Appendix 3.)

Stellar observations, however, are unnecessarily difficult. Fresnel had pointed out that a terrestrial source of light would do just as well. He had also (being a man of exceeding genius) predicted that nothing would happen. Hoek has now tried it in a perfect manner and nothing did happen.

But these facts are not at all disconcerting; they are just what ought to be anticipated, in the light of true theory. The absence of all effect caused by stagnant dense matter inserted in the path of a beam of light, that is of dense transparent matter not artificially moved with reference to the earth--or rather with reference to source and receiver--is explicable on Fresnel's theory concerning the behaviour of ether inside matter.

If the index of refraction of the matter is called μ, that means that the speed of light inside it is 1/μth of the speed outside or in vacuo. And that is only another way of saying that the virtual etherial density inside it is represented by μ², since the velocity of waves is inversely as the square root of the density of the medium which conveys them;--the elasticity being reckoned as constant, and the same inside as out.

But then if the ether is incompressible its density must really be constant,--so how can it be denser inside matter than it is outside? The answer is that presumably the ether is not really extra dense, but is, as it were, loaded by the matter. The atoms of matter, or the constituent electrons, must be presumed to be shaken by the passage of the waves of light, as they obviously are in fluorescent substances; and accordingly the speed of propagation will be lessened by the extra loading which the waves encounter. It is not a real increase of density, but a virtual increase, which is really due to the addition of a certain fraction of material inertia to the inertia of the ether itself. The density of ether outside being 1, and that of the loaded ether inside being μ², the effect of the load is expressible as μ²-1, while the free ether is the same inside as out.

Suppose now that the matter is moved along. The extra loading, being part of the matter, of course travels with it, and thereby affects the speed of light to the extent of the load,--that is to say, by an amount proportional to μ²-1 as contrasted with μ².

This is Fresnel's predicted ratio (μ²-1): μ², or 1-1/μ²; and in Fizeau's experiment with running water--especially as repeated later, with modern accuracy, by Michelson--this represents exactly the amount of observed effect upon the light.

But if, instead of running water, stagnant water is used--that is stationary with respect to the earth, though still moving violently through the ether--then the (μ²-1) effect of the load will be fixed to the matter, and can produce no extra or motile effect. The only part that could produce an effect of that kind would be the free ether, of density 1. But then this--on the above view--is absolutely stationary, not being carried along by the earth at all; hence this can give no effect either. Consequently the whole effect of an ether-drift past the earth is zero, on optical experiments, according to the theory of Fresnel; and that is exactly what all the experiments just described have confirmed.

Since then Prof. Mascart, with great pertinacity, has attacked the phenomena of thick plates, Newton's rings, double refraction, and the rotatory phenomenon of quartz; but he has found absolutely nothing attributable to a stream of ether past the earth.

The only positive result ever supposed to be attained was in a very difficult polarisation observation by Fizeau in 1859. Unless this has been repeated, it is safest to ignore it; but I believe that Lord Rayleigh has repeated it, and obtained a negative result.

Fizeau also suggested, but did not attempt, what seems an easier experiment, with fore and aft thermopiles and a source between them, to observe the drift of a medium by its convection of energy; but arguments based on the law of exchanges tend to show, and do show as I think, that a probable alteration of radiating power due to motion through a medium would just compensate the effect otherwise to be expected.

We may summarise most of these statements as follows:--

Summary.

{ A real and apparent change of wave-length. { Source alone { A real but not apparent error in direction. moving produces { { No lag of phase or change of intensity, { except that appropriate { to altered wave-length.

{ No change of frequency. Medium alone { No error in direction. moving, or { A real lag of phase, but undetectable source and receiver { without control over the moving { medium. together, produces { A change of intensity corresponding { to different distance, { but compensated by change { of radiating power.

{ An apparent change of wave-length. { An apparent error in direction. Receiver alone { No change of phase or of intensity, moving produces { except that appropriate { to different virtual { velocity of light.

I may say, then, that not a single optical phenomenon is able to show the existence of an ether stream near the earth. All optics go on precisely as if the ether were stagnant with respect to the earth.

* * * * *

Well, then, perhaps it is stagnant. The experiments I have quoted do not prove that it is so. They are equally consistent with its perfect freedom and with its absolute stagnation; though they are not consistent with any intermediate position. Certainly, if the ether were stagnant nothing could be simpler than their explanation.

The only phenomena then difficult to explain would be those depending on light coming from distant regions through all the layers of more or less dragged ether. The theory of astronomical aberration would be seriously complicated; in its present form it would be upset (p. 45). But it is never wise to control facts by a theory; it is better to invent some experiment that will give a different result in stagnant and in free ether. None of those experiments so far described are really discriminative. They are, as I say, consistent with either hypothesis, though not very obviously so.

Michelson Experiment.

Mr. Michelson, however, of the United States, invented a plan that looked as if it really would discriminate; and, after overcoming many difficulties, he carried it out. It is described in the Philosophical Magazine for 1887.

Michelson's famous experiment consists in looking for interference between two half-beams of light, of which one has been sent to and fro across the line of ether drift, and the other has been sent to and fro along the line of ether drift.

A semi-transparent mirror set at 45° is employed to split the beam, and a pair of normal and ordinary mirrors, set perpendicular to the two half-beams, are employed to return them back whence they came, so that they can enter the eye through an observing telescope.

It differs essentially from the interference kaleidoscope, Fig. 7, inasmuch as there is now no luminous path B C, and no contour enclosed by the light. Each half-beam goes to and fro on its own path, and these paths, instead of being coincident, are widely separate,--one North and South, for instance, and the other East and West.

Under these conditions the bands are much more tremulous than they were in the arrangement of Fig. 7, and are subject to every kind of disturbance. The apparatus has to be excessively steady, and no fluctuation even of temperature must be permitted in the path of either beam. To secure this, the source, the mirrors, and the observing telescope, were all mounted upon a massive stone slab; and this was floated in a bath of mercury.

The slab could then be slowly turned round, so that sometimes the path A B and sometimes the path A C lay approximately along or athwart the direction of the earth's motion in space.

And inasmuch as the motion along would take a little longer than the motion across, though everything else was accurately the same, some shift of the interference bands might be expected as the slab rotated.

But whereas in all the experiments previously described the effect looked for was a first-order effect, of magnitude one in ten or twenty thousand,--depending, that is to say, on the first power of the ratio of speed of earth to speed of light,--the effect now to be expected depends on the square of that same ratio, and therefore cannot be greater, even in the most favourable circumstances, than 1 part in a hundred million.

It is easy to realise therefore that it is an exceptionally difficult experiment, and that it required both skill and pertinacity to perform it successfully.

That it is an exceptionally difficult experiment will be realised when I say that it would fail in conclusiveness unless one part in 400 millions could be clearly detected.

Mr. Michelson reckons that by his latest arrangement he could see 1 in 4000 millions if it existed (which is equivalent to detecting an error of 1/1000 of an inch in a length of 60 miles); but he saw nothing. Everything behaved precisely as if the ether was stagnant; as if the earth carried with it all the ether in its immediate neighbourhood. And that was his conclusion.

Theory of Michelson Experiment.

The theory of the Michelson experiment can be expressed thus: its optical diagram being the same as is expressed geometrically in Fig. 6.

If a relatively fixed source and receiver move through the ether with velocity u, such that u/v=α the aberration constant; then the time of any to and fro journey S M, inclined at angle θ to the direction of the drift, is increased, above what it would be if there were no drift, in the ratio

√(1-α²sin²θ) / (1-α²)

This follows from merely geometrical considerations.

Hence if a ray is split, and half sent so that θ=0 while the other half is sent so that θ=90 (as in Fig. 10), the one will lag behind the other by a distance ½α² times the distance travelled; which, though very small, may be a perceptible fraction of a wave-length, and therefore may cause a perceptible shift of the bands.

But when the experiment is properly performed, no such shift is observed.

The experiment thus seems to prove that there is no motion through the ether at all, that there is no etherial drift past the earth, that the ether immediately in contact with the earth is stagnant--or that the earth to that extent carries all neighbouring ether with it.

If we wish to evade this conclusion, there is no easy way of doing so. For it depends on no doubtful properties of transparent substances, but on the straightforward fundamental principle underlying all such simple facts as that--It takes longer to row a certain distance and back, up and down stream, than it does to row the same distance in still water; or that it takes longer to run up and down a hill, than to run the same distance laid out flat; or that it costs more to buy a certain number of oranges at three a penny and an equal number at two a penny than it does to buy the whole lot at five for twopence.

Hence, although there may be some way of getting round Mr. Michelson's experiment, there is no obvious way; and if the true conclusion be not that the ether near the earth is stagnant, it must lead to some other important and unknown fact.

That fact has now come clearly to light. It was first suggested by the late Professor G.F. FitzGerald, of Trinity College Dublin, while sitting in my study at Liverpool and discussing the matter with me. The suggestion bore the impress of truth from the first. It independently occurred also to Professor H.A. Lorentz, of Leiden, into whose theory it completely fits, and who has brilliantly worked it into his system. It may be explained briefly thus:--

Electric charges in motion constitute an electric current. Similar charges repel each other, but currents in the same direction attract. Consequently two similar charges moving in parallel lines will repel each other less than if stationary,--less also than if moving one after the other in the same line. Likewise two opposite charges, a fixed distance apart, attract each other less when moving side by side, than when chasing each other. The modification of the static force, thus caused, depends on the squared ratio of their joint speed to the velocity of light.

Atoms of matter are charged; and cohesion is a residual electric attraction (see end of Appendix 1). So when a block of matter is moving through the ether of space its cohesive forces across the line of motion are diminished, and consequently in that direction it expands, by an amount proportioned to the square of aberration magnitude.

A light journey, to and fro, across the path of a relatively moving medium is slightly quicker than the same journey, to and fro, along (see p. 64). But if the journeys are planned or set out on a block of matter, they do not remain quite the same when it is conveyed through space: the journey across the direction of motion becomes longer than the other journey, as we have just seen. And the extra distance compensates or neutralises the extra speed; so that light takes the same time for both.

FOOTNOTES:

The word "stationary" is ambiguous. I propose to use "stagnant," as meaning stationary with respect to the earth, i.e. as opposed to stationary in space.

Lord Rayleigh, Nature, March 25, 1892.