Uniformly Accelerating Charged Particles. A Threat to the Equivalence Principle, Springer, Berlin, Heidelberg, New York (2008)


I spent several years reading only a selection of the literature generated by a debate that has been going on for over 100 years, and which continues. In my view, described in the book and the Bad Honnef talk, some of that debate and a lot of mathematical work that still goes on could be curtailed. Likewise for a large part of the literature concerned with interpretation of the Unruh effect, to which I have added a short section at the end of the Bad Honnef summary. My claims may not please people involved in that area, but they have the right to reply. If I am wrong, they will do me a favour by informing me. Feedback of this kind is my sole reason for publishing, or launching this website. Click on the picture for the Springer link to the book. A summary is given in portable document format as a synopsis of the Bad Honnef talk mentioned above.

One of the points I find most worrying is the naive interpretation of so-called accelerating frames, in particular those that are supposed to be used by Killing observers. The root of the problem here is that there are no canonical accelerating frames adapted to the motion of accelerating observers, unless we are currently wrong about our theories of physics. When observers have inertial motion, there are indeed natural frames adapted to their motion. This is because our theories of non-gravitational physics have a velocity symmetry, in fact, Lorentz or local Lorentz symmetry. But according to current theory, there is no acceleration symmetry. This goes for standard general relativity as well as special relativity.

It may be that we should be building in some kind of acceleration symmetry, but I have never seen a discussion of that possibility in this context. Without that, the naive interpretation of accelerating frames adapted to accelerating observers as though these observers would consider them in the same light as inertial or locally inertial frames is thus at best an approximation, at worst an error of judgement. For the time being, we should suppose that accelerating observers know that they are accelerating.

Apart from the question of how we should treat observations made by accelerating observers, I also discuss whether freely falling charges should radiate electromagnetic energy. Of course it depends on what one means by radiation and what theory one is using. According to a naive special relativistic theory of gravity in which it is construed as a force, they will radiate. According to general relativity, in which gravity is construed as the curvature of spacetime and the theory of electromagnetism is the minimal extension of Maxwell’s theory using the Levi-Civita connection, they will not, to a first approximation.

Here I take electromagnetic radiation to refer to the standard physical quantity as it would be measured by inertially moving detectors. Others redefine it and even invent detectors for the redefined quantity. But detection is a problem here, for the same reason that there are no canonical accelerating frames. Suppose we design two electromagnetic radiation detectors based on different principles. When moving inertially with the same motion and under the same physical conditions, they will always register the same value for the radiation, partly because this is what they were designed for, and partly because our theory of electromagnetism is Lorentz symmetric (or locally Lorentz symmetric). But when they are accelerating, even if they have the same motion and move through the same physical surroundings, there is no guarantee that they will register the same values, precisely because there is no acceleration symmetry in our theory of electromagnetism.

One might choose one detector design and decree that what it measures is what one should mean by EM radiation for the observer moving with it, whatever the motion of that observer. But that will never be a canonical choice as long as our theory of electromagnetism has no acceleration symmetry. And what is to be gained there? Why should we be so concerned about defining, or redefining physical quantities to suit this or that observer? The only important thing is to be able to predict what a given detector design will do when undergoing this or that motion and under whatever physical conditions happen to prevail.

Self-Force and Inertia. Old Light on New Ideas, Springer, Berlin, Heidelberg, New York (2011)

This book is about the origin of most, and maybe all, inertial mass. A summary and update can be found in the pdf file associated with the talk given in Munich in 2011. When spatially extended charge distributions are accelerated, they exert electromagnetic forces on themselves which oppose that acceleration (but see the pdf mentioned after the Oxford talk). In the point particle limit of such charge distributions, the electromagnetic self-force becomes infinite. Here we have the origin of the renormalisation problem which carries over into quantum field theory.

This line of thinking gives many insights into the problems of inertia, renormalisation, the relativistic equivalence of inertial mass and energy, the equality of inertial mass and passive gravitational mass in general relativity, and many other things.

Today everyone looks to the Higgs mechanism, also discussed in the book, to supply inertial mass to quarks and electrons from the outside, as it were, through their interaction with a Higgs field of some kind. But most of the mass of any bound state particle such as the proton comes from strong (and electroweak) self-forces and kinetic energy of constituent elementary particles. The book raises the possibility that all inertial mass may be of this kind. Ontologically, this would require all particles to have spatial extent, hence to be continuous distributions of something or else comprise some kind of infinite hierarchy of substructure.

If the new 125 GeV particle found at Fermilab and CERN turns out to be a Higgs particle, that will not change the fact that most of the inertial mass of bound state particles like baryons and mesons is considered today to arise from their substructure, and hence the relevance of these old ideas which still survive today in a new guise, dressed in the language of Hamiltonian operators and quantum field theory.

There has been a review of this book by J. Gratus of the University of Lancaster: General Relativity and Gravitation 44, 1 (2012) pp. 303-304; DOI 10.1007/s10714-011-1279-2. Click on the picture for the Springer link to the book.