Benjamin Harrow

“ If we are to believe in the “causal relationship between only such things as lie within the realm of observation,” then observation teaches us that bodies move only relative to one another, and that the idea of absolute motion of a body in space is meaningless. Einstein, therefore, postulates that there is no such thing as absolute motion, and that all we can discuss is the relative motion of one body with respect to another. This is just as logical a deduction from Michelson’s experiment as the attempt to explain Michelson’s anomalous results in the light of an all-pervading ether. ”

“ If with the naked eye or with a telescope you watch a clock moving away from you, you will find that its minute hand takes a longer time to cover its five-minute intervals than does the chronometer in your hand, and if the clock travelled with the velocity of light you would forever see the minute hand at precisely the same point. That which is true of the clock is, of course, also true of all time intervals which it measures, so that if you moved away from the earth with the velocity of light everything on it would appear as still as on a painted canvas. ”

“ In those days Ptolemy was in astronomy what Aristotle was in all other knowledge: they were the gods who could not but be right. Did not Aristotle say that earth, air, fire and water constituted the four elements? Did not Ptolemy say that the earth was the center around which the sun revolved? ”

“ In speaking of Newton we are tempted to paraphrase a line from the Scriptures: Before Newton the Solar System was without form, and void; then Newton came and there was light. To have discovered a law not only applicable to matter on this earth, but to the planets and sun and stars beyond, is a triumph which places Newton among the super-men.
What Newton’s law of gravitation must have meant to the people of his day can be pictured only if we conceive what the effect upon us would be if someone—say Marconi—were actually to succeed in getting into touch with beings on another planet. ”

“ The difference between the laws of gravitation of Einstein and Newton come only in special cases. The real interest of Einstein’s theory lies not so much in his results as in the method by which he gets them. If his theory is right, it makes us take an entirely new view of gravitation. If it is sustained that Einstein’s reasoning holds good—and it has survived two very severe tests in connection with the perihelion of mercury and the present eclipse—then it is the result of one of the highest achievements of human thought. The weak point in the theory is the great difficulty in expressing it. ”

“ Our experience is that two particles of matter attract one another. Expressed in terms of world-lines, this means that, if the world-lines of two isolated particles come near each other, the lines, instead of being straight, will be deflected or bent in towards each other. The world-line of any one particle is therefore deformed; and we have just seen that a deformation is the equivalent of a mathematical transformation. In other words, for any one particle it is possible to replace the effect of a gravitational field at any instant by a mathematical transformation of axes. ”

“ So in the space of our world-lines, the space may be deformed in any imaginable manner without introducing any new intersections or changing the sequence of the existing intersections. It is this sequence which gives us the mathematical expression of our so-called experimental laws; a deformation of our space is equivalent mathematically to a transformation of axes, consequently we see why it is that the form of our laws must be the same when referred to any and all sets of axes, that is, must remain unaltered by any mathematical transformation. ”

“ What is true of matter should be true of energy.
The special theory of relativity, however, takes into account only inertia (“inertial mass”) but not gravitation (gravitational pull or weight) of energy. When a body absorbs energy equation 2 (see Note 4) will record a gain in inertia but not in weight—which is contrary to one of the fundamental facts in mechanics.
This means that a more general theory of relativity is required to include gravitational phenomena. Hence Einstein’s General Theory of Relativity. Hence the approach to a new theory of gravitation. ”

“ The revolutionary ideas propounded regarding time and space, the brilliant way in which the most universal property of matter, gravitation, is for the first time linked up with other properties of matter, and, above all, the experimental confirmation of several of his more startling predictions—always the finest test of scientific merit—stamps Einstein as one of [73] those super-men who from time to time are sent to us to give us a peep into the beyond. ”

“ If the solar system would consist of the earth and moon alone, then the path of the moon would be that of an ellipse, with one of the foci of this ellipse occupied by the earth. Unfortunately for the simplicity of the problem, there are other bodies relatively near in space, particularly that huge body, the sun. The sun not only exerts its pull on the earth but also on the moon. However, as the sun is much further away from the moon than is the earth, the earth’s attraction for its satellite is much greater, despite the fact that the sun is much huger and weighs far more than the earth. ”

“ The distances between bodies in the solar system is so immense that, like the number of dollars spent in the Great War, the number of miles conveys little, or no impression. But picture yourself in an express train going at the average rate of 30 miles an hour. If you start from New York and travel continuously you would reach San Francisco in 4 days. If you could continue your journey around the earth at the same rate you would complete it in 35 days. If now you could travel into space and to the moon, still with the same velocity, you would reach it in 350 days. ”

“ Both Newton and Einstein were led to their theory of gravitation by profound studies of the mathematics of motion, but as Newton’s conception of motion differed from Einstein’s, and as, moreover, important discoveries into the nature of matter and the relationship of motion to matter were made subsequent to Newton’s time, we need not wonder that the two theories show divergence; that, as we shall see, Newton’s is probably but an approximation of the truth. If we [17] confine our attention to our own solar system, the deviation from Newton’s law is, as a rule, so small as to be negligible. ”

“ Newton’s law of gravitation made it clear that bodies which have mass attract one another. If light has mass—and very recent work tends to show that it has—there is no reason why light should not be attracted by the sun, or any other planetary body. The question that agitated scientists was not so much whether a ray of light would be deviated from its path, but to what extent this deviation would take place. Would Einstein’s figures be confirmed? ”

“ Newton’s laws of motion are really axioms, like the axioms of Euclid: they do not admit of direct proof; but there is this difference, that the axioms of Euclid seem more obviously true. For example, when Euclid informs us that “things which are equal to the same thing are equal to one another,” we have no hesitation in accepting this statement, for it seems so self-evident. ”

“ In mathematical language, with reference to axes moving with the man the force of gravity had disappeared. This is a case where by the transfer of the axes from the earth itself to the man, the force of the gravitational field is annulled. The converse change of axes from the falling man to a point on the earth could be considered as introducing the force of gravity into the equations of motion. Another illustration of the introduction into our equations of a force by a means of a change of axes is furnished by the ordinary treatment of a body in uniform rotation about an axis. ”

“ When the man with his time machine goes forward he is in the future; when he goes backwards he is in the past.
In reality, if we stop to think a minute, there is no valid reason for the non-existence of a fourth dimension. If one, two and three dimensions, why not four—and five and six, for that matter? ”

“ If we can but picture some such medium we can imagine our magnet giving rise to vibrations in this medium which are carried to the iron. The magnet may give rise to a disturbance in that portion of the medium nearest to it; then this portion hands over the disturbance to its neighbor, the next portion of the medium; and so on, until the disturbance reaches the iron. You see, we are satisfying our sense-perception by arguing in favor of action by actual contact rather than some vague action at a distance; the go-between instead of being a rope is the medium called the ether. ”

“ Matter is less so; it has friction and elasticity. No imperfection has been discovered in the ether space. It doesn’t wear out; there is no dissipation of energy; there is no friction. Ether is material, yet it is not matter; both are substantial realities in physics, but it is the ether of space that holds things together and acts as a cement. My business is to call attention to the whole world of etherealness of things, and I have made it a subject of thirty years’ study, but we must admit that there is no getting hold of ether except indirectly. ”

“ But time and space no longer have the distinct meanings that they had when examined with the help of Newton’s equations. Time and space are not independent but interdependent. They are meaningless when treated as separate entities, giving results which may hold for one body in the universe but do not hold for any other body. To get general laws which are applicable to the cosmos as a whole the Fundamentals of Mechanics must be united. [71]
Einstein’s great achievement consists in applying this revised conception of space and time to elucidate cosmical problems. ”

“ If, as the wave theory teaches us, the ether can be set in motion, then according to laws of mechanics, the ether [30] has mass. If so it is smaller in amount than anything which can be detected with our most accurate balance. Further—and this is a difficulty not easily explained—if this ether has any mass, why does it offer no detectable resistance to the velocity of the planets in it? Why is not the velocity of the planets reduced in time, just as the velocity of a rifle bullet decreases owing to the resistance of the air? ”

“ It is thus possible to picture a mathematical transformation as a deformation of space. Thus I can draw a line on a sheet of paper or of rubber and by bending and stretching the sheet, I can make the line assume a great variety [102] of shapes; each of these new shapes is a picture of a suitable transformation.
Now, consider world-lines in our four-dimensional space. The complete record of all our knowledge is a series of sequences of intersections of such lines. By analogy I can draw in ordinary space a great number of intersecting lines on a sheet of rubber ”

“ The scientist is immediately struck by the way Einstein has utilized the various achievements in physics and mathematics to build up a co-ordinated system showing connecting links where heretofore none were perceived. The philosopher is equally fascinated with a theory, which, in detail extremely complex, shows a singular beauty of unity in design when viewed as a whole. ”

“ The state of motion of an inertia-system, so far as mechanics are concerned, is not restricted by nature to one condition. The condition in the following proposition suffices; a system of coordinates moving in the same direction and at the same rate as a system of inertia is itself a system of inertia. The special relativity theory is therefore the application of the following proposition to any natural process: “Every law of nature which holds good with respect to a coordinate system K must also hold good for any other system K′ provided that K and K′ are in uniform movement of translation.” ”

“ On the other hand, gravitation itself—more universal than anything else in the universe—may be interpreted in terms of strains on world-lines, or, what amounts to the same thing, strains of space-time combinations. ”

“ We know that momentum is carried along on the path of a beam of light. Gravity in acting creates momentum in a direction different from that of the path of the ray and so causes it to bend. For the half-effect we have to assume that gravity obeys Newton’s law; for the full effect which has been obtained we must assume that gravity obeys the new law proposed by Einstein. ”

“ Newton was able to present the problem in a very simple form by pointing out that in a sphere such as the earth or the moon, the entire mass might be considered as residing in the center of the sphere. For purposes of computation, the earth can be considered a particle, with its entire mass concentrated at the center of the particle. This viewpoint enabled Newton to extend his law of inverse squares to the remotest bodies in the universe. ”

“ When, however, we are told by Newton that “the alteration of motion is ever proportional to the motive force impressed,” we are at first somewhat bewildered with the phraseology, and then, even when that has been mastered, the readiness with which we respond will probably depend upon the amount of scientific training we have received.
“Every body continues in its state of rest or of uniform motion in a straight line, unless it is compelled to change that state by forces impressed thereon.” So runs Newton’s first law of motion. A body does not move unless something causes it to move ”

“ In accordance with Einstein’s formulæ a ray of light passing close to a heavy piece of matter, the sun, for instance, should experience a sensible deflection in towards the sun. This might be expected from “general” consideration of energy in motion; energy and mass are generally considered to be identical in the sense that an amount of energy E has the mass where c is the velocity of light; and consequently a ray of light might fall within the province of gravitation and the amount of deflection to be expected could be calculated by the ordinary formula for gravitation. ”