The Aether

by Norman Robert Campbell

The Æther.

By Norman Campbell, Fellow of Trinity College, Cambridge^[1].

§ 1. The position of the conception of "the æther" in modern physics is anomalous and unsatisfactory. From the works of some writers it might appear that at no period was the conception of more fundamental importance or of more indisputable validity, but there are others who have ceased altogether to employ the conception and regard it as a hindrance to progress. And this conflict of opinion is of a somewhat different nature to almost all the previous disagreements which have divided men of science. The question which is involved is not primarily one of the value of experimental evidence, or of the main features of its interpretation. No doubt much of the dissatisfaction with "the æther" is based on the recent theories of the atomic nature of radiation and on the proof that the principle of relativity is an adequate foundation for electromagnetic theory, but it is clear that such theories do not provide either n sufficient or a necessary reason for abandoning the conception. Sir J. J. Thomson, the author of the earliest and most far-reaching atomic theory of radiation, devoted much of his presidential address before the British Association to a description of the properties of the æther, while, on the other hand, I hope to show that a consideration of no ideas more novel than the elements of electrostatics may lead to grave doubts concerning the utility of that conception. If both sides could be induced to express their views in detail, the difference between them would be found to concern the fundamental principles of scientific knowledge rather than more special problems of observation and intuition. Perhaps it is because men of science exhibit considerable shyness in discussing the essential foundations of their study that there has been so little direct attack on or defence of the conception of the æther. The following remarks may help in some measure towards a thorough consideration of the whole of this important problem^[2].

§ 2. We must first inquire what is meant by "the æther," and why it was ever invented. Almost the only definition of the conception with which I am acquainted is that of the late Lord Salisbury, who described it as "the subject of the verb 'to undulate.'" It is not immediately obvious why that verb requires a special subject, but a very little consideration will make out a case which is at least prima facie plausible. The principle of the conservation of energy is perhaps the only proposition that is accepted by all physicists as a necessary basis for their science, and the maintenance of that principle would seem at first sight to require some such conception as the æther. When a body is radiating energy to another at a lower temperature separated from it by a finite distance, there is a finite interval of time during which energy has been lost by the first body and has not been gained by the second; if the energy is not to be regarded as lost altogether for that interval, it might seem that it must be regarded as gained by some third body which is neither the source nor the receiver. This body, the body which is the vehicle of the undulatory energy of light, is the æther.

The development of the electromagnetic theory of light has led to the belief that the energy of radiation is essentially of the same nature as that which is localized around an electrically charged body, at rest or in motion. The æther is regarded as the vehicle, not only of the energy of radiation, but also of all forms of electromagnetic energy, and we may define it simply as "the body in which electromagnetic energy is localized."

So rough a definition will doubtless not be found satisfactory by all, but it will suffice for our purpose because it draws attention clearly to the features of the conception of the æther, as generally understood, which it is my present object to discuss.

§ 3. Of course a definition is not a proposition, and is incapable of being either true or false. Whatever definition of a scientific concept is adopted, it is always possible by framing suitably the propositions concerning it to state a theory in accordance with the observations. But, as a matter of fact, in science, as well as in other studies, the propositions are usually historically prior, though logically subsequent, to the definitions. The propositions are chosen for their simplicity, their suitability for mathematical development, or for some such reason, and the first requisite of the definitions of the concepts concerned in the propositions is that they should be such as to make these propositions true. (An obvious case of such a procedure is afforded by the concept "a perfect gas.")

In the case of the æther the propositions which have to be true are represented by the six equations of Maxwell; the definition of the nether has to be chosen so that these propositions are true, when the axes of reference are "fixed in the æther." If it turns out that, with the definition adopted, these equations are not true when the axes of reference are "fixed in the æther," then we may say roughly that the definition is false, though strictly the falsity should be attributed to the equations. For the purposes of our discussion it will be convenient and will involve no loss of generality if we replace the set of equations by a single simple deduction from them — the proposition that an electric charge $e$ moving with a velocity $u$ relative to the axes of reference is equivalent to a current element of strength $eu$, the direction of which is coincident with the path of the charge.

§ 4. It might seem at first sight that such a definition of the æther as has been given could not possibly render such a proposition untrue, but attention must be drawn to the first words of the definition — "the body" — and to the proviso in the proposition that the axes of reference are "fixed in the æther." The statement that the æther is "the body ..." undoubtedly suggests, and has been commonly taken to mean, that the æther, in so far as the relative motion of its parts is concerned, resembles a block of some solid material: that, except so far as it is disturbed by the vibrations which it transmits, its parts have no relative motion: that the motion of a body relative to the æther is uniquely determined and is, in general, unrelated to the motion of that body relative to any material system. Until quite lately it seems to have been assumed almost universally that the velocity to which the magnetic effect of a moving charge is proportional is not its velocity relative to some material system, but to some system independent of all material bodies, extended throughout the universe and having no relative motion between its parts. That such a proposition is dubitable will not be disputed when it is stated explicitly. My present object is to show that it is so far from being even inherently probable that it would never have been accepted for a moment, if it had not been for the unfortunate invention of so attractive a word as "the æther." It seems to me certain that if "the æther" had been replaced by a word in the plural number, or if to the definition offered above the words "or bodies" had been added, one of the most difficult problems of modern physics would never have been presented.

§ 5. Axes "fixed in the æther" involve the idea of the motion of a material system relative to the æther, or conversely, of the motion of the æther relative to a material body. Let us inquire what can be meant by such a velocity of the æther. When we speak of the velocity of a material body A relative to a body B, one of two definitions of the word "velocity" is implied, according as the bodies are solid or fluid. In the former case the velocity is the rate of change of the distance of a point on A, identified by some property distinguishing it from neighbouring points, from a point on B similarly identified^[3]; in the latter case velocity means the rate of transference of the body (measured by volume) across unit cross-section. It will probably be admitted that the latter definition (which is connected with the former and fundamental definition only by our belief in quasi-solid molecules) is not relevant in the case of the æther, but the former might seem to be applicable. Consider the simple case of two or more electrically charged bodies moving with different uniform velocities relative to some observer. Round each body is distributed electrostatic energy localized in the æther; the positions of the portions of the æther which contain stated amounts of energy (belonging to one and the same body), relative to each other or to the charged nucleus, are not changed by the motion. If the æther is the body where electrical energy is localized, it seems obvious and simple to identify points in the æther, as required by the definition of velocity, by the amounts of energy contained in them. Then the velocity of the æther relative to the observer would be different according as one or other of the charged bodies was considered, and would be in each case the same as the velocity of the corresponding charged body relative to the observer.

§ 6. Such, I think, is the simple and obvious view, leading directly to the principle of relativity, which would have been accepted without question had it not been for the use of the singular word "æther." "If," it was said, "there is only one æther, it cannot have more than one velocity relative to any one observer: hence we must suppose that portions of æther are not to be identified by the energy which they contain, that the energy moves through the pother, being transferred from one portion to another, with a velocity which has nothing to do with the velocity of the pother itself." This view is, I imagine, maintained by those who write of the æther; let us see whither it leads us.

§ 7. It is clear at once that if it be not permitted to identify a point in the æther by the energy localized at it, no other means of identification can be substituted. All optical phenomena prove that the æther (outside material bodies) is perfectly homogeneous, so far as the power to contain energy is concerned; the velocity of radiation is rectilinear and uniform in whatever direction it is propagated. All portions of the æther which contain the same amount of energy are, so far as experiment can tell, perfectly similar, and there is no possible means of distinguishing between them; neither have the boundaries of the æther, if there are such, ever been attained. The first requisite for the application to the æther of the definition of velocity, which is implied in all statements concerning the velocities of material bodies, cannot be fulfilled: until some other definition of velocity is put forward as applicable to the æther, all propositions about velocity of or relative to the æther are meaningless. On the view of the æther which rejects the identification of portions of the æther by their energy-content, the first statement which is made about the velocity of the æther must either be a definition or be wholly devoid of significance. If a man tells me that his watch weighs 100 grammes, his statement is for me a significant proposition, because the ordinary definition of "weight" can be applied to a watch; but if he tells me that the colour of his watch weighs 100 grammes, and refuses to tell me how a colour is to be weighed, I can only conclude that he is uttering meaningless nonsense, or, if this explanation should be excluded by the fact that be is a learned professor, that he means to inform me that, for some reason which may be quite satisfactory, he wishes me to understand "the colour of his watch" when he says "that which weighs 100 grammes."

Accordingly, when one who rejects the principle of relativity, writes down Maxwell's equations, or the simple deduction from them given above, without stating distinctly what is the relative velocity between axes "fixed in the æther," and some material system (relative to which other velocities can be measured), the only meaning which he can convey is that he proposes to call by the term "velocity $u$ relative to the æther," the state of motion of a body bearing a charge $e$ when its magnetic effect measured by any observer is equivalent to a current element of strength $eu$,..... Moreover, it follows that, if he deduces propositions from bis fundamental hypotheses and compares the result with experiment, the only valid information which he can attain by his endeavours is with what velocity relative to the æther (according to his definition) some one or more of the bodies which he observes is moving. He cannot possibly confirm or refute any assumptions which he has made in forming his hypotheses. He is in the position of a mathematician treating equations in which there are one or more unknown variables. The most that he can do is to find tin; values of those variables ; he cannot attain to an identity or non-identity, which will prove that his original equations were either true or false.

§ 8. It may be suggested that I have overlooked an alternative meaning of "velocity" which can be defined independently of the propositions of electromagnetism. There is a quantity termed "absolute velocity" introduced by dynamics, and it may be thought that it is possible to assert that the velocity of a charged body relatively to the æther is its "absolute velocity." Such an assertion is possible and would remove the objections raised in the last paragraph, but it raises far more serious difficulties. For, as is shown in the paper on the "Principles of Dynamics" in this number of the Magazine, "absolute velocity" (or rather Absolute Velocity) is meaningless unless the fundamental propositions of dynamics are assumed to be true. Now those propositions state that the mass of a body is independent of its state of motion. When it is deduced from the equations of electromagnetism that the mass of a charged body varies with its motion, the propositions of dynamics are denied to be true, and, accordingly, the term "Absolute Motion" is deprived of all significance. It is logically impossible to assert at the same time (1) that axes fixed in the æther are axes of which the Absolute Velocity is nil, and (2) that the mass of a body increases with its velocity relative to these axes. If one of the two propositions is taken to be true, the other becomes, not false, but meaningless.

We must assume, therefore, that adherents to the æther believe that "velocity relative to the æther" is neither velocity measured in the ordinary way, or Absolute Velocity. And since these two meanings of "velocity" are the only two employed in physics outside electromagnetism, we must conclude that the velocity of electromagnetism is a new concept and is defined by the first proposition in which it occurs. Let us investigate the consequences of this conclusion.

§ 9. There are two classes of well-known observations which lead thus to a determination of the velocity of some body relative to the æther. The first of these, and the most direct, is represented by Rowland's experiment on the magnetic effect of moving charges. Rowland showed that, if a charge $e$ was moving with a velocity $u$ relative to a system of observing magnets, then the charge was equivalent to a current element $eu$. Therefore, and this is the only deduction possible, the velocity of the charge relative to the æther is its velocity relative to the observing system of magnets.

The second series of observations concern aberration and the experiment of Michelson and Morley. It can be deduced from the fundamental propositions of electromagnetism that, if the velocity of an observer relative to the æther changes by an amount $u$, then the apparent direction of a ray of light seen by the observer is changed through an angle ${\tfrac {u\sin \theta }{V}}$, where $\theta$ is the angle between the direction of the ray and the direction of $u$. Observations on stars show that $u$ is the velocity of the earth in its orbit round the sun and $\theta$ the angle between that velocity and the direction of the star. On the other hand, observations made on terrestrial sources show that $u$ is zero. Accordingly we have to conclude, and this again is the only conclusion possible, that the velocity of the observer relative to the æther is the velocity of the earth in its orbit when stars are considered, and is zero when terrestrial sources are considered. Our observations prove, as the consideration of the simple facts of electrostatics suggested a priori, that the effective velocity in electromagnetic phenomena is the relative velocity between the acting and "observing" systems; the words "fixed in the æther" mean, for any given observer, "fixed in the system the action of which he is observing." Even if we start from the standpoint of the "ætherialist," observation forces us to accept the principle of relativity.

§ 10. But believers in the æther refused to accept the logic of their conclusions; they were so obsessed by ideas derived from their constant use of the word, that they would not accept the idea that an observer could have at the same time several different velocities relative to the nether. They talked of "reconciling" the results of aberration and of the Michelson experiment; but there was no "reconciliation" needed. The results formed a perfectly logical whole without, any trace of contradiction. It is true that, if velocity is defined as for a solid material body, a conclusion that one body has several different velocities relative! to another does prove that there has been some fallacy in the argument; but they had defined velocity in a perfectly different way, and there was no reason to suppose that the new definition of velocity would have the same limitations as the old. As well might a mathematician, previously acquainted only with real quantities, who had established a system for the solution of quadratic equations, think there was need for "reconciliation" when first ho encountered an imaginary root.

The "reconciliation" which was effected was in truth a revolution and a most disastrous revolution. The "ætherialists" declared that they were going to throw over their old definition and substitute a new one; that this decision was wise everyone will agree, but there will not be agreement as to the wisdom of their new choice. It was now said that the difference between the velocities relative to the æther of any two bodies was equal to their relative velocity, but that the velocity relative to the æther of any body was uncertain to the extent of a constant. They then proceeded to show with great care that no experiment which we could possibly hope to perform, until our appliances attain a perfection of a different order, could give us any information as to the value of that constant; but that if such experiments ever could be performed, there was no reason for supposing that the quantity which was assumed to be constant would actually be found to be constant. And then they settled down with a sigh of satisfaction in the happy conviction that a solution of all the difficulties connected with the æther had been found which would meet with universal approval.

§ 11. But the approval has not been universal. M. Poincaré has attacked the scheme on the "round that it needs a fresh assumption whenever the delicacy of our instruments is increased. And it has also occurred to many people that there is something very unsatisfactory in introducing into the fundamental equations of a science a quantity which cannot be measured experimentally, either directly or with the help of those equations.

It is probable that the future historian of physics will be astounded that the vast majority of physicists should accept a system of such bewildering complexity and precarious validity rather than abandon ideas which seem to have their sole origin in the use of the word "æther," and reject those to which so many lines of thought point insistently. Unless a perfectly arbitrary assumption is made as to the value of the "velocity of the æther" relative to some observing system, observation forces us to the adoption of the principle of relativity — to the belief that the axes "fixed in the æther," to which Maxwell's equations must be referred, are axes fixed in the charged system which is the source of the energy of which the transformations are investigated. It has been asserted that such ideas are really even less satisfactory than those based on the conception of a single æther, because "they require such a very complex structure for the æther." But if we abandon the use of the word "æther" their essential simplicity appears. The system in which electromagnetic energy is localized ceases to be a single body independent of all material bodies; it becomes a collection of portions which are to be regarded as parts of every separately moving charged body; if the charged body is in uniform motion relative to the observer the portion of the æther in which its energy is localized moves with the same velocity relative to that observer. The principle of relativity does not complicate our interpretation of electrical phenomena; it simplifies it in reducing by one the number of bodies that have to be taken into account.

§ 12. It would be easy to proceed to attack in like manner other confusions to which the use of the concept "æther" has given rise, to analyse the many and mutually inconsistent attempts which have been made to estimate its density, rigidity, and even atomic weight. My object is not to marshal all the arguments that might be brought against the use of that concept, but only those which appear to me to be especially destructive at the present time. The recent work of Bucherer, and the atomic theories of J. J. Thomson and Planck (the latter recently developed by Stark^[4] so as to resemble the former very closely) will be found very difficult for believers in the æther to assimilate or to explain away; if they attempt to do so it will doubtless be in the belief that the concept of the æther is worth retaining. A demonstration that the case for the æther is ludicrously weak, where it was thought to be strongest, that the concept has never been the source of anything but fallacy and confusion of thought, may serve to expedite its relegation to the dust-heap where now "phlogiston" and "caloric" are mouldering.

Note.

It is desirable that a few remarks should be made on the relation between this paper and another on "The Principles of Dynamics," which is published in the same number of this Magazine; for it might appear that some statements made above are inconsistent with those made elsewhere. One of these statements is that to which the footnote on p. 184 is appended. In the "Principles of Dynamics" it is pointed out that the velocity which is discussed in physics is almost always Velocity, and that it is not definable immediately in terms of distances and times. (The notation used in this Note is the same as that used in the paper to which reference is made.)

I have not reconciled these apparent inconsistencies by adopting the terms employed in the "Principles of Dynamics," which was written considerably later, because it seems to me that the argument as it is stated here, though objectionable in form, is more convincing than it would have been otherwise, and requires less subtlety of thought. But I propose in this Note to point out how it would appear if viewed from the standpoint of the later ideas.

The only meaning which is given to the word "velocity" in scientific discussion, which can be stated without assuming the truth of a scientific theory, is ${\tfrac {dr}{dt}}$, where $r$ and $t$ are Distances and Times bearing relation A to distances and times. Other quantities, like Absolute Velocity, which are called velocities because they are related in a certain way to Relative Velocities, can only be defined by stating the relation in the form of an equation, which is, in fact, the expression of a scientific theory. If we reject the identification of particles of the æther by their energy-content, we reject the possibility of measuring the distance of such a particle from any other particle, and consequently of defining the Relative Velocity of such a particle by means of relation A. The "velocity of the æther," defined by those who reject this possibility, must be meaningless without assuming the truth of the first theory in which it is mentioned (Maxwell's equations), just as the quantity "b" is meaningless without assuming the truth of Van der Waals's equation.

On solving the equations by which the "velocity of the æther" is defined, it is found that different values for this velocity for any particle are found in different cases — a conclusion which shows that this "velocity" has properties different from those of Relative Velocity. It would be analogous if the quantity "b" were found to be negative or imaginary, showing that "b" has different properties from those attributed to a Volume by definition. In the last case two alternatives would be open: the conclusion might be accepted, or a new theory might be stated which would lead to a different conclusion. In the case of the "æther," all arc agreed that the conclusion is to be rejected and a new theory stated. Adherents to the principle of relativity point out that a new theory can be stated which avoids all necessity for any such quantity as "velocity of the æther": it can be stated in terms of quantities which arc related to measurements by relation A alone. The "ætherialists," on the other hand, propose a new theory which introduces again a quantity of the same nature as before, but avoid the possibility of the occurrence of fresh undesirable conclusions about it by stating the theory so that the value of the quantity cannot be found by any experiment that is ever likely to be performed.

My contention is that the former procedure is the more satisfactory, and to what I have said I will only add one argument derived from the analogy of dynamics. I imagine that physicists would agree that it" dynamics could be stated in terms of Relative Motion only, without complicating the equations so that they would be unamenable to mathematical treatment, that course should certainly be adopted. "Absolute Motion" is a disagreeable necessity forced on us by the insufficiency of our powers of mathematical treatment. The case against "velocity of the æther" is stronger than that against Absolute Motion, for we can find the value of Absolute Velocity by assuming the truth of the equations by which it is defined, and we cannot find the value of "velocity of the æther," even by assuming the truth of those equations. On the other hand, there is no argument in favour of "velocity of the æther" derived from the necessities of mathematics, because the equations based on the principle of relativity are just as simple as those based on the conception of the æther.

September 1909.

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1. Communicated by the Author.
2. Note.—It may he pointed out that the gist of the argument is contained in chap. xiv. of 'Modern Electrical Theory' (Cambridge, 1907), and in an article in the 'New Quarterly Review' No. 3.
3. See note at the end of the paper.
4. J. Stark, Phys. Zeit. Sept. 1909, p. 570.