Abstract
We present an English translation of Erwin Schrödinger’s paper on “On the Reversal of the Laws of Nature‘’. In this paper, Schrödinger analyses the idea of time reversal of a diffusion process. Schrödinger’s paper acted as a prominent source of inspiration for the works of Bernstein on reciprocal processes and of Kolmogorov on time reversal properties of Markov processes and detailed balance. The ideas outlined by Schrödinger also inspired the development of probabilistic interpretations of quantum mechanics by Fényes, Nelson and others as well as the notion of “Euclidean Quantum Mechanics” as probabilistic analogue of quantization. In the second part of the paper, Schrödinger discusses the relation between time reversal and statistical laws of physics. We emphasize in our commentary the relevance of Schrödinger’s intuitions for contemporary developments in statistical nano-physics.
Highlights
Erwin Schrodinger had the rare privilege to be elected to the Prussian Academy of Science in February 1929, about 1 year and a half after his appointment to the chair of theoretical physics at the University of Berlin [23]
In the second part of the paper, Schrodinger discusses the relation between time reversal and statistical laws of physics
In Quantum Mechanics, the complex conjugation operation is interpreted as time reversal
Summary
Erwin Schrodinger had the rare privilege to be elected to the Prussian Academy of Science in February 1929, about 1 year and a half after his appointment to the chair of theoretical physics at the University of Berlin [23]. The second discrepancy resides in√the following fact: whilst in both cases the differential equation is of first order in time, the presence of a factor −1 confers to the wave equation a hyperbolic or, physically stated, reversible character at variance with the parabolic-irreversible character of the Fokker[-Planck] equation In both these points, the example considered above shows a much closer analogy with wave mechanics it concerns a classical, originally irreversible system. This is because what they say in the particular case depends only upon the time boundary conditions at two “cross sections” (t0 and t1) and is completely symmetric with respect to these cross sections without any special consequence associated with their time ordering This fact is only somewhat concealed inasmuch we in general consider only one of the two “cross sections” as really observed whilst for the other the reliable rule holds that if it is removed sufficiently far in time, one may assume that the state of maximum disorder or of maximum entropy applies there. The scope of this commentary is to offer the reader a first brief overview, admittedly incomplete in spite of our effort, of the significance of Schrodinger’s paper for current research from a non-equilibrium statistical physics perspective
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