MODIFYING OUR IDEAS OF NATURE: THE EINSTEIN

THEORY OF RELATIVITY.1

By HENRY NORRIS RUSSELL,

Professor of Astronomy in Princeton University.

I.

It is probably a long time since there has been any occasion on which a matter so definitely belonging to pure science as the "theory of Einstein " has excited so much popular interest.

Although the statements in the newspapers concerning "the overthrow of Newton's laws" and similar "scare heads" have gone beyond the more sober statements of scientific authorities, it is nevertheless true that the theory of relativity, of which the recent work of Einstein forms an extension, has modified our conceptions of nature in a very remarkable fashion.

Einstein's reported statement that there were not more than 12 men in the world who could read and fully understand his book was probably quite within the facts. But the elementary ideas on which the theory of relativity is based do not involve any difficult mathematics, and the only obstacle to grasping or holding them is their remarkable novelty. We can understand them easily enough, or at least understand what they are about, if only we begin at the beginning.

It probably has not occurred to all of you that while I was speaking the last sentence we traveled several hundred miles. Yet, of course, we did. If we had not, the earth would have left us behind it somewhere in empty space.

In fact, we are undergoing a very complicated series of motions, carried around with the rotating earth and swinging along much more rapidly and in a much vaster curve with its orbital motion.

But of this fact we are blissfully unconscious. Why? Because the motion is perfectly smooth, without jar or shock, and in particular because not merely we ourselves, but all the objects that constitute our environment, are moving together.

1 Reprinted by permission from Princeton Lectures, No. 2, Princeton, N. J., May 1,

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MOTION AND DISTANCE ORDINARILY MEASURED BY "TYING UP"

TO DEFINITE OBJECTS.

So we come to one of the main conceptions of the theory of relativity, the moving frame of reference.

We ordinarily refer our measurements and indeed our notions of distance and of motion to some frame, what the mathematician would call some system of co-ordinates, which, so to speak, is "tied" to some definite objects-ordinarily to that portion of the earth's surface on which we may have set ourselves or over which we may be traveling at the moment.

Though we and all our well-informed ancestors for two centuries. have known very well that this frame of reference is not at rest but is in rapid and intricate motion, we are, nevertheless, still accustomed to referring our motions to this moving frame and saying that a thing has not budged when its position with respect to the ground has not altered.

And in doing this we not only follow the promptings of common sense, but find a practical and working basis for the scientific description of almost all terrestrial affairs.

But the moment we begin to look off the earth into space things are different. It then becomes obvious that the earth is not at rest but moving, both on its own axis and about the sun.

I say "obvious;" but it is worth remembering that these factsat present so familiar even to the man in the street-aroused, when their truth was first advocated, the most violent disbelief and agitation, and that it took a century or more of controversy to displace the old innate belief in the fixity of the earth, that is, of our frame of reference, and substitute the belief that it was in motion.

NECESSITY OF FINDING OTHER MEANS OF MEASURING MOTION AND DISTANCE.

So far as our solar system goes we may comfortably treat the sun as being at rest and attach our frame of reference to it. But when we come to look still farther afield at the stars we find them in motion and later detect a drifting tendency among them which indicates beyond question that our sun itself is moving.

So next we hitch our frame of reference on to a sort of average position of all the stars visible to the naked eye, and find that with respect to this new frame of reference the sun and planets are moving at the rate of about 12 miles per second in a definitely known direction.

We were content with this until within the last decade, when observations upon the nebulae, which we know now to be enormously

farther off than the naked eye stars, revealed extremely rapid motions.

If we try now to hang a frame of reference, so to speak, to the average of these nebulae, it begins to look as if our solar system was moving, compared with this, at a speed of something like 400 miles per second, which motion of course the system of stars visible to the naked eye must substantially share.

But now, which of all these systems is really moving?

Are the stars at rest and the nebulae moving, or are the nebulae at rest and the stars moving, or are they both moving past each other in different directions, and is there anything at rest? Can we really find anything anywhere in the material universe upon which we can really set the feet of our imagination and say "J'y suis, j'y reste" with the conviction that we are at last upon the firm rock of the absolutely motionless?

It is from a search for an answer to this question that the theory of relativity grew.

The first great contribution was made by Newton. An immediate consequence of his fundamental principles of physical science is that if we have a number of objects moving together in space, which we may call a system, acting upon one another in any fashion, however complicated, but free from outside influence, then the relative motions of the bodies in that system will not depend at all upon the rate at which the system as a whole is moving through space, or the direction of its motion, but only upon the mutual interaction of its parts.

Simple uniform motion in a straight line (what we technically call a "motion of translation") does not influence the things that happen in the system at all, even to the minutest degree. Therefore an observer within the system cannot hope to detect it unless he has something outside to observe. It is on account of this great dynamic principle that we are unconscious of the motion of the earth about the sun.

In our proposed search, then, for "absolute motion" we must use some other means, and our most efficient tools are likely to be the waves of light. We know that light spreads out from any hot body into space in all directions and at the great speed of 186,000 miles a second.

TAKING THE ETHER AS A BASIS IN THE SEARCH FOR ABSOLUTE MOTION.

Despite this enormous velocity, something real actually travels outward, because it carries with it energy, which is, to the modern physicist, one of the most fundamental of all realities.

This energy may still be perceptible to our eyes or apparatus when reaching us from the stars after a journey which has consumed many thousands of years.

We know, too, that this energy, while it is on its way, travels in a manner strikingly similar to the propagation of waves, so much so that we feel justified in describing light as consisting of waves of definite lengths and properties.

Now how does this energy travel through apparently empty space with these singular wave properties? The natural answer, almost the intuitive answer, is to say that it travels through a medium, and so we invent the "ether," simply as the medium which carries the light.

But if there is such a medium in space, and light travels through it in every direction at the same speed, it would seem as if here, at last, in this undisturbed ether, we had our frame of reference which we could use as our basis for the measurement of all other motions.

DETECTION AND MEASUREMENT OF MOTION BY LIGHT SIGNALS THROUGH THE ETHER.

If this be true, we can detect whether this world of ours is moving through the ether or not by sending light signals through equal distances in different directions and seeing whether they come back to us at the same interval of time.

To see how the thing works, let us suppose first that we have an observer at rest with respect to the ether and surrounded by a circle of mirrors set in various directions from him but all at a distance of 186,000 miles.

If he then produces a flash of light at his own position this light will travel out and in one second will reach all the mirrors simultaneously, will be reflected at each and at the end of another second will come back to him simultaneously from all the mirrors. (If this hypothetical apparatus appears to you inconveniently large, you can just as well imagine one a million times smaller, which would make the radius of the circle about a thousand feet, and count your time in millionths of a second instead of whole seconds.)

So far so good. But now suppose that the observer and his whole circle of mirrors, big or small, are not at rest but are all moving together uniformly at a speed of half the velocity of light.

Now let the observer send out a light signal and wait for its reflection from that mirror which is directly on the line of his track and in the direction toward which he is moving.

The light traveling out toward this mirror would itself move 186,000 miles a second but would have a "stern chase," since the

mirror is receding half as fast as it is traveling, and it is easy to see that it would take two whole seconds to reach the mirror.

On the return journey the observer will be advancing to meet it with half the speed of light, and this part of the process will take only two-thirds of a second. The elapsed time for the round trip of the light will be two and two-thirds seconds, considerably longer than if the observer was at rest.

Consider next a ray of light which gets reflected in the mirror whose direction from the observer is at right angles to the first.

It will not have the long stern chase which the first ray has, but nevertheless it will lose something, because in order to reach the moving mirror it will have to travel "on the bias," so to speak, through space, so that it will reach not the point where the mirror was when the light started, but the point where it will be when it gets there, and something quite similar will happen on the return journey

When this is calculated it is found that the round trip will in this case take about two and one-third seconds. (The exact amount involves calculating a square root that we need not bother with here.)

The important point is that in this case, where the observer and mirrors are moving through the ether, the ray of light which has traveled up and down the direction of motion will take a longer time for the round trip than the ray which has traveled crosswise to the motion over a path of exactly the same length.

We should, therefore, in this way be able to detect motion of our own system through the ether, and if our measurements were sufficiently accurate, determine its direction and rate.

FAILURE OF EARLY EXPERIMENTS.

This was attempted in the famous Michelson-Morley experiment. The distance of the round trip was in this case only a few feet, and the difference in time over the two paths only something like a millionth part of one billionth of a second.

But this minute interval could be measured by splitting a ray of light into two parts by letting part of it be reflected sidewise from a transparent mirror and the rest go through, and reuniting the parts after their trip.

If one had gained on the other by even a fraction of the time of vibration of a single light wave the fact could be detected, and the waves which we ordinarily call light vibrate at the rate of about six hundred thousand billion per second.

Michelson and Morley tried their experiment, and in place of the easily measurable result which they anticipated, they got nothing.