Originally posted by davefoc
For instance if an electron is falling in a gravitational field are there photons being emitted?
You sure don't shy away from the hard questions, do you?
There is a nice
thread about that in the archives of the sci.physics.research newsgroup. (Follow the "Next by thread" links to read the whole discussion.)
Actually, I'm not sure it really addresses your question, because it mainly treats radiation classically, and central to the discussion is the fact that it is gravity which is providing the acceleration. You're asking about any acceleration regardless of the cause, I think, but you want to treat the radiation quantum mechanically, i.e., as consisting of photons.
Roughly speaking, yes, an accelerating electron emits photons. But the fine print is that if classical acceleration is a reasonably accurate description of the electron's behavior, it will be emitting a large number of photons; and conversely, the emission of a single photon by an electron is inherently a quantum mechanical sort of thing, and an accurate description of it must treat the electron, not just the photon, quantum mechanically.
Here's something from Feynman's Lectures on Physics (volume 1, chapter 26) that might be relevant:<blockquote>This is the first of a number of chapters on the subject of
electromagnetic radiation. Light, with which we see, is only one small part of a vast spectrum of the same kind of thing, the various parts of this spectrum being distinguished by different values of a certain quantity which varies. This variable quantity could be called the "wavelength." As it varies in the visible spectrum, the light apparently changes color from red to violet. If we explore the spectrum systematically, from long wavelengths toward shorter ones, we would begin with what are ususally called
radiowaves. Radiowaves are technically available in a wide range of wavelengths, some even longer than those used in regular broadcasts; regular broadcasts have wavelengths corresponding to about 500 meters. Then there are the so-called "short waves," i.e., radar waves, millimeter waves, and so on. There are no actual boundaries between one range of wavelengths and another, because nature did not present us with sharp edges, The number associated with a given name for the waves are only approximate and, of course, so are the names we give to the different ranges.
Then, a long way down through the millimeter waves, we come to what we call the
infrared, and thence to the visible spectrum. Then going in the other direction, we get into a region which is called the
ultraviolet. Where the ultraviolet stops, the x-rays begin, but we cannot define precisely where this is; it is roughly at 10<sup>-8</sup> m, or 10<sup>-2</sup> microns. These are "soft" x-rays; then there are ordinary x-rays and very hard x-rays; then gamma rays, and so on, for smaller and smaller values of this dimension called the wavelength.
Within this vast range of wavelengths, there are three or more regions of approximation which are especially interesting. In one of these, a condition exists in which the wavelengths involved are very small compared with the dimensions of the equipment available for their study; furthermore, the photon energies, using the quantum theory, are small compared with the energy sensitivity of the equipment. Under these conditions we can make a rough first approximation by a method called
geometrical optics. If, on the other hand, the wavelengths are comparable to the dimensions of the equipment, which is difficult to arrange with visible light but easier with radiowaves, and if the photon energies are still negligibly small, then a useful approximation can be made by studying the behavior of the waves, still disregarding the quantum mechanics. This method is based on the
classical theory of electromagnetic radiation, which will be discussed in a later chapter. Next, if we go to very short wavelengths, where we can disregard the wave character but the photons have a very
large energy compared with the sensitivity of our equipment, things get simple again. This is the simple
photon picture, which we will describe only very roughly. The complete picture, which unifies the whole thing into one model, will not be available to us for a long time.</blockquote>