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Irreversible disorder in the world of atoms

International team measures the increase in entropy in carbon nuclei for the first time

Example of an increase in entropy: one cannot fully, spontaneously reverse the breaking of a plate

LÉO RAMOSExample of an increase in entropy: one cannot fully, spontaneously reverse the breaking of a plateLÉO RAMOS

Brazilian and European physicists have demonstrated for the first time that a tiny atomic nucleus also suffers a common phenomenon, well known to humans: the irreversible effects of the passage of time. Using the equipment in the laboratory of the Brazilian Center for Physics Research (CBPF), in Rio de Janeiro, they recorded an irreversible increase in the degree of disorder inside a carbon atom.

In physics, the degree of disorder is measured by a quantity called entropy, which is almost always growing in macroscopic phenomena—at most it remains stable, but never decreases in systems defined as isolated. One of the consequences of the fact that entropy never decreases is that, the greater the disorder, the more difficult it is to revert a phenomenon perfectly. “You cannot un-mix coffee and milk after mixing them, for example,” says physicist Roberto Serra, a researcher at the Federal University of the ABC (UFABC) and a member of the team that carried out the experiments at CBPF.

This is because coffee and milk—and everything else in the macroscopic world—are made of absurdly large numbers of atoms moving in the most diverse ways, most of them randomly and uncontrollably.  Despite the enormous number of possible combinations, there is even a chance that the coffee atoms will separate from the milk atoms, but it is close to zero. This is also why we do not see pieces of a broken plate fitting back together spontaneously.

In everyday life, humans associate the irreversibility of these phenomena to the passing of time and to the concepts of past and future. Under normal conditions, coffee and milk are only separate before mixing and a perfectly whole plate only exists before breaking. The notion of irreversibility led the English astronomer and mathematician Arthur Eddington to state in 1928, in the book The Nature of the Physical World, that the only arrow of time known to physics was the increase of entropy in the Universe, given by the second law of thermodynamics—the only irreversible law in physics. The concept of the arrow of time expresses the idea that time passes in one direction: from the past to the future.

“Although the perception that time never stops and always marches into the future is obvious in our daily experience, this is not trivial in terms of physics,” says Serra. This difficulty arises because the laws that govern nature at the microscopic level are symmetrical in time—and, therefore, reversible. This means that there would be no difference between going from the past to the future and vice-versa.

Many physicists thought that the increase in entropy could be a phenomenon unique to the macroscopic world because, in the 19th century, Austrian physicist Ludwig Boltzmann explained the second law of thermodynamics through the movements of a large number of atoms. During the last 60 years, however, many researchers have been working to expand Boltzmann’s theory to systems consisting of a few or even just one atom. And current theories have already established that a single particle must obey the second law of thermodynamics.

Serra’s team was the first to measure entropy variations in a system so small that it could only be described by the laws of quantum mechanics, which govern the submicroscopic world. Physicist Tiago Batalhão, Serra’s doctoral student at UFABC and currently in Austria for a research internship, has been carrying out experiments since 2014 in partnership with Alexandre Souza, Roberto Sarthour and Ivan Oliveira, from CBPF, Mauro Paternostro, of Queen’s University, in Ireland, and Eric Lutz of the University of Erlangen-Nuremberg, in Germany.

The experiments use electromagnetic fields to manipulate the nuclei of carbon atoms in a chloroform solution (see Pesquisa FAPESP Issue nº 226). The nuclei have a property called spin that acts like a compass needle and points up or down. Each direction has a different energy. The tests began with the spins of trillions of nuclei pointing in one way—most pointing up, but some pointing down, depending on the temperature. Then a radio wave pulse was fired at the chloroform tube. Lasting a microsecond, the pulse was too short to allow each nucleus to interact with its neighbors or the environment. Thus, the pulse affected each nucleus separately. “It’s as if each of them were isolated from the rest of the universe,” explains Serra.

Made up of waves whose amplitude increased over time, the first pulse disturbed the spins of each nucleus, which vibrated quickly and changed direction. A little later, the researchers fired a second pulse, identical to the first in almost all respects, except that the amplitude of the waves decreased over time. With the second pulse, which was a time-inverted version of the first, they expected that the spin of each nucleus would return to its original state. In fact, the spins returned to a state very close to the initial one. But precise measurements showed that the initial and final states were not equal. There was a discrepancy resulting from transitions between the different energy states of the spins associated with the entropy produced during the process of increasing and decreasing the amplitude of the waves, according to an article published in Physical Review Letters.

Vlatko Vedral, a physicist at the University of Oxford, in the United Kingdom, who performs similar experiments using lasers, considers the work a beautiful demonstration of quantum thermodynamics predictions. “But it’s not surprising,” he says. He says he would like to know if the entropy measured on the subatomic scale is produced by phenomena described by the laws of physics or if a part is due to some unknown phenomenon acting on the arrow of time.

National Institute of Quantum Information Science and Technology (nº 2008/57856-6); Grant Mechanism Thematic Project; Principal Investigator Amir Ordacgi Caldeira (Unicamp); Investment R$1,977,654.30 (for the entire project ).

Scientific article
BATALHÃO, T. B. et al. Irreversibility and the Arrow of Time in a Quenched Quantum System. Physical Review Letters. Nov. 6, 2015