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Some consequences of time-reversal symmetry

David P. Maroun

Published Jan 1, 2011• 1 citation
Publisher

Abstract

The purpose -of this work is to discuss the symmetry, or lack of it, under reversal of motion in physical objects, states and processes. Considerations of such symmetry are made in both classical and quantum physics, notably in the problem of reconciling the assumed time-reversal symmetry of microscopic processes with the observed asymmetry of macroscopic processes. In the case of classical mechanics, a simple model of a free particle colliding with a series of almost stationary or stationary particles of smaller mass is introduced in order to show how a friction-like phenomenon can arise from processes all of which have symmetry under reversal of motion. It is maintained throughout that symmetry under reversal of motion is a property of all fundamental states and processes in nature.

DOI
10.14288/1.0085950

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The purpose -of this work is to discuss the symmetry, or lack of it, under reversal of motion in physical objects, states and processes. Considerations of such symmetry are made in both classical and quantum physics, notably in the problem of reconciling the assumed time-reversal symmetry of microscopic processes with the observed asymmetry of macroscopic processes. In the case of classical mechanics, a simple model of a free particle colliding with a series of almost stationary or stationary particles of smaller mass is introduced in order to show how a friction-like phenomenon can arise from processes all of which have symmetry under reversal of motion. It is maintained throughout that symmetry under reversal of motion is a property of all fundamental states and processes in nature.
This is Part 1 of a four part paper, intended to redress some of the most fundamental confusions in the subject of physical time directionality, and represent the concepts accurately. There are widespread fallacies in the subject that need to be corrected in introductory courses for physics students and philosophers. Parts 1 and 2 are about quantum mechanics, Part 3 is about fundamental concepts, and Part 4 is about cosmology. We start in Part 1 by analysing the time reversal symmetry of quantum probability laws. Time reversal symmetry is defined as the property of invariance under the time reversal transformation, T: t -> -t. It is shown that quantum mechanics (classical or relativistic) is strongly time asymmetric in its probability laws. This contradicts the orthodox analysis, found throughout the conventional literature on physical time, which claims that quantum mechanics is time symmetric or reversible. This is widely claimed as settled scientific fact, and large philosophical and scientific conclusions are drawn from it. But it is an error. The fact is that while quantum mechanics is widely claimed to be reversible on the basis of two formal mathematical properties (that it does have), these properties do not represent invariance under the time reversal transformation. A recent experiment (Batalhao at alia, 2015) showing irreversibility of quantum thermodynamics is discussed as an illustration of this result. Most physicists remain unaware of the errors, decades after they were first demonstrated. Orthodox specialists in the philosophy of time who are aware of the error continue to refer to the ‘time symmetry’ or ‘reversibility’ of quantum mechanics anyway – and exploit the ambiguity to claim false implications about physical time reversal symmetry in nature. The excuse for perpetrating the confusion is that, since it is has now become customary to refer to the formal properties of quantum mechanics as ‘reversibility’ or ‘time reversal symmetry’, we should just keep referring to them by this name, even though they are not time reversal symmetry. This causes endless confusion, in attempts to explain the physical irreversibility of our universe, and in philosophical discussions of implications of physics for the nature of time. The failure of time reversal symmetry in quantum mechanics changes the interpretation of modern physics in a deep way. It changes the problem of explaining the real irreversibility found throughout nature.
The first question to ask about the phenomenon of relaxation is why it occurs at all. Both the Newton and the Schrödinger equations are symmetrical under time reversal: The Newton equation, dx/dt = v ; dv/dt = −∂V/∂x, implies that particles obeying this law of motion will retrace their trajectory back in time after changing the sign of both the time t and the particle velocities v. The Schrödinger equation, ∂ψ/∂t = −(i/.h) Ĥ ψ, implies that if (ψ (t) is a solution then ψ *(−t) is also one, so that observables which depend on |ψ|2 are symmetric in time. On the other hand, nature clearly evolves asymmetrically as asserted by the second law of thermodynamics. How does this asymmetry arise in a system that obeys temporal symmetry in its time evolution? Readers with background in thermodynamics and statistical mechanics have encountered the intuitive answer: Irreversibility in a system with many degrees of freedom is essentially a manifestation of the system “getting lost in phase space”:Asystem starts from a given state and evolves in time. If the number of accessible states is huge, the probability that the system will find its way back to the initial state in finite time is vanishingly small, so that an observer who monitors properties associated with the initial state will see an irreversible evolution. The question is how is this irreversible behavior manifested through the reversible equations of motion, and how does it show in the quantitative description of the time evolution. This chapter provides an introduction to this subject using the time-dependent Schrödinger equation as a starting point. Chapter 10 discusses more advanced aspects of this problem within the framework of the quantum Liouville equation and the density operator formalism.
Dynamical collapse models embody the idea of a physical collapse of the wave function in a mathematically well-defined way. They involve modifications to the standard rules of quantum theory in order to describe collapse as a physical process. This appears to introduce a time reversal asymmetry into the dynamics since the state at any given time depends on collapses in the past but not in the future. Here we challenge this conclusion by demonstrating that, subject to specified model constraints, collapse models can be given a structurally time symmetric formulation in which the collapse events are the primitive objects of the theory. Three different examples of time asymmetries associated with collapse models are then examined and in each case it is shown that the same dynamical rule determining the collapse events works in both the forward and backward in time directions. Any physically observed time asymmetries that arise in such models are due to the asymmetric imposition of initial or final time boundary conditions, rather than from an inherent asymmetry in the dynamical law. This is the standard explanation of time asymmetric behaviour resulting from time symmetric laws.
Classic Mechanics and Electromagnetism, conventionally taken as time-reversible, share the same concept of motion (either of mass or charge) as the basis of the time reversibility in their own fields. This paper focuses on the relationship between mobile geometry and motion reversibility. The goal is to extrapolate the conclusions to the quantum frame, where matter and radiation behave just as elementary mobiles. The possibility that the asymmetry of Time (Time’s arrow) is an effect of a fundamental quantum asymmetry of elementary particles, turns out to be a consequence of the discussion.
Collapse models are modifications of quantum theory where the wave function is treated as physically real and the collapse of the wave function is a physical process. This appears to introduce a time reversal asymmetry into the dynamics of the wave function since the collapses affect only the future state. This paper challenges this conclusion, showing that in three different examples of time asymmetries associated with collapse models, if the physically real part of the model can be reduced to the locations in space and time about which collapses occur, then such a model works both forward and backward in time, in each case satisfying the Born rule. Despite the apparent asymmetry of the collapse process, these models in fact have time reversal symmetry. Any physically observed time asymmetries that arise in such models are due to the asymmetric imposition of initial or final time boundary conditions, rather than from an inherent asymmetry in the dynamical law. This is the standard explanation of time asymmetric behaviour resulting from time symmetric laws.