3.5  A Quintessence of So Subtle A Nature

 

For his art did express

A quintessence even from nothingness,

From dull privations and lean emptiness;

He ruined me, and I am re-begot

Of absence, darkness, death; things which are not.

                                                                John Donne, 1633

 

Descartes (like Aristotle before him) believed that nature abhors a vacuum, and insisted that the entire universe, even regions that we commonly call "empty space", must be filled with (or, more precisely, must consist of) some kind of substance. He believed this partly for philosophical reasons, which might be crudely summarized as "empty space is nothingness, and nothingness doesn't exist". He held that matter and space are identical and co-extant (ironically similar to Einstein's later notion that the gravitational field is identical with space). In particular, Descartes believed an all-pervasive substance was necessary to account for the propagation of light from the Sun to the Earth (for example), because he rejected any kind of "action at a distance", and he regarded direct mechanical contact (taken as a primitive operation) as the only intelligible means by which two objects can interact. He conceived of light as a kind of pressure, transmitted instantaneously from the source to the eye through an incompressible intervening medium. Others (notably Fermat) thought it more plausible that light propagated with a finite velocity, which was corroborated by Roemer's 1675 observations of the moons of Jupiter. The discovery of light's finite speed was a major event in the history of science, because it removed any operational means of establishing absolute simultaneity. The full significance of this took over two hundred years to be fully appreciated.

 

More immediately, it was clear that the conception of light as a simple pressure was inadequate to account for the different kinds of light, i.e., the phenomenon of color. To remedy this, Robert Hooke suggested that the (longitudinal) pressures transmitted by the ether may be oscillatory, with a frequency corresponding to the color. This conflicted with the views of Newton, who tended to regard light as a stream of particles in an empty void. Huygens advanced a fairly well-developed wave theory, but could never satisfactorily answer Newton's objections about the polarization of light through certain crystals ("Iceland spar"). This difficulty, combined with Newton's prestige, made the particle theory dominant during the 1700's, although many people, notably Jean Bernoulli and Euler, held to the wave theory.

 

In 1800 Thomas Young reconciled polarization with the wave theory by postulating the light actually consists of transverse rather than longitudinal waves, and on this basis - along with Fresnel's explanation of diffraction in terms of waves - the wave theory gained wide acceptance. However, Young's solution of the polarization problem immediately raised a new one, namely, how a system of transverse waves could exist in the ether, which had usually been assumed to be akin to a tenuous gas or fluid. This prompted generations of physicists, including Navier, Stokes, Kelvin, Malus, Arago, and Maxwell to become actively engaged in attempts to explain optical phenomena in terms of a material medium; in fact, this motivated much of their work in developing the equations of state for elastic media, which have proven to be so useful for the macroscopic treatment of fluids. However, despite the fruitfulness of this effort for the development of fluid dynamics, no one was ever able to accurately account for all optical and electro-magnetic phenomena in terms of the behavior of an ordinary fluid medium, with or without viscosity and/or compressibility.

 

There were a number of reasons for this failure. First, an ordinary fluid (even a viscous fluid) can't sustain shear stresses at rest, so it can propagate only longitudinal waves, as opposed to the transverse wave structure of light implied by the phenomenon of polarization. This implies either that the luminiferous ether must be a solid, or else we must postulate some kind of persistent dynamics (such as vortices) in the fluid so that it can sustain shear stresses. Unfortunately, both of these alternatives lead to difficulties. The assumption of a solid ether is difficult to reconcile with the fact that the equations of state for ordinary elastic solids always yield longitudinal waves accompanying any transverse waves - typically with different velocities. Such longitudinal disturbances are never observed with respect to optical phenomena. On the other hand, the assumption of a fluid ether with persistent flow patterns to sustain the required shear stresses entails a highly coordinated and organized system of flow cells that could persist only with the active participation of countless tiny “Maxwell demons” working furiously at each point to sustain it. Lacking this, the vortices are inherently unstable (even in an ideal perfect inviscid fluid, in which vorticity is strictly conserved), so these flow cells could not exert the effects on ordinary matter that they must if they are to serve as the mechanism of electromagnetic forces. Even the latter-day concept of an ether consisting of a superfluid (i.e., the viscosity-free quantum hydrodynamical state achieved by some substances such as helium when cooled to near absolute zero) faces the same problem of sustaining its specialized state while simultaneously interacting with ordinary matter in the required ways. As Maxwell acknowledged

 

No theory of the constitution of the ether has yet been invented which will account for such a system of molecular vortices being maintained for an indefinite time without their energy being gradually dissipated into that irregular agitation of the medium which, in ordinary media, is called heat.

 

Thus, ironically, the concept of transverse waves - proposed by Young and Fresnel as a means of accounting for polarization of light in term of a mechanical wave propagating in some kind of material ether - immediately led to considerations that ultimately undermined confidence in the physicality and meaningfulness of that ether.

 

Even aside from the difficulty of accounting for exclusively transverse waves in a material medium, the idea of a substantial ether filling all of space had always faced numerous difficulties. For example, Newton had shown (in his demolition of Descartes' vortex theory) that the evidently drag-free motion of the planets and comets was flatly inconsistent with the presence of any significant density of interstitial fluid. This problem is especially acute when we remember that, in order to account for the high speed of light, the density and rigidity of the putative ether must be far greater than that of steel. Serious estimates of the density of the ether varied widely, but ran as high as 1000 tons per cubic millimeter. It is then necessary to explain the interaction between this putative material ether and all other known substances. Since the speed of light changes in different material media, there is clearly a significant interaction, and yet apparently this interaction does not involve any appreciable transfer of ordinary momentum (since otherwise the unhindered motions of the planets are inexplicable).

 

One interesting suggestion was that it might be possible to account for the absence of longitudinal waves by hypothesizing a fluid that possesses vanishingly little resistance to compression, but extremely high rigidity with respect to transverse stresses. In other words, the shear stresses are very large, while the normal stresses vanish. The opposite limit is easy to model with the Navier-Stokes equation by setting the viscosity to zero, which gives an ideal non-viscous fluid with no shear stresses and with the normal stresses equal to the pressure. However, we can't use the ordinary Navier-Stokes equations to represent a substance of high viscosity and zero pressure, because this would simply zero density, and even if we postulate some extremely small (but non-zero) pressure, the normal stresses in the Navier-Stokes equations have components that are proportional to the viscosity, so we still wouldn't be rid of them. We'd have to postulate some kind of adaptively non-isotropic viscosity, and then we wouldn't be dealing with anything that could reasonably be called an ordinary material substance.

 

As noted above, the intense efforts to understand the dynamics of a hypothetical luminiferous ether fluid led directly to modern understanding of fluid dynamics, as modeled by the Navier-Stokes equation for fluids of arbitrary viscosity and compressibility. This equation can be written in vector form as

 

 

where p is the pressure, r is the density, F the external force vector (per unit mass), n is the kinematic viscosity, and V is the fluid velocity vector. If the fluid is incompressible then the divergence of the velocity is zero, so the last term vanishes. It’s interesting to consider whether anything can be inferred about the vacuum from this equation. By definition, a vacuum has vanishing density, pressure, and viscosity - at least in the ordinary senses of those terms. Setting these quantities to zero, and in the absence of any external force F, the above equation reduces to dV/dt = -Ńp/r. Since both p and r are to equal zero, this equations can only be evaluated on the basis of some functional relationship between those two variables. For example, we may assume the ideal gas law, p = rRT where R is the gas constant and T is temperature. In that case we can evaluate the limit of Ńp/r as p and r approach zero to give

 

 

This rather ghostly proposition apparently describes the disembodied velocity and temperature of a medium possessing neither density nor heat capacity. In a sense it is a medium of pure form and no substance. Of course, this is physically meaningless unless we can establish a correspondence between the terms and some physically observable effects. It was hoped by Stokes, Maxwell, and others that some such identification of terms might enable a limiting case of the Navier-Stokes equation to represent electromagnetic phenomena, but the full delineation of Maxwell's equations for electromagnetism make it clear that they do not describe the movement of any ordinary material substance, which of course was the basis for Navier-Stokes equation.

 

Another interesting suggestion was that the luminiferous ether might consist of a substance whose constituent parts, instead of resisting changes in their relative distances (translation), resist changes in orientation. A theory along these lines was proposed by MacCullagh in 1839, and actually led to some of the same formulas as Maxwell's electromagnetic theory. This is an intriguing fact, but it doesn't represent an application (or even an adaptation) of the equations of motion for either an ordinary elastic substance, whether gas, fluid, or solid. It's more properly regarded as an abstract mathematical model with only a superficial resemblance to descriptions of the behavior of material substances.

 

Some of the simplest material ether theories were ruled out simply on the basis of first-order optical phenomena, especially stellar aberration. For example, Stokes' theory of complete convection could correctly model aberration (to first order) only with a set of hypotheses that Lorentz later showed to be internally inconsistent. (Stokes erroneously assumed the velocity of a potential flow stream around a sphere is zero at the sphere’s surface.) Fresnel's theory of partial convection was (more or less) adequate, up until it became possible to measure second-order effects, at which point it too was invalidated. But regardless of their empirical failures, none of these theories really adhered to the laws of ordinary fluid mechanics. William Thomson (Lord Kelvin), who was perhaps the most persistent of all in the attempt to represent electromagnetic phenomena in terms of the mechanics of ordinary macroscopic substances, aptly summarized the previous half-century of progress in this line of research at a jubilee in his honor in 1896:

 

One word characterizes the most strenuous efforts for the advancement of science that I have made perseveringly during fifty-five years; that word is failure. I know no more of electric and magnetic force, or of the relation between ether, electricity, and ponderable matter… than I knew… fifty years ago.

 

We might think this assessment was too harsh, especially considering that virtually the entire science of classical electromagnetism - based on Maxwell’s equations - was developed during the period in question. However, in the course of this development Maxwell and his followers had abandoned the effort to find mechanical analogies, and Kelvin equated progress with finding a mechanical analogy. The failure to find any satisfactory mechanical model for electromagnetism led to the abandonment of the principle of qualitative similarity, which is to say, it led to the recognition that the ether must be qualitatively different from ordinary substances. This belief was firmly established once Maxwell showed that longitudinal waves cannot propagate through transparent substances or free space. In so doing, he was finally able to show that all electromagnetic and optical phenomena can be explained by a single system of "stresses in the ether", which, however, he acknowledged must obey quite different laws than do the elastic stresses in ordinary material substances. E. T. Whittaker’s book “Aether and Electricity” includes a review of the work of Kelvin and others to find a mechanical model of the ether concludes that

 

Towards the close of the nineteenth century… it came to be generally recognized that the aether is an immaterial medium, sui generis, not composed of identifiable elements having definite locations in absolute space.

 

Thus by the time of Lorentz it had become clear that the "ether" was simply being arbitrarily assigned whatever formal (and often non-materialistic) properties it needed in order to make it compatible with the underlying electromagnetic laws, and therefore the "corporeal" ether concept was no longer exerting any positive heuristic benefit, but was simply an archaic appendage that was being formalistically superimposed on top of the real physics for no particular reason.

 

Moreover, although the Navier-Stokes equation is as important today for fluid dynamics as Maxwell's equations are for electrodynamics, we've also come to understand that real fluids and solids are not truly continuous media. They actually consist of large numbers of (more or less) discrete particles. As it became clear that the apparently continuous dynamics of fluids and solids were ultimately just approximations based on an aggregate of more primitive electromagnetic interactions, the motivation for trying to explain the latter as an instance of the former came to be seriously questioned. It is rather like saying gold consists of an aggregate of sub-atomic particles, and then going on to say that those sub-atomic particles are made of gold! The effort to explain electromagnetism in terms of a material fluid such as we observe on a macroscopic level, when in fact the electromagnetic interaction is a much more primitive phenomenon, appears today to have been fundamentally misguided, an attempt to model a low-level phenomenon as an instance of a higher level phenomenon.

 

During the last years of the 19th century a careful and detailed examination of electrodymanic phenomena enabled Lorentz, Poincare, and others to develop a theory of the electromagnetic ether that accounted for all known observations, but only by concluding that "the ether is undoubtedly widely different from all ordinary matter". This is because, in order to simultaneously account for aberration, polarization and transverse waves, the complete absence of longitudinal waves, and the failure of the Michelson/ Morley experiment to detect any significant ether drift, Lorentz was forced to regard the ether as strictly motionless, and yet subject to non-vanishing stresses, which is contradictory for ordinary matter.

 

Even in Einstein's famous essay on "The Ether and Relativity" he points out that although "we may assume the existence of an ether, we must give up ascribing a definite state of motion to it, i.e. we must take from it the last mechanical characteristic...". He says this because, like Lorentz, he understood that electromagnetic phenomena simply do not conform to the behavior of disturbances is any ordinary material substance - solid, liquid, or gas. Obviously if we wish to postulate some new kind of “substance” whose properties are not constrained to be those of an ordinary substance, we can "back out" whatever properties are needed to match the equations of any field theory (which is essentially what Lorentz did), but this is just an exercise in re-stating the equations in ad hoc verbal terms. Such a program has no heuristic or explanatory content. The question of whether electromagnetic phenomena could be accurately modeled as disturbances in an ordinary material medium was quite meaningful and deserved to be explored, but the answer is unequivocally that the phenomena of electromagnetism do not conform to the principles governing the behavior of ordinary material substances. In fact, we now understand that the latter are governed by the former, i.e., elementary electromagnetic interactions underlie the macroscopic behavior of ordinary material substances.

 

We shouldn't conclude this review of the ether without hearing Maxwell on the subject, since he devoted his entire treatise on electromagnetism to it. Here is what he says in the final article of that immense work:

 

The mathematical expressions for electrodynamic action led, in the mind of Gauss, to the conviction that a theory of the propagation of electric action [as a function of] time would be found to be the very keystone of electrodynamics. Now, we are unable to conceive of propagation in time, except either as the flight of a material substance through space, or as the propagation of a condition of motion or stress in a medium already existing in space...  If something is transmitted from one particle to another at a distance, what is its condition after it has left the one particle and before it has reached the other? ...whenever energy is transmitted from one body to another in time, there must be a medium or substance in which the energy exists after it leaves one body and before it reaches the other, for energy, as Torricelli remarked, 'is a quintessence of so subtle a nature that it cannot be contained in any vessel except the inmost substance of material things'. Hence all these theories lead to the conception of a medium in which the propagation takes place, and if we admit this medium as an hypothesis, I think it ought to occupy a prominent place in our investigations, and that we ought to endeavour to construct a mental representation of all the details of its action, and this has been my constant aim in this treatise.

 

Surely the intuitions of Gauss and Torricelli have been vindicated. Maxwell's dilemma about how the energy of light "exists" during the interval between its emission and absorption was resolved by the modern theory of relativity, according to which the absolute spacetime interval between the emission and absorption of a photon is identically zero, i.e., photons are transmitted along null intervals in spacetime. The quantum phase of events, which we identify as the proper time of those events, does not advance at all along null intervals, so, in a profound sense, the question of a photon's mode of existence "after it leaves one body and before it reaches the other" is moot (as discussed in Section 9). Of course, no one from Torricelli to Maxwell imagined that the propagation of light might depend fundamentally on the existence of null connections between distinct points in space and time. The Minkowskian structure of spacetime is indeed a quintessence of a most subtle nature.

 

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