Optics And Electricity

Fresnel’s Theory

The best example that can be chosen is the theory of light and its relations to the theory of electricity.

The science of optics is more advanced than any other branch of physics because of Fresnel.

The theory called the theory of undulations forms a complete whole. But we must not ask from it what it cannot give us.

We do not expect mathematical theories to reveal the real nature of things.

• Their only object is to coordinate the physical laws with which physical experiment makes us acquainted, the enunciation of which, without the aid of mathematics, we should be unable to effect.

Whether the ether exists or not matters little. Let us leave that to the metaphysicians.

What is essential for us is:

• that everything happens as if it existed
• that this hypothesis can explain phenomena.

After all, our belief in the existence of material objects is also only a convenient hypothesis.

The difference is that it will never cease to be so. Bur some day, no doubt, the ether will be thrown aside as useless.

But at the present moment the laws of optics, and the equations which translate them into the language of analysis, hold good—at least as a first approximation.

It will therefore be always useful to study a theory which brings these equations into connection.

The undulatory theory is based on a molecular hypothesis.

This is an advantage to those who think they can discover the cause under the law. But others find in it a reason for distrust; and this distrust seems to me as unfounded as the illusions of the former.

These hypotheses play but a secondary rôle. They may be sacrificed, and the sole reason why this is not generally done is, that it would involve a certain loss of lucidity in the explanation.

In fact, if we look at it a little closer we shall see that we borrow from molecular hypotheses but 2 things:

• The principle of the conservation of energy
• The linear form of the equations
  • This is the general law of small movements as of all small variations.

This explains why most of the conclusions of Fresnel remain unchanged when we adopt the electro-magnetic theory of light.

Maxwell’s Theory

Maxwell connected by a slender tie 2 branches of physics:

• optics
• electricity

Until then unsuspected of having anything in common. Thus blended in a larger aggregate, in a higher harmony, Fresnel’s theory of optics did not perish.

Parts of it are yet alive, and their mutual relations are still the same. Only, the language which we use to express them has changed.

On the other hand, Maxwell has revealed to us other relations, hitherto unsuspected, between the different branches of optics and the domain of electricity.

The first time a French reader opens Maxwell’s book, his admiration is tempered with a feeling of uneasiness, and often of distrust.

It is only after prolonged study, and at the cost of much effort, that this feeling disappears.

Some minds of high calibre never lose this feeling.

Why is it so difficult for the ideas of this English scientist to become acclimatised among us French?

The education received by most enlightened Frenchmen predisposes them to appreciate precision and logic more than any other qualities. In this respect the old theories of mathematical physics gave us complete satisfaction.

All our masters, from Laplace to Cauchy, proceeded along the same lines.

Starting with clearly enunciated hypotheses, they deduced from them all their consequences with mathematical rigour, and then compared them with experiment. It seemed to be their aim to give to each of the branches of physics the same precision as to celestial mechanics.

A mind accustomed to admire such models is not easily satisfied with a theory.

Not only will it not tolerate the least appearance of contradiction, but it will expect the different parts to be logically connected with one another, and will require the number of hypotheses to be reduced to a minimum.

There will be other demands which appear to me to be less reasonable.

Behind the matter of which our senses are aware, and which is made known to us by experiment, such a thinker will expect to see another kind of matter—the only true matter in its opinion—which will no longer have anything but purely geometrical qualities, and the atoms of which will be mathematical points subject to the laws of dynamics alone.

Yet he will try to represent to himself, by an unconscious contradiction, these invisible and colourless atoms, and therefore to bring them as close as possible to ordinary matter.

Then only will he be thoroughly satisfied, and he will then imagine that he has penetrated the secret of the universe.

Even if the satisfaction is fallacious, it is none the less difficult to give it up. Thus, on opening the pages of Maxwell, a Frenchman expects to find a theoretical whole, as logical and as precise as the physical optics that is founded on the hypothesis of the ether.

He is thus preparing for himself a disappointment which I should like the reader to avoid; so I will warn him at once of what he will find and what he will not find in Maxwell.

Maxwell does not give a mechanical explanation of electricity and magnetism; he confines himself to showing that such an explanation is possible.

He shows that the phenomena of optics are only a particular case of electro-magnetic phenomena. From the whole theory of electricity a theory of light can be immediately deduced.

Unfortunately the converse is not true; it is not always easy to find a complete explanation of electrical phenomena.

In particular it is not easy if we take as our starting point Fresnel’s theory; to do so, no doubt, would be impossible.

But none the less we must ask ourselves if we are compelled to surrender admirable results which we thought we had definitively acquired.

That seems a step backwards, and many sound intellects will not willingly allow of this.

Should the reader consent to set some bounds to his hopes, he will still come across other difficulties.

The English scientist does not try to erect a unique, definitive, and well-arranged building; he seems to raise rather a large number of provisional and independent constructions, between which communication is difficult and sometimes impossible.

Take, for instance, the chapter in which electro-static attractions are explained by the pressures and tensions of the dielectric medium.

This chapter might be suppressed without the rest of the book being thereby less clear or less complete, and yet it contains a theory which is self-sufficient, and which can be understood without reading a word of what precedes or follows. But it is not only independent of the rest of the book; it is difficult to reconcile it with the fundamental ideas of the volume.

Maxwell does not even attempt to reconcile it; he merely says: “I have not been able to make the next step—namely, to account by mechanical considerations for these stresses in the dielectric.”

This example will be sufficient to show what I mean;

I could quote many others. Thus, who would suspect on reading the pages devoted to magnetic rotatory polarisation that there is an identity between optical and magnetic phenomena?

We must not flatter ourselves that we have avoided every contradiction, but we ought to make up our minds.

Two contradictory theories, provided that they are kept from overlapping, and that we do not look to find in them the explanation of things, may, in fact, be very useful instruments of research; and perhaps the reading of Maxwell would be less suggestive if he had not opened up to us so many new and divergent ways. But the fun- damental idea is masked, as it were.

So far is this the case, that in most works that are popularised, this idea is the only point which is left completely untouched.

To show the importance of this, I think I ought to explain in what this fundamental idea consists; but for that purpose a short digression is necessary.