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Physics World

Experiment sees the arrow of time – at last!

Nick E. Mavromatos

Published Dec 1, 1998• 2 citations
Publisher

Abstract

Everyday experience tells us that it is impossible to travel backwards in time, no matter what science-fiction writers and movie directors tell us. However, this seemingly natural impossibility is actually one of the greatest mysteries in physics. Currently most physicists associate the irreversibility of time with the production of entropy in the warm macroscopic world. One consequence of this irreversibility – often called the “arrow of time” in thermodynamics is the ageing process. In plain terms, one grows old because of the irreversible physical processes that occur during one's life. However, the fundamental classical laws of physics discovered by Galileo, Newton and Einstein do not distinguish between the future and the past. In other words, they appear to be symmetric in time.

DOI
10.1088/2058-7058/11/12/19

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Everyday experience tells us that it is impossible to travel backwards in time, no matter what science-fiction writers and movie directors tell us. However, this seemingly natural impossibility is actually one of the greatest mysteries in physics. Currently most physicists associate the irreversibility of time with the production of entropy in the warm macroscopic world. One consequence of this irreversibility – often called the “arrow of time” in thermodynamics is the ageing process. In plain terms, one grows old because of the irreversible physical processes that occur during one's life. However, the fundamental classical laws of physics discovered by Galileo, Newton and Einstein do not distinguish between the future and the past. In other words, they appear to be symmetric in time.
The problem of time’s arrow is (roughly) to understand why macroscopic physical processes typically evolve in a specific direction (the one we call “the future”) even though the underlying laws of physics describing the individual microscopic systems are time-reversal invariant. The standard answer to this problem is given by Boltzmann’s explanation of the II law of thermodynamics: a classical system starting in a non-equilibrium state spontaneously (i.e. with a high level of probability) tends towards equilibrium, thus implementing an irreversible process. However, this explanation has two drawbacks: 1. it needs a further assumption on the entropy of the initial state of the universe (past hypothesis); 2. microscopic systems (e.g. molecules in a box) should be represented as quantum states and not classical states. In this talk, I want to propose a different hypothesis to explain the origin of time’s arrow, based on quantum mechanics, specifically on decoherence theory. Differently from isolated systems, open quantum systems described by decoherence theory showirreversible behavior, as they evolve towards decoherence and von Neumann entropy increase. Is this behavior a sign of genuine irreversibility? And, if so, can this be linked to thermodynamic irreversibility?
Abstract Quantum mechanics for describing the behavior of microscopic entities and thermodynamics for describing macroscopic systems exhibit separate time concepts. Whereas many theories of modern physics interpret processes as reversible, in thermodynamics, an expression for irreversibility and the so-called time arrow has been developed: the increase of entropy. The divergence between complete reversibility on the one hand and irreversibility on the other is called the paradox of time. Since more than hundred years many efforts have been devoted to unify the time concepts. So far, the efforts were not successful. In this paper a solution is proposed on the basis of matter-energy equivalence with an energetic distinction between matter and mass. By refraining from interpretations predominant in modern theoretical physics, the first and second laws of thermodynamics can be extended to fundamental laws of nature, which are also valid at quantum level.
Time asymmetry and irreversibility are signal features of our world. They are the reason of our aging and the basis for our belief that effects are preceded by causes. These features have many manifestations called arrows of time. In classical physics, some of these arrows are described by the increase of entropy or probability, and others by time‐asymmetric boundary conditions of time‐symmetric equations (e.g., Maxwell or Einstein). However, there is some controversy over whether probability or boundary conditions are more fundamental. For quantum systems, entropy increase is usually associated with the effects of an environment or measurement apparatus on a quantum system and is described by the von Neumann‐Liouville equation. But since the traditional (von Neumann) axioms of quantum mechanics do not allow time‐asymmetric boundary conditions for the dynamical differential equations (Schrödinger or Heisenberg), there is no quantum analogue of the radiation arrow of time. In this paper, we review consequences of a modification of a fundamental axiom of quantum mechanics. The new quantum theory is time asymmetric and accommodates an irreversible time evolution of isolated quantum systems.
Lindblad's theorem Although the fundamental laws of physics explain a great deal of the material world, they often seem to contradict our immediate experience. For instance, as physicists we believe that all elementary interactions are reversible, but as people we are immersed in irreversibility. The collision of two atoms may well be reversible and predictable, but for us time flows in a definite direction and life is sometimes unpredictable. “What then is time? If no one asks me, I know what it is. If I wish to explain it to him who asks, I do not know. ” (Attributed to Augustine.) Nevertheless, as we try to explain in this section, one can include irreversibility, the true arrow of time, into quantum mechanics in a concise and elegant form put on solid mathematical ground in Lindblad's theorem (Lindblad, 1976). Having then understood the basics of irreversible quantum dynamics, life may not be quite the same any more. Irreversibility A beam splitter is a reversible optical instrument: one could collect the outgoing light beams and bring them together again in a second beam splitter where they constructively interfere to re-establish the light in its original state. But now imagine a light beam is scattered many times. For example, light entering biological tissue is interacting with each of the cells along its path. Some of the light is scattered and only a part of the light continues in the original direction.
Within the general formalism of quantum theory irreversibility and the arrow of time and the in the evolution of various physical systems are studied. Irreversible behavior often manifests itself in the guise of “entropy production.” This motivates me to begin this chapter with a brief review of quantum-mechanical entropy, a subject that Elliott Lieb has made outstanding contributions to, followed by an enumeration of examples of irreversible behavior and of an arrow of time analyzed in later sections. Subsequently, a derivation of the laws of thermodynamics from (quantum) statistical mechanics, and, in particular, of the Second Law of thermodynamics, in the forms given to it by Clausius and Carnot, is presented. In a third part, results on diffusive (Brownian) motion of a quantum particle interacting with a quasi-free quantum-mechanical heat bath are reviewed. This is followed by an outline of a theory of friction by emission of Cherenkov radiation of sound waves in a system consisting of a particle moving through a Bose–Einstein condensate and interacting with it. In what may be the most important section of this chapter, the fundamental arrow of time inherent in Quantum Mechanics is discussed.