Quantum Statistical Mechanics in the Natural Sciences

Leo P. Kadanoff, Gordon Baym, John Dezendorf Trimmer

Anouk Barberousse

Philosophical reflections on physics and its theories have been shaping the agenda of general philosophy of science, including issues such as the nature of scientific theories, the meaning of scientific terms, and scientific modeling. But physics is also well worth being considered a special science of its own, whose methods and tools raised specific questions for philosophers of science: this is the approach followed in this chapter, which has as its main thread the role of mathematics in physical theories. It tackles classical issues concerning measurement and determinism and long-standing controversies in the philosophy of statistical mechanics (how may the reversible laws of mechanics account for the irreversible principles of thermodynamics?) and in the philosophy of quantum physics (does quantum mechanics provide us a with a complete description of quantum phenomena?). It also addresses emerging issues in the field, such as computer simulations and their role between theory and observation.

Rosario N. Mantegna

This article was found by Majorana's brother among Ettore Majorana's files and was published in 1942 after Majorana's disappearance in the international Italian journal Scientia.It is a rather special article in several respects.It was intended to present the point of view of a physicist about the value of statistical laws in physics and social sciences to scholars of a broad spectrum of different disciplines such as sociology and economics.It also considers philosophical aspects related to the nature and value of deterministic and statistical laws in science.In his article, Majorana considers quantum mechanics as an irreducible statistical theory because the theory is not able to describe the time evolution of a single particle or atom in a controlled environment at a deterministic level.He concludes that quantum mechanics suggests that there is an "essential analogy between physics and the social sciences, between which an identity of value and method has turned out".By analyzing the messages of this paper we conclude that Majorana deserves a great tribute not only for his exceptional achievements in theoretical physics but also for his fresh and original views on the importance and role of statistical laws in physics and in other disciplines such as the social sciences.

Walter T. Grandy

Rosario N. Mantegna

This article was found by Majorana’s brother among Ettore Majorana’s files and was published in 1942 after Majorana’s disappearance in the international Italian journal Scientia. It is a rather special article in several respects. It was intended to present the point of view of a physicist about the value of statistical laws in physics and social sciences to scholars of a broad spectrum of different disciplines such as sociology and economics. It also considers philosophical aspects related to the nature and value of deterministic and statistical laws in science. In his article, Majorana considers quantum mechanics as an irreducible statistical theory because the theory is not able to describe the time evolution of a single particle or atom in a controlled environment at a deterministic level. He concludes that quantum mechanics suggests that there is an “essential analogy between physics and the social sciences, between which an identity of value and method has turned out”. By analyzing the messages of this paper we conclude that Majorana deserves a great tribute not only for his exceptional achievements in theoretical physics but also for his fresh and original views on the importance and role of statistical laws in physics and in other disciplines such as the social sciences.

N. N. Bogolyubov, A. M. Kurbatov, A. S. Shumovskiǐ