From Newton to Einstein, Benjamin Harrow [most read books in the world of all time TXT] 📗
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A number of books deal with the subject, and all of them are more or less mathematical. However, in every one of these volumes certain chapters, or portions of chapters, may be read with profit even by the non-mathematical reader. Some of these books are: Erwin Freundlich, The Foundations of Einstein’s Theory of Gravitation (University Press, Cambridge, 1920). (A very complete list of references—up to Feb., 1920—is also given); A. S. Eddington, Report on the Relativity Theory of Gravitation for the Physical Society of London (Fleetway Press, Ltd., London, 1920); R. C. Tolman, Theory of the Relativity of Motion (University of California Press, 1917); E. Cunningham, Relativity and the Electron Theory (Longmans, Green and Co., 1915); R. D. Carmichael, The Theory of Relativity (John Wiley and Sons, 1913); L. Silberstein, The Theory of Relativity (Macmillan, 1914); and E. Cunningham, The Principle of Relativity (University Press, Cambridge, England, 1914).
To those familiar with the German language Einstein’s book, Über die spezielle und die allgemeine Relativitätstheorie (Friedr. Vieweg und Sohn, Braunschweig, 1920), may be recommended.10
The mathematical student may be referred to a volume incorporating the more important papers of Einstein, Minkowski and Lorentz: Das Relativitätsprinzip, (B. G. Teubner, Berlin, 1913).
Einstein’s papers have appeared in the Annalen der Physik, Leipzig, volume 17, page 132, 1905, volume 49, page 760, 1916, and volume 55, page 241, 1918.
1 A circle—in our case the horizon—is measured by dividing the circumference into 360 parts; each part is called a degree. Each degree is divided into 60 minutes, and each minute into 60 seconds. ↑
2 See page 113. ↑
3 See Note 4. ↑
4 See Note 5. ↑
5 See Note 6. ↑
6 See Note 7. ↑
7 See Note 8. ↑
8 See Note 9. ↑
9 See page 93. ↑
10 This has since been translated into English by Dr. Lawson and published by Methuen (London).
Since the above has been written two excellent books have been published. One is by Prof. A. S. Eddington, Space, Time and Gravitation (Cambridge Univ. Press, 1920). The other, somewhat more of a philosophical work, is Prof. Moritz Schlick’s Space and Time in Contemporary Physics (Oxford Univ. Press, 1920).
Though published as early as 1897, Bertrand Russell’s An Essay on the Foundations of Geometry (Cambridge Univ. Press, 1897) contains a fine account of non-Euclidean geometry. ↑
“On this earth there is indeed a tiny corner of the universe accessible to other senses [than the sense of sight]: but feeling and taste act only at those minute distances which separate particles of matter when ‘in contact:’ smell ranges over, at the utmost, a mile or two, and the greatest distance which sound is ever known to have traveled (when Krakatoa exploded in 1883) is but a few thousand miles—a mere fraction of the earth’s girdle.”—Prof. H. H. Turner of Oxford.
Huyghens and Leibniz both objected to Newton’s inverse square law because it postulated “action at a distance,”—for example, the attractive force of the sun and the earth. This desire for “continuity” in physical laws led to the supposition of an “ether.” We may here anticipate and state that the reason which prompted Huyghens to object to Newton’s law led Einstein in our own day to raise objections to the “ether” theory. “In the formulation of physical laws, only those things were to be regarded as being in causal connection which were capable of being actually observed.” And the “ether” has not been “actually observed.”
The idea of “continuity” implies distances between adjacent points that are infinitesimal in extent; hence the idea of “continuity” comes in direct opposition with the finite distances of Newton.
The statement relating to causal connection—the refusal to accept an “ether” as an absolute base of reference—leads to the principle of the relativity of motion.
Sir Oliver Lodge goes to the extreme of pinning his faith in the reality of this ether rather than in that of matter. Witness the following statement he made recently before a New York audience:
“To my mind the ether of space is a substantial reality with extraordinarily perfect properties, with an immense amount of energy stored up in it, with a constitution which we must discover, but a substantial reality far more impressive than that of matter. Empty space, as we call it, is full of ether, but it makes no appeal to our senses. The appearance is as if it were nothing. It is the most important thing in the material universe. I believe that matter is a modification of ether, a very porous substance, a thing more analogous to a cobweb or the Milky Way or something very slight and unsubstantial, as compared to ether.”
And again:
“The properties of ether seem to be perfect. 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.”
“I consider the ether of space,” says Lodge, in conclusion, “the one substantial thing in the universe.” And Lodge is certainly entitled to his opinion.
For the benefit of those readers who wish to gain a deeper insight into the relativity principle, we shall here discuss it very briefly.
Newton and Galileo had developed a relativity principle in mechanics which may be stated as follows: If one system of reference is in uniform rectilinear motion with respect to another system of reference, then whatever physical laws are deduced from the first system hold true for the second system. The two systems are equivalent. If the two systems be represented by xyz and 
, and if they move with the velocity of v along the x-axis with respect to one another, then the two systems are mathematically related thus: (1)
(1)
and this immediately provides us with a means of transforming the laws of one system to those of another.
With the development of electrodynamics (which we may call electricity in motion) difficulties arose which equations in mechanics of type (1) could no longer solve. These difficulties merely increased when Maxwell showed that light must be regarded as an electromagnetic phenomenon. For suppose we wish to investigate the motion of a source of light (which may be the equivalent of the motion of the earth with reference to the sun) with respect to the velocity of the light it emits—a typical example of the study of moving systems—how are we to coordinate the electrodynamical and mechanical elements? Or, again, suppose we wish to investigate the velocity of electrons shot out from radium with a speed comparable to that of light, how are we to coordinate the two branches in tracing the course of these negative particles of electricity?
It was difficulties such as these that led to the Lorentz-Einstein modifications of the Newton-Galileo relativity equations (1). The Lorentz-Einstein equations are expressed in the form: (2)
(2)
c denoting the velocity of light in vacuo (which, according to all observations, is the same, irrespective of the observer’s state of motion). Here, you see, electrodynamical systems (light and therefore “ray” velocities such as those due to electrons) are brought into play.
This gives us Einstein’s special theory of relativity. From it Einstein deduced some startling conceptions of time and space.
The velocity (v) of an object in one system will have a different velocity (v′) if referred to another system in uniform motion relative to the first. It had been supposed that only a “something” endowed with infinite velocity would show the same velocity in all systems, irrespective of the motions of the latter. Michelson and Morley’s results actually point to the velocity of light as showing the properties of the imaginary “infinite velocity.” The velocity of light possesses universal significance; and this is the basis for much of Einstein’s earlier work.
“Euclid assumes that parallel lines never meet, which they cannot do of course if they be defined as equidistant. But are there such lines? And if not, why not assume that all lines drawn through a point outside a given line will eventually intersect it? Such an assumption leads to a geometry in which all lines are conceived as being drawn on the surface of a sphere or an ellipse, and in it the three angles of a triangle are never quite equal to two right angles, nor the circumference of a circle quite π times its diameter. But that is precisely what the contraction effect due to motion requires.”
(Dr. Walker)
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