Time and Time Reversal Symmetry in Quantum Chemical Kinetics

Abstract

After an introduction into some aspects of the motivation of research and researchers in general and the motivation of our research on the topic of this paper in particular we first introduce the basics of the physical definition and measurement of time intervals with atomic and molecular clocks. We then discuss the question of the definition and experimental determination of the direction of time. Time reversal symmetry (T) is introduced among a set of discrete, fundamental symmetry operations in physics (C, P, T). We briefly mention the relations between symmetries, conservation laws and fundamentally “non observable” quantities as well as the three concepts of spontaneous, de facto, and de lege symmetry breaking. In this context we cover in particular also the question of the space inversion symmetry (P) in relation to molecular chirality and charge conjugation (C), the symmetry between matter and antimatter, as well as the analogies between these symmetries.

Irreversibility in molecular kinetics is first to be understood as a de facto breaking of time reversal symmetry. Some experimental results on the molecular short time quantum dynamics on the femtosecond to nanosecond time scale demonstrate the increase with time of entropy in single isolated molecules in the gas phase. Nevertheless, these processes show, in principle, time reversal symmetry. However, one finds fundamentally different dynamical behaviour for the quantum vibrational motion of molecules depending upon anharmonicity — at the same level of “quantization” — which is an important experimental result of our more recent research.

Not all forces of nature (strong nuclear force, weak nuclear force, electromagnetic force and gravitational force) show the separate discrete symmetries C, P, T. Indeed, the weak nuclear force leads to de lege parity violation (violation of space inversion symmetry) and in recent experiments from high energy physics also de lege violation of time reversal symmetry was proven. These symmetry violations are important for our understanding of molecular chirality and we show, how an “absolute molecular clock” measuring absolute time direction and time intervals could be constructed with chiral molecules provided that the combined symmetry CPT were violated de lege. According to our current knowledge CPT symmetry seems, however, to be maintained.

In a speculative final section of this article we address the consequences of our findings in molecular kinetics for a hypothetical molecular quantum psychology, which is a new concept introduced here, which relates to the possible molecular origin of the formation of thoughts and decisions in our brain, depending upon the type and symmetry of the dynamics relevant for actual molecular processes. This complements molecular biology in our understanding of life. The question of free decision and free will is discussed from the physical-chemical point of view of this molecular quantum psychology. We conclude with some personal recollections of Per-Olov Löwdin as a teacher.