselves to wielding arguments with which to question the kinetic theory. Assuming that the second law was the final touchstone, they employed two apparent contradictions that are known as the reversibility paradox (or Lochsmidt) and the paradox of recurrence. According to them, these two paradoxes demonstrated the incompatibility between the second law and the kinetic theory.

The paradox of reversibility

They were two defenders of the atomic hypothesis, as it was known then, William Thomson (Lord Kelvin) in 1874 and Josef Loschmidt in 1876, who discovered the paradox of reversibility. It was not considered as a serious objection to the kinetic theory until twenty years later. The paradox is based on the simple fact that Newton's laws of motion are reversible in time.

For example, if we see a video of a bouncing ball, it is easy to know if the videotape is moving forward or backward: we know that the collisions of the ball with the ground are inelastic and that the ball rises less each time that bounces However, if the ball made perfectly elastic bounces, it would rise to the same height after each bounce. In this case we could not say the video goes forward or backward.

In kinetic theory, it is assumed that molecules produce perfectly elastic collisions. Imagine that you could make a video of gas molecules colliding elastically according to this assumption. When watching this video, there would be no way of knowing if it is going forward or backward. In any case it would show valid sequences of collisions. But here is the paradox: consider videos of interactions involving large objects, which contain many molecules. We can immediately tell the difference between the direction of time forward (true) and backward (impossible). For example, a broken light bulb is not rebuilt in real life, although a video that runs backwards can make it look like it does. And this contradicts a basic principle of Newton's laws.

In effect, the kinetic theory is based on laws of motion that assume that the movements are reversible for each individual molecular interaction. How, then, can you explain the existence of irreversible large-scale processes that involve many molecular collisions? The existence of such processes seems to indicate that time flows in a definite direction, that is, from the past to the future. This contradicts the possibility, implicit in the laws of Newton's movement, that when it comes to observing physical phenomena, it does not matter if we think that time flows forward or backward. Thomson expressed it this way:

If the movement of every particle of matter in the Universe were reversed precisely at any moment, the course of nature would simply reverse forever. The bubble of foam that explodes at the foot of a waterfall would reform and descend to the water; the thermal movements would re-concentrate their energy and throw the mass upwards through the waterfall into drops that become a closed column of rising water. The heat generated by the friction of the solids and dissipated by conduction, and radiation by absorption, would return again to the place of contact and throw the body in movement against the force to which it had previously given way. . . . But the real phenomena of life infinitely transcend human science; and speculation regarding the consequences of their imaginary reversal is completely unproductive.

Thomson himself, and later Boltzmann, used statistical probability to explain why we did not observe such large-scale reversals. There is an almost infinite number of possible disordered arrangements of water molecules in the fall of a waterfall. Only an extremely small number of these provisions would lead to the process described by Kelvin. Reversals of this kind are possible in principle but, for all practical purposes, the statistical nature of the second law makes them impossible.

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