Understanding the Time-Asymmetry of Radiation

Abstract

I discuss the nature of the puzzle about the time-asymmetry of radiation and argue that its most common formulation is flawed. As a result, many proposed solutions fail to solve the real problem. I discuss a recent proposal of Mathias Frisch as an example of the tendency to address the wrong problem. I go on to suggest that the asymmetry of radiation, like the asymmetry of thermodynamics, results from the initial state of the universe.

Sharpening the Electromagnetic Arrow(s) of Time

“…31 The experimental results reported in Angelopoulos et al (1998) give a direct demonstration of time reversal invariance in the sense that they do not (as earlier results did) appeal to observed CP violation and the CP T theorem. 32 T mech := m R d u u (x z). 33 An exception to the rule will be mentioned shortly.…”

“…a charge-current distribution J , satisfying r J = 0, is speci…ed, and one seeks to …nd the corresponding solution to the Maxwell equations. One could add a second well-de…ned problem: an external electromagnetic …eld ext F and a nonelectromagnetic force nem F are speci…ed, and one seeks to find the worldline z ( ) of a point mass carrying charge q by using the Lorentz force law and solving the resultant equation of motionma = q( ext F u ) + nem F(23)And combining the two also leads to a harmonious situation in that (i) the coupled Maxwell-Lorentz equations have a well-posed initial value problem and (ii) the total stress-energy tensor, consisting of the sum of the stressenergy tensor of the electromagnetic …eld and the mechanical stress-energy tensor of the particle,32 is conserved.Unfortunately, equation(23)is empirically inadequate, for accelerated charges radiate and, as a result, they experience a damping force that is not re ‡ected in (23). 33 The generally accepted equation of motion describing this phenomenon for a point charge in Minkowski spacetime is called the Lorentz-Dirac equation:ma = q( ext F u ) + nem F ext F u ) + nem F + 2 3 q 2 ( + u u ) _ awhere a := a a is the magnitude of the four-vector acceleration and is the Minkowski metric.…”

“…It would seem that in a natural sense of 'most', in F is not approximately zero in the visible part of the electromagnetic spectrum for most of the systems of which we are aware, since otherwise we would not be aware of them. And the ubiquity of the cosmic background radiation makes one think that in a natural sense of 'most', in F is not approximately zero in the microwave spectrum for most systems, whether we are aware of them or not (seeNorth 2003).…”

“…I take it thatNorth (2003) is proposing that the judgment of what electromagnetic …eld is produced by a charged source is to be formed relative to the representation that has the most natural source-free …eld. I do not object to this as long as 'produce'means just this.…”

Mathias Frisch, Inconsistency, Asymmetry, and Non-locality: A Philosophical Investigation of Classical Electrodynamics. Oxford: Oxford University Press (2005), 222 pp., $49.95 (cloth).

“…The account in the book is a revised version of Frisch's (2000). I have argued against this solution elsewhere (North 2003), but let me say a few things about it here.…”