Thursday, December 20, 2018

Irreversible processes

Those physicists who consider the arrow of time as an illusion have a problem: not all physics is compatible with a reversible time, as the equations and theories mentioned in an earlier article of this blog seem to indicate. The second principle of thermodynamics is known since the mid-nineteenth century (1850), when Clausius introduced the concept of entropy and it was proved that the value of this physical magnitude always increases, if it is measured in an isolated system that does not exchange matter or energy with its outside. Since the universe is an isolated system, we have at least one physical quantity that makes it possible to unequivocally signal the direction of time flow.
Aware of this problem, physicists in favor of the reversibility of time have answered in different ways: it has been said that the second principle of thermodynamics is a fictitious, subjective law that does not conform to reality; a mental illusion; an approximation; a consequence of the initial conditions of the universe. It has been hypothesized that, if the universe were cyclic, the arrow of time would be reversed during the contraction stage. (This theory has been abandoned). To escape the problem, Stephen Hawking proposed a universe without initial conditions in his book A Brief History of Time. It is curious, this desire to defend at any price the reversibility of time, when it was precisely Hawking who proposed the existence of an arrow of time in black holes, which rather than being permanent, would disintegrate.
In 1928, a year after inventing the term the arrow of time, Arthur Eddington challenged the physicists who defend the reversibility of time with the following devastating words: If your theory is found to be against the second law of Thermodynamics... there is nothing for it but to collapse in deepest humiliation (The Nature of the Physcal World, 1928).
This dilemma has a name, which was invented in 1876 by Johann Joseph Loschmidt: the paradox of irreversibility, which can be described as follows:
·         According to the laws of mechanics that we know, there does not seem to be an arrow of time in the microscopic world. If we accept the reductionist hypothesis, there shouldn’t be one in the macroscopic world.
·         But according to experience and thermodynamic experimentation, there is an arrow of time in the macroscopic world.
·         Consequently, mechanics and thermodynamics must be incomplete, for they reach incompatible conclusions.
As Alfred North Whitehead said, a clash of doctrines is not a disaster, it is an opportunity (Science and the Modern World, 1967).
Are the laws of mechanics and the microscopic world really reversible, as asserted by those who deny the existence of the arrow of time? It is not so clear. Let us see:
1.      Newton's mechanics not only explains the movements of celestial bodies, but also much closer phenomena, such as the fall of an apple, whose irreversibility is fully evident. Imagine you are shown a film where several pieces of apple are on the ground, which suddenly start moving and come together at the same point, turning into a piece of fruit that flies upwards, until it stops hanging from a branch of a tree. Would we have any difficulty in detecting that the direction of time has been reversed when projecting this film? No, for this example makes use, not just of only Newton's mechanics (which explains the motion of the apple when it is falling), but also of the second principle of thermodynamics, which tells us that the change from a disordered state (the pieces of the apple) to an ordered state (the apple hanging from the branch of the tree) cannot take place spontaneously.
Even in celestial bodies it is possible to detect if the film showing their movements has been inverted. Imagine a recording of Mercury's orbit where the sun can be seen. By looking at the movement of the sunspots (which are a consequence of thermodynamic phenomena) it is possible to find out if the image is correct or has been inverted. Once again the interaction of mechanics and thermodynamics makes time irreversible.
2.      There are reversible chemical reactions, such as the dissolution of calcium carbonate in carbonated water, which when taking place in the opposite direction is responsible for the existence of stalagmites and stalactites. But there are also irreversible reactions, such as the precipitation of barium sulfate when mixing two solutions of sodium sulfate and barium chloride. Also in this case, detecting the correct direction of projection of a film is very simple.
There are also irreversible nuclear reactions, such as the series of disintegrations of uranium-238 ending in lead-206. The inverse chain is so unlikely, that the analysis of the proportion of these two substances in the same rock provides a means of ascertaining its age.
3.      Quantum mechanics also contains indications that time is irreversible, such as the measurement problem: if we measure the state of a particle in a superposition of quantum states, it collapses in one of them with a certain probability. The reverse phenomenon, however, never happens.
Another indication is the CPT symmetry. So far we know no violation of this symmetry, which consists of simultaneously changing the sign of the charge of a particle, its parity and the direction of time. However, a violation of CP symmetry has been detected in the disintegration of a kaon-0: in one out of every billion disintegrations, this particle becomes a positive pion, an electron and an antineutrino, while its normal disintegration turns it into a negative pion, a positron and a neutrino. If the CPT symmetry is true, as it is suspected, the violation of the CP symmetry implies that time is irreversible.
4.      As noted by the biologist Stephen Jay Gould (Wonderful life, 1989), the history of the evolution of living beings is asymmetric: as the number of species grows, the types of organization decrease. There would be, therefore, an arrow of evolutionary time (Time's arrow, time's cycle, 1988).
Roger Penrose
Finally, it is not true that all modern cosmological theories lead to a reversible time. Physicist Roger Penrose has spent years trying to find an alternative theory that unifies gravitation, explained today by Einstein's general relativity, with quantum mechanics. His unified cosmological theory, which has not yet been satisfactorily defined, would imply the existence of an arrow of time. In his own words: ...time-asymmetry of time [is] a necessary feature of Nature’s quantum-gravity union (The Road to Reality, 2004). Our present picture of physical reality... in relation to the nature of time, is due for a grand shake-up, even greater, perhaps, than that provided... by relativity and quantum mechanics (The Emperor's New Mind, 1989).

The same post in Spanish
Manuel Alfonseca

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