Part 1

TEN CENT POCKET SERIES NO. 408 Edited by E. Haldeman-Julius

Introduction to Einstein

William F. Hudgings

Copyright, 1923, by the author Copyright, 1923, Haldeman-Julius Company

HALDEMAN-JULIUS COMPANY GIRARD, KANSAS

_A Popular Explanation of the Einstein Theory That Approaches an Actual Visualization of the Subject._

The preparation of this essay on the Principle of Relativity has been undertaken after a careful study of practically all the literature hitherto published on the subject purporting to be of a popular or semi-popular nature. With due appreciation of the merit of many of these works, a perusal of them has made it increasingly apparent that the writers have not succeeded in eliminating technical phraseology sufficiently to bring the subject down to the level of the untrained reader, and that a _really_ popular exposition of both the Special and the General Theory is needed.

Notwithstanding the laudable efforts of some to meet this need it is manifest that the public continues to be in the dark and many erroneously suppose that “only twelve men in the world” can really comprehend this new theory of the universe. Even book reviews ofttimes betray a surprising lack of appreciation of the fundamentals of Einstein’s noble contribution to science.

It is the purpose of this booklet therefore, to bring within the scope of visualization, as nearly as possible, the very essence of relativity, and to state its principles in terms devoid of unfamiliar phrases and illustrations. The popular mind is not satisfied with vague statements, mathematical equations and formulæ. It calls for an explanation in words of every day usage, and where a technical term _must_ be employed then a definition of that term in language simple and lucid. To meet these requirements without sacrificing scientific accuracy has been the earnest endeavor of the author.

Acknowledgment is hereby made to Dr. S. I. Bailey and Dr. G. D. Birkhoff of Harvard, Dr. Edward Kasner of Columbia, Prof. Victor Schmidt of Cincinnati, and Dean J. A. Robison of the Oakland Technical High School (Calif.), all of whom have kindly criticized the manuscript and made valuable suggestions for improvement of the text.--W. F. H.

New York, Dec., 1922.

Introduction to Einstein and Universal Relativity

What Is Einstein’s Contribution?

Albert Einstein, orthodox Jew of German birth and ardent Zionist, is the most discussed figure in intellectual circles in the world today. It is not as a Jew nor as a Zionist, however, that we find him so much in the limelight of public opinion, although as such he is a distinguished figure and has only recently toured Europe and America in the interest of the Zionist movement. What has lately made the name of Einstein a byword upon the lips of scientists, philosophers and the multitudes of more common mortals is his revolutionary treatment of time, space and gravitation which materially affects various branches of accepted science and thereby threatens to throw certain portions of our school books and other scholarly works into the discard.

The ideas which led to the development of Einstein’s theory are not new. Newton appreciated the principle of mechanical relativity and presented it in much detail. But to Einstein belongs the credit of completely disentangling the idea of relativity of motion from the ancient conception of absoluteness of velocity and carrying out the relativistic viewpoint to its logical conclusion. In so doing, however, he found it necessary to discard or revamp many popular theories and “laws of nature.” But consistency is a jewel wherever found, and Einstein seems to have placed the gem into its proper setting.

This Jewish scientist, born in 1878 of humble parentage, began delving into the mysteries of the universe at an early age. When only sixteen, it is said, he contributed a paper, modest in its brevity, which was read before an assemblage of German scientists with marked appreciation of its merit, and soon thereafter his active mind began to traverse new and unbeaten paths of scientific thought. During the years that followed his ideas took more definite form, and in 1905, while occupying a chair in a Swiss university, Einstein published his first “Principle of Relativity,” now called the “Special Theory of Relativity,” which treats the physical laws relating to uniform, rectilinear motion, i. e., motion in its simplest form.

Einstein’s hypothesis, unlike most theories advanced, did not originate with any physical “discovery” or observation. In a sense it grew out of the philosophic notion of the relativity of all knowledge. He laid hold of the idea that everything is measured by or considered _relative_ to something else; that our concepts of absolute position, absolute motion and absolute time are groundless for the reason that we have no immovable and unchangeable standard anywhere in the universe as a starting point. While there is nothing new or revolutionary in this fact, yet it actually produced certain scientific “revolutions” when carried out to a consistent end.

Prior to Einstein, the principle of relativity had been recognized and philosophized upon to a certain point and then dropped when it ran counter to hitherto unquestioned conceptions. Einstein, on the contrary, contended that if the principle is admitted at all it must be admitted at every point irrespective of what it contradicts. After, therefore, his theory was fully developed it was then subjected to certain physical tests, with the result that it has been quite fully confirmed. This mode of theoretical development is called _a priori_ as against the more usual _a posteriori_ method, wherein the theory _follows_ rather than precedes certain particular phenomena.

It was in 1915, during the stress of the great war, that Professor Einstein, working unconcernedly in his laboratory in Berlin, completed and published what is now called his “General Principle of Relativity.” Due to hostilities, the details of his developed theory did not reach the outside world until after the armistice in 1918; but such meagre accounts of it as did cross the German border were sufficient to awaken Eddington and other British scientists to the extent that they hastily equipped two research expeditions, dispatching one to the Island of Principe off the coast of Africa and the other to Sobral, Brazil, to test Einstein’s hypothesis about the deflection of light rays in a gravitational field, by taking photographs of stars near the sun during the solar eclipse of May 29, 1919, which was total in the regions mentioned.

It was the announced results of these expeditions, confirming as they did this new theory of gravitation, that has made Albert Einstein famous.

There are, of course, opponents of the Einstein theory in the circle of scientists in both Europe and America, though they are comparatively few in proportion to the number who see merit in his postulates if not, indeed, a complete solution of gravitational and other phenomena which have baffled the sages of every century. Sir Oliver Lodge is a leading opponent of the Einstein theory among a certain few British scientists, but his opposition is easily accounted for when it is remembered that Einstein, by ignoring the ether and denying other unproven hypotheses, has materially upset Sir Oliver’s spiritistic playground.

Einstein, to say the least, has stimulated the scientific thought of the world to an extent unprecedented by anyone since the days of Newton. If the Principle of Relativity is not universal, then any theory concerning it cannot long stand; it would predict results which actual experiment would disprove. It must be admitted, however, that experiments to date tend to confirm the Theory of Relativity as propounded by Einstein.

=Concepts Versus Reality=

Relativity is a term appropriately applicable to that school of thought standing midway between mathematics, physics and astronomy, which concerns itself with determining the relationship between observers and their objects. Two or more observers may view a certain phenomenon or set of phenomena and reach divergent conclusions as to distance, position, size or other physical quantities commonly involved. It is not for anyone to arbitrarily conclude that one particular observation is correct and that all the others are consequently in error.

It is the task of the relativist to consider the findings of the various observers, note the conditions attending each, eliminate the peculiarities of the varying viewpoints and the qualities which have been unmindfully superimposed by each observer upon the external object. He must then set down a general rule or law which will embody the inter-relations of the data before him and which will also hold good for all other observers regardless of distance, position or motion of their frames of reference.

_A frame of reference_ is simply an arbitrary set of mutually perpendicular lines or planes from which measurements may be made for purposes of describing the location of points within a given area or region. If a _two_-dimensional area (i. e., a _plane_ surface) is being dealt with, then our frame of reference would consist merely of two _lines_ drawn perpendicular to each other. Thence, any point within the right-angle formed by these two lines may be described by specifying its distance from each line.

If we are to locate a given point in a _three_-dimensional region (i.e., where length, breadth and also _height_ are involved), then our frame of reference must consist of _planes_ instead of lines, three in number, each perpendicular to the other two, like the floor and two adjacent walls of a room. If any point within a room is to be located we would first select as a frame of reference, let us say, the east and south walls together with the floor. The location of the point may then be described with accuracy by simply specifying its distance from each of the two walls together with its height above the floor.

The perpendiculars of a frame of reference are called its _axes_, and the distances from a given point to the axes are called its _co-ordinates_. A little reflection will suffice to show that it is quite impossible to record the exact location of anything, either in space or in a plane, without making use of a reference frame and two or more co-ordinates.

=Unlimited Choice of Reference Frames=

We are not limited in our selection or choice of reference frames. They may be close by or relatively remote from the point or object whose location we wish to describe. The axes may be physical or purely imaginary. They may be in any direction or position whatsoever, so long as they are mutually perpendicular and embrace the area in which the point or object is located. They may be at rest relative to the object and in motion relative to the observer, or vice versa, or either at rest or in motion relative to both. If the relative velocity is known, the co-ordinates may be determined as certainly as though both the object and the observer, together with his reference frame, were relatively at rest.

An observer usually prefers to select a frame of reference which partakes of his own motion, for the sake of convenience and simplicity. Hence for purposes of either local or astronomical observation we may choose an imaginary axis perpendicular to the surface of the earth. But we must admit that as the earth rotates our perpendicular rotates with it. Consequently it is really changing its direction from moment to moment. Such rotation, however, is not detected so long as we confine our observations to terrestrial things, because our frame of reference is at rest relative to the earth and to all things fixed upon the earth; but for astronomical observations the matter becomes somewhat complicated due to the various relative motions involved.

Astronomers often choose as a reference frame an imaginary line reaching from the earth’s center to the center of the sun, together with another line perpendicular thereto extending from the earth to some other planet or point in space. But neither the earth or the sun, or in fact any other body of matter, is at rest; nor do they move in a perfectly straight line or plane. The axes of such a frame of reference continuously undergo a change of direction. Indeed, a reference frame attached to any physical body in the universe must of necessity move, because all matter of which we have any knowledge is in motion; and a frame of reference attached to nothing would be meaningless.

By reason of the motion of all objects and of frames of reference it is necessary that the latter be supplemented by clocks for determining the times of occurrences of physical events encountered in our measurements. We may therefore say that no frame of reference, when used for physical purposes, is complete without a set of accurately synchronized timepieces. The element of time is an essential factor in any calculation of physical quantities because motion is forever involved.

Velocity (rate of motion) means distance traveled within a given time. Only when distance and time are combined can we determine our co-ordinates with universal accuracy. This will be more fully understood when we come to consider the four-dimensional aspect of the universe. But for all practical purposes the time element cannot be divorced from the distance measurement of moving bodies even when viewed in the ordinary three-dimensional sense.

Suppose, for sake of illustration, we are assigned the task of charting or recording the precise course of a ball shot from a cannon. In order to specifically state the history of its flight it will be necessary to indicate the position of the cannon ball during each moment of its journey. We will say this is a possibility without attempting an explanation of the method of measurement used. When our task is completed we will have a set of four figures for each successive second, as follows:

(1) distance from cannon. (2) distance from ground. (3) distance to right or left. (4) duration of time.

When these four sets of figures are carefully set down they may be transmitted on paper or by telegraph and the recipient will be able to determine therefrom the history of the fired ball with as much accuracy as though he had been personally present and made the observations himself. This, however, would be impossible were the time factor omitted.

The foregoing illustration is given merely to show that time is fully as important as distance measurement in specifying the location of any moving body (and everything in the universe is moving). It is in no sense intended to show how time is really a fourth dimension. This fact will be brought out in subsequent pages; but thus far we have followed, rather, our ordinary concepts of time as an independent element, detached from any unit of space measurement whatsoever. Such a conception, however, comes from a lifelong training which is based upon a limited scope of vision.

=Knowledge Broadens Many Concepts=

Concepts do not necessarily represent the reality merely because they are easy to believe. They may be simply following in a groove caused by centuries of “thoughtless reasoning.” Prior to Galileo, human concept taught that “up” and “down” were absolute directions which never vary. It was easy to so believe, and nobody even thought to call such concept in question. But eventually it became known that two plumb lines which point “down” to earth do not hang parallel to each other. They each point to a common center like the spokes of a wheel.

Now if two plumb lines happen to be about six thousand miles (one-fourth the circumference of the earth) apart, they then hang practically perpendicular to each other. When this erstwhile paradox was established as a certain fact mankind were obliged to change their former concepts of the absoluteness of the “up” and “down” directions. Einstein now asks us to revise our concepts of the absoluteness and independence of time and space and gives us his reasons therefor.

In the light of Einstein’s treatment of the principle of relativity it is seen that no particular reference frame possesses any advantage over any other for mathematical accuracy irrespective of the physical laws involved. It would not be difficult, of course, to grasp this fact in a mechanical sense provided units of length and of time were absolute quantities which are unaffected by the motion of the reference frame. But as will be subsequently seen, such units when viewed independently, do vary constantly, and rigidity becomes in reality a meaningless term.

In the face of this apparently insurmountable difficulty, however, Einstein shows in his Special Theory that any unaccelerated (i.e., uniformly moving) frame of reference is as suitable as any other for the mathematical expression of physical laws. This is accomplished by regarding the universe and all objects therein as existing in four dimensions, viz., length, breadth, thickness and _time_--the latter altering the length unit according to the relative velocities of the reference frames.

It is naturally impossible to mentally visualize or graphically portray more than three dimensions, but they can be mathematically conceived. We shall endeavor presently to show how time takes its place alongside the ordinary three dimensions in the true geometry of the universe, possessing the value of a fourth co-ordinate or dimension. In reality it supersedes in importance the other three in the sense that it possesses the illusive quality of automatically correcting or adjusting physical values which otherwise would be inconsistently altered by the velocities of our frames of reference.

Irrespective of whether we can visualize the matter or not, it will be necessary for the reader to divest himself of all previous conceptions of time and of space as universally absolute, separate and unvarying in their unit length if he would comprehend the Einstein Theory of Relativity. He must guard against the notion that time and space are independent elements that should be measured separately. He must adjust himself to the relativistic viewpoint that time and space are so interlinked that either, when taken alone, becomes meaningless except by analogy. When, therefore, we measure the distance between bodies or the dimensions of the bodies themselves, we are not calculating the miles or units of _space_ merely, but of _space-time_.

We will not attempt but will purposely avoid, in a work of this scope, the setting out of algebraic equations, believing they would not tend to make the essay _popularly_ readable however much they may appeal to the mathematical student. Therefore it must suffice here to state that the numerical value of time required for a light ray to traverse a given distance, together with the relative velocity between the frame of reference and the object, become considerable physical factors in calculation where great distances and enormous velocities are being dealt with. These items, however, are infinitesimal when merely earthly distances and ordinary velocities are involved.

Einstein’s equations, therefore, may be said to have no practical bearing upon the ordinary things with which we have to do in daily experience--we may continue to use our yardstick and our pocket timepiece exactly as before. But this in no wise diminishes the fundamental importance of the matter. Scientific interest rests not in the _amount_ of variance from accustomed laws, but rather in the fact that a variance exists and why.

=Universe a Four-Dimensional Continuum=

We shall at this point merely touch upon the space-time character of the universe as Einstein sees it, leaving the subject for treatment in appropriate order later on. Einstein did not originate the geometry which he uses; he has simply made a masterful application of the work of Riemann, Minkowski and others in the outworking of his theory. Various geometers, notably Minkowski, departing from the beaten path of Euclid, had come to view the universe as a four-dimensional continuum in which space and time are inseparably interlinked, and Einstein saw in this a solution of several phenomenal problems which had arisen in recent years to which the laws of Newton appeared inapplicable.

The term _continuum_ denotes a continuity of units. The geometer speaks of a straight line as a one-dimensional continuum, because it consists of a continuity of _points_ extending in one direction. A plane, likewise, is termed a two-dimensional continuum for the reason that it is a continuity of _lines_ laid side by side producing an area of length and also breadth. Accordingly the whole spatial universe has been long regarded as a three-dimensional continuum, i. e., a continuity of _planes_ piled one on top of another, extending from infinity to infinity.

As for _time_, it has been commonly looked upon as something entirely separate and apart from space. Humanity has habitually regarded it as an independent one-dimensional continuum, i. e., a continuity of _instants_, each being of universally definite duration, beginning where its predecessor ended and ending where its successor begins, and thus flowing on forever regardless of motion, location or any physical condition.

=Time and Space Inseparable=

But what ground have we for regarding space and time as independent and unrelated continua? Does not _time_ thrust itself upon us at every turn, wherever we undertake a measurement in space? This might not be so if we could regard space as motionless and then really measure it from point to point. But absolute space cannot be measured. The best that can be done is to measure from one body of matter to another body of matter--and all matter is in motion and continuously changing position, hence the entrance of time into all physical calculation.

Everything in the universe is somewhere at some time and somewhere else at some other time. Thus it is seen that time must intersect space at every point wherever moving matter is involved. And if for any reason whatsoever the time units are shortened or lengthened then the points which they intersect are in reality distorted irrespective of what our conception of such a state of affairs might be.

Instead, therefore, of regarding the universe as a continuity of immovable points it is in reality a continuity of _events_ in each one of which _time_ is an essentially governing factor. Consequently the term _event_ in a four-dimensional continuum is analogous to the term _point_ in a three-dimensional continuum. Something does not necessarily need to _happen_ at each _event_ in the continuum in order to constitute them “events.” On the contrary, the continuum of events exists as a background for phenomena, and when happenings occur in any region whatsoever, the events (time and space points combined) are there, ready to give forth their testimony to the mathematician when he calls for his location data.