The classical universe entertains a `vacuum' in which there is nothing. Since Dirac, physicists have accepted the existence of a (potentially infinite) `zero point' background which we don't notice because it's everywhere. The difference here has a great deal to do with the subtle implications of observation.

In the Victorian era, James Clark Maxwell formalised what experimenters had discovered about electric and magnetic phenomena into what have come to be known as Maxwell's equations (though, in fact, the form in which they are most widely know is due to Oliver Heaviside). These (by giving the speed of light) presented physics with a problem whose resolution required, as Albert Einstein noticed, rejection of what has since come to be known as `Gallilean invariance': since Einstein, we have known that space and time are more entangled with one another than was previously imagined. Out of Maxwell's work on `electromagnetism' and Einstein's work disentangling physics from the assumption Gallileo (among a great many others) had made, Einstein built up `General Relativity' which provides a `field equation' describing the geometry of space-time (which describes gravity) and its relationship with Maxwell's `electromagnetic field' (which describes electric and magnetic phenomena) and matter. I'll refer to the resulting equation as `the E/M field equation', in which E/M is short for Einstein/Maxwell (but the pun on a standard abbreviation for electro-magnetic is intended).

The unity of the E/M field equations invites a description, of the universe, distinguishing the fields (describing gravity and electromagnetism) from their `sources' (the matter which inhabits the universe and `causes' the fields). In such a description, the sources take up a tiny proportion of space-time - each particle of matter tracing out a thin trail on that vast canvas - while the fields are all-pervasive. A group of particles (e.g. several protons, as many electrons and some neutrons) may, together, form an ensemble (e.g. an atom or planet) which, though `mostly empty', takes up a (more nearly) appreciable volume but otherwise behaves (mostly) `as if' it were a simple source - this proves useful when the composite is, in its turn, small by comparison with the spaces around it. Either way, throughout most of space-time, in any solution to the field equations, we solve the `free field' or `source-free' form of the equations: the field equations in the `vacuum' betweeen the particles of matter.

It is easiest to study solutions to differential equations in which a `homogeneous' (i.e. it's the same everywhere and looks the same no matter which way round you look at it) background serves as the substrate on which we add a perturbation which describes the solution we're up to. This is somewhat more fiddly for the E/M equations (in which one of the things to solve for is the geometry of the region in which the equations are to be solved) than for Maxwell's equations (as Maxwell and Heaviside described them - on a given flat background universe). All the same, the same ideal is pursued - Swartzchild's solution and the Kerr/Newman solution presume a `boring' universe as context.

Maxwell's equations, even in the absence of sources, support (in principle)
arbitrary solutions whose form is light (or X-rays, or radio waves; physics
describes the whole electromagnetic spectrum as light, even when it doesn't
match up with natural language's presumption that light is the *visible*
portion of the spectrum) of some particular frequency (and phase - variation in
which amounts to moving the wave forward or backwards through some fraction of a
wavelength) travelling in some particular direction: I'll call these `the Hertz
solutions'. One cute property of these solutions is that `subtracting' one
Hertz solution is the same as `adding' another with the same frequency (of
oscillation) and amplitude (a jargon word for size, when applied to waves) but
with `opposite' phase (i.e. half a cycle out of sync with the original).
Furthermore, these solutions may be combined in (substantially) arbitrary
superpositions of waves: just as the surface of a lake supports wave motions of
various regular forms, it also allows the combinations of these which take the
form of a `choppy' surface in which few clear wave fronts are visible, yet the
surface is lumpy and goes up and down in a seemingly random mess (albeit the
analogy here is poor - water's waves obey a non-linear equation, which
contributes to the choppiness it supports).

In the same way, we may anticipate that, in reality, the electromagnetic field is generally a `choppy' superposition of the Hertz solutions - the background isn't simply homogeneous as we typically supposed when constructing solutions. Indeed, one of Maxwell's other major contribution to physics (aside from formalising electromagnetism) was to provide a framework describing thermodynamics (i.e. what heat is and why it behaves the way it does): this formalism necessarily calls on us, when describing any system, to entertain a `grand canonical ensemble' of solutions compatible with the known data, with reality showing the features which show up in `most' such solutions. I here assert that `most' solutions of Maxwell's equations of electrodynamics have a background of a `choppy' combination of Hertz waves.

Maxwell and Hertz, when solving Maxwell's equations, could discuss the matter in terms of an empty vacuum whose geometry was given. In such a context, Maxwell's field equations are linear - which means that if we take two solutions to the equations and add them, we get another solution; and if we simply re-scale one solution, we get another. This is the process of `superposition' needed to build up the `choppy' solutions just discussed. When we come to discuss the E/M field equations, however, we find that the geometry of the `vacuum' depends on the electromagnetic field, albeit weakly. The `gravito-dynamics' Einstein gives for the geometry are, furthermore, non-linear: none the less, for small enough perturbations in the boundary conditions one can expect solutions to vary by small perturbations depending linearly on the change in boundary conditions.

Equally, we can take a given solution to the E/M field equations, add to it any particular Hertzian solution, vary the amplitude and phase of the latter and see what solution we get. For `large enough' amplitude we'll find the result may even differ qualitatively from the original solution; there may also be qualititave dependence on the phase, at least for large enough amplitude. None the less, we may thereby obtain a family of (exact) solutions to the E/M field equations, differing continuously (and `slowly') from one another in their geometry, parameterised by the amplitude and phase of our Hertzian perturbation. We can, naturally, take any member of the resulting family and use it as the start-point for a similar family of Hertzian variants; and we can take any of our exact solutions and explore linear perturbation by small enough choppy solutions.

If our `base solution' is sufficiently choppy (i.e. not `small enough' in the sense above), it'll be able to disguise Hertzian perturbations of modest amplitude: they'll just shift the pattern of choppiness around, rather than revealing themselves in a discernible periodic structure. Furthermore, the electromagnetic field's energy content is not manifestly determined by the theory: one gets to make a gauge choice for a nominal zero point, after which differences in the field yield differences in the energy content. Thus, when we come to look at solutions to the E/M field equations which resemble the real universe (i.e. have a choppy background), we have no absolute way of picking one solution, in any given context, to regard as the `zero point' or `ground state'. At best, we can hope to find a small range in variation of the Hertzian term(s), outside which we can honestly say that variation towards the given range yields a `simpler' solution: but the range will allow some variation in phase and amplitude and, at least for some portion of the amplitude range, arbitrary variation in phase of each added Hertzian wave.

The crucial part of this story is that the `choppy' background, taken with the non-linearity and lack of natural zero point in the E/M field equations, suffices to hide modest amounts of any Hertzian wave we care to add. This, in turn, means that we cannot distinguish between matter absorbing energy from a spectral line of the electromagnetic field and matter emitting energy (half a cycle out of phase with the alleged absorption) to that field.

Niels Bohr discovered, as the nineteenth century gave way to the twentieth, that: interaction between matter and the electromagnetic field happens in discrete transitions, during each of which the latter gains or loses energy only at finitely many frequencies, at each of which the amount of energy transferred is a whole multiple of an energy proportional to the frequency. For the present, attend only to the fact that such transfers occur in discrete lumps with (at each frequency) a granularity. Consequently, we can expect our `choppy' Hertzian superposition to lack spikes large enough to transfer their energy to matter - because such spikes will typically have found some matter to which to transfer the energy - at least in the presence of matter which isn't very hot. (The choppiness is a thermodynamic superposition, whose characteristics will encode the temperature of the electromagnetic field; and we can expect the field to be in (at least approximate) thermodynamic equilibrium with any matter in the vicinity.)

So we can expect `real' solutions to the E/M field equations to have a choppy background electromagnetic field in which the spikes are typically small compared to the doses of energy matter is capable of absorbing in a single interaction.

Written by Eddy.$Id: empty.html,v 1.3 2001/11/13 14:50:58 eddy Exp $