theory of light and the Newtonian theory of gravitation held good simultaneously, would the light continue in its original path.

We see then that a merely qualitative investigation of this predicted deflection would be inconclusive; it would still leave the choice open between the corpuscular and undulatory theories of light on the one hand, between the Newtonian and Einsteinian theories of gravitation on the other. Precise measurement is called for, and this, as it happens, is by no means easy to secure. The sun is the only body, massive enough to produce a measurable deflection, open to our study; the necessary observations can be made only during a total eclipse; a mean precision is required, in the measurement of the eclipse photographs. of one hundred-thousandth of an inch—an attainment on the verge of the impossible; moreover, it is not quite certain, at any rate in the case of the deflections hitherto observed, that they were wholly due to solar gravitation.

As everyone knows, the test applied to Einstein's prediction during the eclipse of 1919 was, at least, partially successful. Three independent sets of observations—one of them not too reliable, owing to imperfections in the photographs which rendered measurement uncertain-were in unequivocal agreement as to the fact of the deflection; the individual mean results, derived from the two best sets, were also in moderately good agreement as to its amount, while their mean, in its turn, was practically identical with the value predicted by general relativity. There was, however, considerable discordance between the results computed from individual stars, and it cannot be said that the Einstein law of variation of deflection with distance was verified at all. Until this is effected, it is open to anyone to ascribe a part of the observed deflection to meteorological changes accompanying the passage of the moon's shadow. Sir Arthur Schuster has attempted to show that the effects due to such meteorological changes are of a lower order of magnitude than the Einstein effect, but his argument is scarcely conclusive.

It is hoped that the observations, taken during the recent eclipse of 1922, will have done something to clear up these points, as the instrumental equipment, especially that devoted to investigating the law of variation, was much better suited to the work than that employed in 1919. But it still remains to be seen whether any portable equipment can afford a really conclusive test by the study of a single eclipse, or whether we

must wait for cumulative evidence, derived from a series of eclipses of different duration, and therefore differently affected by the meteorological conditions.

our

We

With the discussion of the eclipse observations, survey of the physical evidence really comes to an end. do not include in it Einstein's second prediction, to the effect that the frequency of vibration of an atom would be found to depend on the magnitude of the gravitational field in which it existed. The reason for the omission is that the prediction itself is suspect; Jeffries, in England, and Priestly, in Australia, have shown, in different ways, that the fundamental equations of relativity, as presented by Einstein, are susceptible of more than one interpretation in this respect, and that Einstein may not have-probably has not-hit upon the right one. This suspicion is strengthened by Weyl's brilliant extension of the theory, according to which the relation between atomic frequency and gravitational field is wholly indeterminate. Even if the predicted relation were verified, the verification could scarcely be regarded as evidence for the reliability of the theory, though it would certainly attest its usefulness; but the prediction has not been verified. A number of the most competent investigators, both in Europe and America, have taken up the problem; but their results are in flat contradiction. The predicted difference in frequency between a solar and a terrestrial atomic vibration-about one part in three-quarters of a million—is not in itself beyond the reach of measurement; modern spectroscopy has dealt successfully with even smaller quantities. But the effect sought for, if it be real, appears to be masked by those of a number of actions, part mechanical and part purely photographic, our knowledge of which is, as yet, incomplete.

To conclude. The direct and incontestable physical evidence for the theory of relativity is at present confined to the Kaufmann-Bucherer experiments, Sommerfeld's verified predictions, and the motion of the orbit of Mercury; to these we may add, with some probability, the gravitational deflection of light; but that is all. On the other hand, not a single known physical fact is opposed to it—which is more than can be said for any other physical theory in existence-and it unifies departments of knowledge, such as dynamics, optics, and astronomy —also, in Weyl's development, electromagnetism—previously regarded as independent. Pragmatically speaking, its position, if by no means impregnable, is certainly strong.

28

I

RELATIVITY AND REAL LENGTH.

By

W. R. BOYCE GIBSON, M.A., D.Sc., Professor of
Philosophy, University of Melbourne.

T is a rash thing sometimes to ask an innocent question. This is particularly the case where one has to answer the question oneself, and in such a way as to satisfy the relativist. I glance at a ruler lying on my study table, and turning to my relativist friend, I ask him to tell me, if he can, how long the ruler really is. I soon discover that the whole relativist universe has been set vibrating by the question, and that its import is well-nigh unfathomable.

The very first step towards a solution brings the difficulties full into view. The ruler's real length, we are told, is a matter that concerns not the ruler only, but oneself also as observer. Length, we are assured, is not a quality of the ruler, but a relation between ruler and observer. Sitting opposite to the ruler I may assess its length at one foot, but flashing past it at a speed approaching that of light, I must judge it to be six inches or less. Length, then, is a relation, not a quality, and the same holds good of duration. They "are not things inherent in the external world; they are relations of things in the external world to some specified observer." (Eddington, "Space, Time and Gravitation," p. 34.)

For simplicity's sake we will assume that the ruler is a perfectly rigid rod, and not liable, therefore, to change its length with fluctuations of temperature, or its straightness with conditions favouring flexure.* Still, despite its rigidity, the relativist rod will show a length that varies with the rate at which the observer increases or decreases his distance from it.

Common-sense is apt to stumble over this fundamental requirement of Relativity Theory. The ruler we handle seems to us so manifestly to possess a length of its own, a length perfectly constant if the bar be a rigid one. And our first rejoinder to the relativist may very well be that he is confusing the ruler's own natural length with the observer's measure of that length. The measured length may vary according to relativist requirements, but the rod's own length, surely, remains steadfast throughout. But to this objection the relativist replies: "I cannot conceive of any 'length' in nature

The discrepancy between the ideally rigid body and the body as it occurs in nature is covered in practice through the mediation of accurately tested measuringrods. "It is not a difficult task," says Einstein (Sidelights on Relativity, pp. 36-37), "to determine the physical state of a measuring-rod so accurately that its behaviour relatively to other measuring bodies shall be sufficiently free from ambiguity to allow it to be substituted for the rigid body. It is to measuring-bodies of this kind that statements as to rigid bodies must be referred."

independent of a definition of the way of measuring length. And, if there is, we may disregard it in physics, because it is beyond the range of experiment." (Eddington, id. p. 8). It is indeed only as measured that facts have any relevancy for physics, and even our common-sense perception, we are told, is “a kind of crude physical measurement" (id. p. 15). If we insist on accepting the rod's own extendedness as a real length that remains constant through all variations in the measuring, we shall have to explain how we know the unmeasured length to be constant, or, in default, retain on our hands the old spectral thing in itself, about whose properties, as we know, it is wisest to say nothing.

A more promising line of criticism might be the following. We might argue that though the measured length of a rigid rod might vary with its motion relatively to an observer (according to the Restricted Theory), or with its place and position in the gravitational field (as the General Theory requires), this would not compel us to admit that the rod had no objective length or extendedness at all. Might it not have as its intrinsic property an "indeterminate length," relation to the observer having the effect not indeed of first introducing the length relation, but only of rendering an indeterminate quality of the rod determinate?

The suggestion has a certain plausibility, and, no doubt, some share of truth. It seems prima facie reasonable that the real length of the rod should be its algebraical length x, and that the measurable arithmetical lengths should record its various appearances according to circumstance and in accordance with law.

We recall the Boundless of Anaximander, and the Primary Matter of Aristotle. We recall the view that space and time are, in themselves, not actualities, but possibilities, real possibilities of figure, measure, duration. In language familiar to philosophy we would now say that the rod's real length is its universal length, and that its particular lengths are its lengths as they appear according to changing conditions of movement and position. Moreover, this view of real length would fit in quite well with geometrical requirements. Consider the real length of the hypotenuse AB of the Euclidean right-angled triangle ABC. This mathematically real length is precisely any length. What is determinate here is simply the relation of the length of the hypotenuse C to the lengths of the sides A B containing the right angle, as given by the equation c2=a2+b2 but a and b may have any arithmetical values we please to give them. So the radius of a Euclidean circle has a purely indeterminate length. Its proper length is any length.

But despite the simplicity of the view that the rod's real length is indeterminate, it is not scientifically satisfactory. And this for two main reasons. First, not being measurable or countable, its reality is not strictly a physical reality, which must rest on number and measure as a basis; and second, being intrinsically indeterminate, it cannot satisfy the requirement that the real shall be something permanent and abiding, something that abides through change. Instead of being an invariant, the indeterminate length is intrinsically a variable.

It is not easy to see how these two main requirements of measurability and of invariancy can be simultaneously met. If we return to the view that the rigid ruler's real length, in so far as it is measurable, is indeed its natural length as an objective fact controlling the empirical measurings of the individual observer, and that in no other sense is it both measurable and real-real, that is, in the sense of being just what it is, and not what the measurer would wish it or think it to be we seem driven to add that it cannot then be an invariant, the same for all fields and observers, for has not Einstein shown that length is a function of the mobile gravitational field as well as of the relative movement of the particular observer?

Certainly the requirements conflict. But may not the conflict arise from a tendency to simplify the matter overmuch?

The Logic of Relativist Reality can be understood, I would venture to say, only if we bear in mind the complexity of the requirements of physical theory as an organised system: the need for direct contact with measurable fact, on the one hand; the equally imperative need for organised unity of scientific grasp, on the other; and thirdly, the need for keeping these two fundamental requirements in working harmony through the binding force of mathematics. Now, Einstein has succeeded in adequately meeting these three main needs. "Whatever can be measured," says Planck, "is real."* Einstein's whole procedure is controlled by respect for this dictum, and to this extent and in this sense he is a radical empiricist. One fundamental feature, at any rate, of the reality of the rigid ruler, is, in his eyes, its measurability through the help of sense and muscle, through the sensori-motor mechanism of the individual human body. And yet this respect for fact is dominated by respect for law, and above all by the basic recognition that it is only as an element in a natural order, only as conforming to law and measure, that

*Quoted by Moritz Schlick, "Space and Time in Contemporary Physics,” p. 23.