Art. 13.-EINSTEIN ON TIME AND SPACE.

Of all the surprises which Einstein's theory of space and time has brought to us, perhaps the greatest is the intense interest aroused among those who are not accustomed to follow the progress of science closely. The interest is partly due to the dramatic fulfilment of a prediction arrived at by abstruse mathematical calculation; partly to the catchword 'light on the bend' and to the strange paradoxes of time and space that are implied. But it is evident that there is beyond this a real desire to obtain some insight into this latest achievement of human thought, and to share in the new conceptions of the world of nature to which scientific men are with great difficulty attempting to accustom themselves.

There are truths, ideas, emotions, which cannot be conveyed in familiar language. The poet, the painter, and the musician, by their inspiration, can speak direct to the mind and awake the response they desire. The mathematician deprived of his x's, and thrown back on words inadequate for his meaning, has no such access. He can only experiment on the reader, throwing out suggestions and analogies in the hope that something of what it all means to him may be conveyed. But it is on the reader that the main effort must fall to follow it up with his imagination. And if he is inclined to say with Hippolyta, This is the silliest stuff that ever I heard,' we reply with Theseus, The best in this kind are but shadows; and the worst are no worse, if imagination amend them.'

The theory of relativity was produced by Einstein in two stages. The first stage was based directly on known experimental evidence. It was not so much an attempt to explain the results of experiment, as a logical deduction from them. It was a statement of conclusions reached, when certain unproven and useless hypotheses, which had crept into the common mode of stating the results, were discarded. The second stage was not immediately based on experiment; it was a bold generalisation of the views reached in the first stage. The suggested generalisation was followed by an abundance of mathematical analysis; and, in the end, certain deductions

were made which could be put to an experimental test. The principal deductions related to gravitation; and a new law of gravitation was enunciated, agreeing approximately with Newton's, but presumably more accurate. There was already a necessity for a new law of gravitation, because the modern discovery that the mass of a body depends on its velocity had rendered the old law ambiguous. Even those who were most reluctant to tamper with a law which had served so well felt that it was absurd to appeal to the verbal inspiration of Newton, interpreting his words textually in conditions never contemplated by him.

There were two tests of Einstein's new law. One referred to the motion of the planet Mercury, and was at once verifiable. It explained exactly an anomaly in the motion of the planet, which was the most celebrated discordance between observation and Newtonian gravitational theory. The second test related to the deflexion of light passing near the sun, and was verified by observations made during the recent solar eclipse. A third test was also indicated, which relates not to the new law of gravitation but to another part of the relativity theory. This was a minute displacement of the spectral lines on the sun relatively to corresponding lines in laboratory spectra. This has not been verified, and it is claimed that the evidence, so far as it goes, is adverse. No final conclusion can yet be reached; but, if this displacement should be disproved, while profoundly affecting certain parts of the theory, it would not cast doubt on the validity of the new law of gravitation.

The general ideas of the relativity theory are foreign to our usual mode of thought and are difficult to grasp. The would-be expositor of the theory seems to be indulging a taste for paradox, and his audience can scarcely be persuaded to take his remarks seriously. It has been suggested that the new conceptions are justified because they have proved their worth in unifying diverse phenomena and predicting results that can be verified, but they need not be regarded as describing the reality of things. We are not averse to the view that in scientific conceptions the test is utility rather than absolute truth. We vaguely believe that our progress in knowledge is bringing us nearer to a true understanding

of the nature of things; but absolute truth is too elusive a quality to count on with confidence. Thus we are willing to allow that our conception of nature may be merely illustrative, but on one condition-that all other current conceptions of nature are to be regarded in the same way. If the relativity conception is figurative, so too is the everyday conception of the external world.

The two ideas in the new theory which seem most mysterious are-to use the popular expressions-time as a fourth dimension, and the warping of space. These correspond to the two principal stages of Einstein's work. The amalgamation of space and time into one fourdimensional continuum belongs to the restricted principle of relativity, which he arrived at in 1905. It almost immediately won acceptance by a large number of physicists. The warping, or non-Euclidean character, of space in a gravitational field of force was a new development, published in its final form in 1915. Since experimental tests were indicated, it was natural to reserve judgment pending trial; but to many the extraordinary elegance of the theory, and the great unification of the phenomena of nature which it implied, had already brought a confident hope that it might be true.

We shall try to explain the meaning of the statement that time is a fourth dimension. We recognise that the happenings of nature around us are arranged in a certain order, which we call an order in space. There is also an apparently independent order-an order in time. The idea that these two orders could be amalgamated into one is not new. Just as we can think of an ordinary solid as built up of a pile of plane slices, so we can think of a solid at any moment as being a slice of something four-dimensional; and the slices corresponding to successive moments will build up a four-dimensional figure in combined space-time. An individual as he grows from childhood to old age makes up such a four-dimensional figure; what we see of him at any time is just the threedimensional section corresponding to that time.

So far, this is merely a picturesque way of stating things, rather entertaining to amuse oneself with, but without any inner meaning in physics. We are putting together two different things, time and space, in an

arbitrary way, just as we put together temperature and time when we draw a thermometer-chart. But the relativity view is that the space-order and time-order in nature are not independent, so that our putting together of them is not merely permissible but compulsory in contemplating the external world. You can build up a pile of sheets of paper until you form a cube; but there is a difference between a solid cube of paper and one which is a pile of sheets. The relativity view is that the combination of space and time is analogous to the solid cube; it can be regarded as made up of a pile of thin slices, but there is no particular direction in which the slices have to run. The combined space-time order is one which does not fall apart naturally into a particular space-order and time-order; we can make the slices in any way we like, and no one way is more fundamental than another. In fact, we must not merely put together space and time-we must weld them.

The separation of the four-fold order of events into a single order of time and a three-fold order of space is not a separation inherent in the external world, but is something contributed by the observer and dependent on his circumstances. The observer himself is like a line or cylinder in this world of four-dimensions-a long chain of successive positions at successive instants. He is an asymmetrical body in the symmetrical world; and, when he contemplates nature, he introduces into it his own asymmetry. If he makes no effort to move, he is nevertheless conscious that he is not stationary in the world, and that he is progressing in what he calls time. Thus his linear extension, as we have pictured it, is interpreted by him as progress of time. He singles out this particular dimension as time and calls the other three dimensions space; but the discrimination has nothing to do with the order of external nature, it is simply a reflexion of his own track through the world.

We thus see the possibility that observers taking different tracks will have different perceptions and measures of space and time. It may seem strange that this has not long ago introduced confusion. We have to remember that in general all observers take the same track through the world, namely, that taken by the Earth on which they live. It is true that we can slightly vary

the track by making a railway journey; but it is unusual to carry out accurate experiments in a train, and the more delicate effects are likely to escape notice. Moreover, an observer in a train does not perceive the same space as an observer on the platform; the motion of objects relatively to him is quite different; but it is easy to make the rough mental allowance of subtracting the velocity of the train, and we scarcely regard this as a genuine difference of space.

Until recently it was supposed that the only difference between the space and time of observers taking different tracks through the world was this difference of velocity, which we habitually allow for. But it is clear that the choice of a different time-direction involves a more fundamental kind of change. The additional effects are very small indeed, but they have been detected by observation; and indeed it was these experimental results that suggested the relativity theory of space and time.

Returning to our analogy of the paper cube, the direction perpendicular to all the sheets of paper is fundamental and can be distinguished from directions running obliquely through them, whereas in a solid block of paper there is no direction having unique properties. Similarly, if our union of space and time is merely a piling together of distinct things, it ought to be possible to detect experimentally a corresponding fundamental direction. We should naturally say that a body whose track through the world was in this special direction was progressing in time alone, that is to say, at rest in space. The terminology does not much matter; the essential point is that physical experiment has not succeeded in detecting any such track distinguishable from all others. Many delicate tests have been made ; and in the attempt to account for their failure a most extraordinary series of compensatory phenomena have been attributed to nature, as though all the natural forces were leagued in a conspiracy to prevent our detecting any standard of rest. Einstein's theory, by accepting the solid block of paper as the true picture instead of the pile of sheets, solves all our puzzles. We detect no track with unique properties, because there cannot be any unique track in a homogeneous continuum.