Part 3

From the foregoing it will be seen that the difficulty of making clear in few words the substance of the Einstein theory is due to its radical departure from our ordinary concepts of things. Many pages might be utilized to fully define such apparently simple terms as time, space, distance, straight line, etc., and after these are seen from the viewpoint of the relativist, then the reader is equipped to proceed with his study of relativity, but not before.

The aforementioned handicap has been apparent to every writer who has attempted to make the theory of relativity popularly readable. The following pages will discuss these terms in an applied fashion and will attempt to give the necessary foundation knowledge without which it would be impossible to appreciate the theory as expounded later in this essay and in other works on the same subject. The reader will undoubtedly find it profitable to review the foregoing paragraphs after he has perused the arguments which follow.

=Relativity and Its Effects=

Relativity, as applied to motion of all matter and systems of matter in the universe, stands opposed to the idea of absolute velocity. If nothing is stationary in the entire universe from which we may determine the actual rate of motion of bodies, then the best we can do to describe the velocity of anything is to say that it moves at such and such a speed relative to something else which is also moving at some unknown rate except as it is related to some other moving body.

We may say that the earth is traveling at the rate of over eighteen miles per second in its annual trip around the sun. But this does not represent the actual velocity of our earth. It describes merely our motion relative to the sun; but who shall say how rapidly our sun is moving through space and carrying us with it, just as we carry the moon with us as we revolve around the sun. We know the sun is apparently approaching a distant star cluster, but we cannot determine whether our system is moving toward it or whether the cluster is moving toward us, or both. We may be, in fact, chasing it through the heavens as a dog chases a rabbit, and gaining on it a trifle each century; or it may be really chasing us. All we know about it is that the distance between the two systems is growing gradually less.

Then, again, who knows but that the entire stellar universe, including not only our solar system but all other systems as well, may be revolving about one common center located in the remote regions of space? And if so, in what general direction does it revolve? These reflections immediately convince us that all motion is purely relative; that no velocity can be looked upon as being absolute. Hence our eighteen-mile-per-second velocity around the sun is probably infinitesimal in comparison to our actual speed through space, if such could really be determined by some stationary standard.

Einstein did not originate the doctrine of relativity; it has been a much discussed philosophic subject for centuries and particularly of the nineteenth century. What he did, however, was to formulate a particular theory concerning it which co-ordinates and satisfies the observed laws of nature and accounts for discrepancies which have long troubled mathematicians and scientists who have based their calculations on the theories of the past, notably Newton’s laws.

=Mercury’s Perihelion=

A striking example of such a discrepancy which Einstein has accounted for, is the unusual yearly advancement of the perihelion of Mercury’s orbit. Due to gravity, all planets revolve about the sun in ellipses rather than in perfect circles, with the sun a trifle to one side of the center of such ellipse. This brings the planet nearer to the sun at one end of the ellipse than at the other. The near end of the orbit is called the perihelion, while the distant end is called the aphelion. See Fig. 1.

Newton’s law would indicate that if our spherical sun had but one planet revolving around it, the orbit of that planet would never change its position unless disturbed by some outside cause, its perihelion and aphelion being fixed. But where there are more than one planet in a system, a slow annual advance of the perihelion would be produced. The amount of such advance is easily calculated; hence it has been an astonishment to astronomers to find that the perihelion of Mercury actually advances 42 minutes (that is, seven-tenths of a degree) per century more than Newton’s law allows for. Einstein, however simply points out that at perihelion a planet is moving with greater velocity than at aphelion because of its relative nearness to the sun, and that its velocity (the time element) must be reckoned with in addition to the Newtonian gravitational advance. He computed that this should increase the advance of Mercury’s perihelion by 43 minutes per century, which most fully accounts for the observed discrepancy.

Opponents of Einstein have attempted to account for the aforementioned discrepancy on the ground that the sun is not a perfect sphere, and that its equatorial diameter exceeds its polar diameter sufficiently to add the required amount to the attraction at perihelion. But this involves other difficulties, as for instance, a change of 3 minutes per century in the inclination of the orbit, which manifestly does not exist. The orbits of the other planets in our solar system are not sufficiently eccentric to reveal any marked difference between Newton’s and Einstein’s calculated results. But Einstein’s success in connection with Mercury has placed his theory upon a very satisfactory foundation.

We have seen that all motion is relative. The same is true of time because motion and time are inseparable. But even if this were not so, where would we find an absolute standard or universal unit of time any more than an absolute rate of motion of matter? We on earth count time according to the rotation of the earth on its axis, and we call the period of rotation a day, but the other planets in our solar system have days of very different length from ours, some shorter and some longer.

All heavenly bodies possess their respective time standards, all different from ours and different from each other. Which shall be taken as the absolute standard? There is no universal standard. Time is not an absolute quantity; it is relative even as motion is relative. A “perfect timekeeper” if suddenly transferred from earth to Jupiter would immediately be seen to keep a different time due to the differences in velocity of the two planets.

=The Universal Unit=

We have already emphasized that conceptual time, as an independent one-dimensional continuum, is fictitious. It does not really exist as such, but is a component part of space-time. The question naturally arises in our minds: if time does not exist in and of itself, and if there is no universal time unit, then how is it possible for Einstein or anybody else to make a calculation in which time is involved and arrive at any definite conclusion? The answer is that there is a universal unit, but not a universal time unit. This true unit is the separation-interval between events in the space-time continuum. It is a combination of distance and time.

Such a combination unit may be partially illustrated by a crude analogy. Suppose we are calculating the distance between two points in a plane. We would first describe a triangle and let the hypotenuse of the triangle connect the two points in question. But somebody else might erect a different triangle from ours which would describe the distance between the two points equally well. The triangles would have the same hypotenuse, but their respective bases and altitudes would be dissimilar, as shown in Figure 2.

Let us think of the bases as representing time and the altitudes as representing space, while the hypotenuse stands for our separation-interval. Even as we may have many base-altitude combinations for our common hypotenuse, so we may have numerous combinations of space and time for the same separation-interval. In certain combinations the space element is greater than in others, while the time element is correspondingly smaller, and vice versa, although the separation-interval, like our hypotenuse, remains a constant.

It may be somewhat easier for the reader to appreciate the non-existence of a universal unit of length than it is for him to comprehend the unreality of independent time. No unit of length can be taken as a universal standard of measure, because measurements are relative and dependent upon the motion of the observer and his reference frame, or upon the velocity of the object relative thereto. This has been scientifically established by experiments made with particles emitted by radioactive substances whose velocities range from 20,000 to 170,000 miles per second.

Lorentz and Fitzgerald, previous to Einstein, had suggested that all moving matter suffers a physical contraction in the direction of its motion, but their theory is not particularly convincing. To Einstein belongs the credit of postulating upon this subject in a manner that agrees with experiment and satisfactorily answers several phenomenal questions. He points out that there is an apparent contraction which is proportional to the relative velocity between object and observer, but that this “contraction” does not exist if the observer happens to be moving along with the object which he is measuring.

To illustrate: If an ocean liner measures 1,000 feet in length while lying at the pier, theoretically it would be a trifle less than 1,000 feet while under way if viewed by an observer on shore. If, however, the measurement were taken by an observer aboard the moving ship, using the same yardstick that was used at the pier, the result would still be 1,000 feet. Einstein’s contention is that the ship undergoes no physical shortening such as Lorentz and Fitzgerald supposed, but it is simply the victim of a phenomenon of observation. The apparent contraction, however, holds good for all object or bodies of matter in exact ratio to their velocity relative to the observer as specified in Einstein’s mathematical formula, and is just as real in practical calculation as though it were a physical factor.

=Motion and Contraction=

It is within the realm of possibility, of course, that some degree of physical contraction does result from motion, on the theory that the electro-magnetic forces operating between the atoms and molecules of matter undergo a change due to velocity. If, therefore, the yardstick and everything else aboard the moving ship suffered a physical contraction exactly proportional to the length of the ship itself, then there would be no way of detecting it by any measurement taken aboard the vessel.

It hardly appears reasonable, however, that materials of different density would undergo the same proportional contraction, as for instance a wooden yardstick and the steel sides of a ship, inasmuch as they are of entirely different molecular composition. The Einstein theory therefore proposes an observational variation rather than a physical contraction of the object, and shows that it equally exists whether we regard ourselves as at rest and the object as moving away from us, or whether we consider the object as stationary and ourselves as speeding past it.

Let us suppose our observational instruments are lifted from their fixed position on shore and placed aboard a railway train and carried in the same direction and at the same velocity as the coastwise vessel. In this event the ship would measure full 1,000 feet in length just as it did when we measured it at the pier, because the observer under the conditions stated would be at rest relative to the moving ship. But if our train carried us faster than the ship, then the ship would again begin to measure short because our relative motion would be the same as though we were stationary and the ship were moving away from us in the opposite direction.

The foregoing illustration is merely theoretical, however, because the variation is too small for observation in cases of small distances and low velocities. Nevertheless, when the velocity approximates that of light rays the apparent contraction becomes plainly visible. Some of the particles emitted by radioactive substances possess a velocity of about nine-tenths that of light and in such cases the amount of apparent shortening which they undergo can be computed because it is very great. And should the velocity become equal to that of light rays (i. e., 186,300 miles a second), then, says Einstein, the observed length of the particle would be reduced to zero.

Einstein does not claim that relative velocities greater than 186,300 miles a second cannot be attained, but he does contend that velocities greater than that relative to an observer cannot be observed. Thus if a body of matter were moving away from an observer at only half the velocity of light, and the observer himself should suddenly become accelerated in the opposite direction until the relative velocity between the two became equal to or greater than that of light, then the observed length of the body in the direction of motion would be zero, although its width would be unaffected.

=“Absolute Length” Fictitious=

All this leads us ultimately to the conclusion that there is no such thing as determining the absolute dimensions of anything, because relativity of motion and the time element are undeniable factors in all measurements. The assertion that these are infinitesimal so far as the quantities we ordinarily have to deal with are concerned does not alter the fact that “absolute length” is a fictitious phrase. For this reason we cannot reckon the absolute distance between any two conceptual points in the universe; we must calculate in units of space and time combined or else accept the fact that our conclusions are simply of local and not of universal significance.