Part 7
But when the physicist thus reduces matter to a small italic _m_ some people are sure to say that he is denying the existence of matter. What would they say about Riemann who considers matter to be holes in the ether? A definition is a different thing from a denial. There are people among us who deny the existence of matter and they call themselves “Scientists,” too, but they are not the ones who are devoting their days and nights to the study of the workings of matter in order to make it the servant of man.
A professor of chemistry would not think of asking his students if the atomic theory is true any more than he would ask them if the atomic theory is blue. He does not care whether they believe the atomic theory or not. He only wants them to be able to use the atomic theory for getting certain valuable results. Consequently, he watches with interest and without apprehension the progress of discovery in radio-activity which is undermining the old conception of the atom. He would be glad to get rid of the atomic theory if he could find something better because after all it is a clumsy thing and will not hold half the facts he wants to put into it. He would have no more hesitation about dropping it than he has in setting down one beaker to pick up a larger one when what he has in the first is frothing over. He does not want to spill anything, but he does not care what vessel it is in. Revolutions in science never go backward and they differ from political revolutions in that nothing worth saving is lost in transition. The new theory must always include all that the old one does and more. In their struggle for existence, formulas fight like snakes; the one that can swallow the other beats. Now a four-dimensional universe can take in a three-dimensional universe and have space to spare for whatever the narrower conception could not include so it seems likely to prevail.
We now know how to sympathize with those poor frightened people who lived in the times of Copernicus and Galileo when they were told that the solid earth on which they stood was not supported by anything, but whirling about and rushing around through empty space and that half the time they hung with their heads down over immeasurable space with nothing to hold on to. But they got used to it in time and lived happily ever after. So may we.
For the benefit of those who want to get their information at first hand I append an article by Dr. Einstein himself which appeared in the London _Times_ of December 13, 1919, and in _Science_ of January 6, 1920:
TIME, SPACE, AND GRAVITATION
_By Dr. Albert Einstein_
I respond with pleasure to your Correspondent’s request that I should write something for the _Times_ on the Theory of Relativity.
After the lamentable breach in the former international relations existing among men of science, it is with joy and gratefulness that I accept this opportunity of communication with English astronomers and physicists. It was in accordance with the high and proud tradition of English science that English scientific men should have given their time and labor, and that English institutions should have provided the material means, to test a theory that had been completed and published in the country of their enemies in the midst of war. Although investigation of the influence of the solar gravitational field on rays of light is a purely objective matter, I am none the less very glad to express my personal thanks to my English colleagues in this branch of science; for without their aid I should not have obtained proof of the most vital deduction from my theory.
There are several kinds of theory in Physics. Most of them are constructive. These attempt to build a picture of complex phenomena out of some relatively simple proposition. The kinetic theory of gases, for instance, attempts to refer to molecular movement the mechanical, thermal, and diffusional properties of gases. When we say that we understand a group of natural phenomena, we mean that we have found a constructive theory which embraces them.
But in addition to this most weighty group of theories, there is another group consisting of what I call theories of principle. These employ the analytic, not the synthetic method. Their starting-point and foundation are not hypothetical constituents, but empirically observed general properties of phenomena, principles from which mathematical formulæ are deduced of such a kind that they apply to every case which presents itself. Thermodynamics, for instance, starting from the fact that perpetual motion never occurs in ordinary experience, attempts to deduce from this, by analytic processes, a theory which will apply in every case. The merit of constructive theories is their comprehensiveness, adaptability, and clarity, that of the theories of principle, their logical perfection, and the security of their foundation.
The theory of relativity is a theory of principle. To understand it, the principles on which it rests must be grasped. But before stating these it is necessary to point out that the theory of relativity is like a house with two separate stories, the special relativity theory and the general theory of relativity.
Since the time of the ancient Greeks it has been well known that in describing the motion of a body we must refer to another body. The motion of a railway train is described with reference to the ground, of a planet with reference to the total assemblage of visible fixed stars. In physics the bodies to which motions are spatially referred are termed systems of coördinates. The laws of mechanics of Galileo and Newton can be formulated only by using a system of coördinates.
The state of motion of a system of coördinates cannot be chosen arbitrarily if the laws of mechanics are to hold good (it must be free from twisting and from acceleration). The system of coördinates employed in mechanics is called an inertia-system. 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 coördinates 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 coördinate system K must also hold good for any other system K′, provided that K and K′ are in uniform movement of translation.”
The second principle on which the special relativity theory rests is that of the constancy of the velocity of light in a vacuum. Light in a vacuum has a definite and constant velocity, independent of the velocity of its source. Physicists owe their confidence in this proposition to the Maxwell-Lorentz theory of electro-dynamics.
The two principles which I have mentioned have received strong experimental confirmation, but do not seem to be logically compatible. The special relativity theory achieved their logical reconciliation by making a change in kinematics, that is to say, in the doctrine of the physical laws of space and time. It became evident that a statement of the coincidence of two events could have a meaning only in connection with a system of coördinates, that the mass of bodies and the rate of movement of clocks must depend on their state of motion with regard to the coördinates.
But the older physics, including the laws of motion of Galileo and Newton, clashed with the relativistic kinematics that I have indicated. The latter gave origin to certain generalized mathematical conditions with which the laws of nature would have to conform if the two fundamental principles were compatible. Physics had to be modified. The most notable change was a new law of motion for (very rapidly) moving mass-points, and this soon came to be verified in the case of electrically-laden particles. The most important result of the special relativity system concerned the inert mass of a material system. It became evident that the inertia of such a system must depend on its energy-content, so that we were driven to the conception that inert mass was nothing else than latent energy. The doctrine of the conservation of mass lost its independence and became merged in the doctrine of conservation of energy.
The special relativity theory, which was simply a systematic extension of the electro-dynamics of Maxwell and Lorentz, had consequences which reached beyond itself. Must the independence of physical laws with regard to a system of coördinates be limited to systems of coördinates in uniform movement of translation with regard to one another? What has nature to do with the coördinate systems that we propose and with their motions? Although it may be necessary for our descriptions of nature to employ systems of coördinates that we have selected arbitrarily, the choice should not be limited in any way so far as their state of motion is concerned. (General theory of relativity.) The application of this general theory of relativity was found to be in conflict with a well-known experiment, according to which it appeared that the weight and the inertia of a body depended on the same constants (identity of inert and heavy masses). Consider the case of a system of coördinates which is conceived as being in stable rotation relative to a system of inertia in the Newtonian sense. The forces which, relatively to this system, are centrifugal must, in the Newtonian sense, be attributed to inertia. But these centrifugal forces are, like gravitation, proportional to the mass of the bodies. Is it not, then, possible to regard the system of coördinates as at rest, and the centrifugal forces as gravitational? The interpretation seemed obvious, but classical mechanics forbade it.
This slight sketch indicates how a generalized theory of relativity must include the laws of gravitation, and actual pursuit of the conception has justified the hope. But the way was harder than was expected, because it contradicted Euclidean geometry. In other words, the laws according to which material bodies are arranged in space do not exactly agree with the laws of space prescribed by the Euclidean geometry of solids. This is what is meant by the phrase “a warp in space.” The fundamental concepts “straight,” “plane,” etc., accordingly lose their exact meaning in physics.
In the generalized theory of relativity, the doctrine of space and time, kinematics, is no longer one of the absolute foundations of general physics. The geometrical states of bodies and the rates of clocks depend in the first place on their gravitational fields, which again are produced by the material systems concerned.
Thus the new theory of gravitation diverges widely from that of Newton with respect to its basal principle. But in practical application the two agree so closely that it has been difficult to find cases in which the actual differences could be subjected to observation. As yet only the following have been suggested:--
1. The distortion of the oval orbits of planets round the sun (confirmed in the case of the planet Mercury).
2. The deviation of light-rays in a gravitational field (confirmed by the English Solar Eclipse expedition).
3. The shifting of spectral lines toward the red end of the spectrum in the case of light coming to us from stars of appreciable mass (not yet confirmed).
The great attraction of the theory is its logical consistency. If any deduction from it should prove untenable, it must be given up. A modification of it seems impossible without destruction of the whole.
No one must think that Newton’s great creation can be overthrown in any real sense by this or by any other theory. His clear and wide ideas will forever retain their significance as the foundation on which our modern conceptions of physics have been built.
A final comment. The description of me and my circumstances in _The Times_ shows an amusing feat of imagination on the part of the writer. By an application of the theory of relativity to the taste of readers, today in Germany I am called a German man of science, and in England I am represented as a Swiss Jew. If I come to be regarded as a _bête noire_, the descriptions will be reversed, and I shall become a Swiss Jew for the Germans and a German man of science for the English!
FOOTNOTES:
[Footnote 1: Bergson: “Time and Free Will,” p. 221.]
[Footnote 2: Bergson in his “Laughter” traces all humor back to this fundamental absurdity of making a man act mechanically.]
[Footnote 3: “We can thus say that all these paradoxical phenomena (or rather negations of phenomena) which have been enumerated above can only happen after the end or before the beginning of eternity” (De Sitter).]
[Footnote 4: If you insist upon seeing just what is the difference between Einstein’s and Newton’s laws of gravitation here it is as given in _The Scientific Monthly_ of January, 1920:
Any particle or light pulse moves so that the integral of _ds_ between the two points of its path (in four dimensions) is stationary where
(according to Einstein) _ds^{2}_ = -(1 - 2_m_/_r_)^{-1}_dr^{2}_-_r^{2}_ _d θ^{2}_ + (1 - 2_m_/_r_)_dt_
or (according to Newton) _ds^{2}_ = _dr^{2}_ - _r^{2}_ _d θ^{2}_ + (1 - 2_m_/_r_)_dt_
These expressions are in polar coördinates for a particle of gravitational mass _m_.
The new factor introduced by Einstein is, as shown above,
1/{1-(2_m_/_r_)} ]
[Footnote 5: _Nineteenth Century_, December, 1919.]
[Footnote 6: Quoted by Eddington in _Contemporary Review_, December, 1919.]
[Footnote 7: Sir Joseph Thomson in _Nature_, December 4, 1919.]
And finally
IF YOU WANT TO READ MORE ABOUT THE EINSTEIN THEORIES
_For the non-mathematical reader_:
ABBOTT, EDWIN.
Flatland, by A Square. Boston, 1891.
An amusing way of leading up to the fourth dimension.
CAMPBELL, NORMAN.
The Commonsense of Relativity. _Philosophical Magazine_, April, 1911.
CARR, WILDON.
The Metaphysical Implications of the Theory of Relativity. _Philosophical Review_, Jan., 1915.
CARUS, PAUL.
The Principle of Relativity. Chicago: Open Court Publishing Co., 1913.
COMSTOCK, D. F.
The Principle of Relativity. _Science_, May 20, 1910, vol. 31, p. 767.
CUNNINGHAM, E.
Einstein’s Relativity Theory of Gravitation. _Nature_, Dec. 4, 11, and 18, 1919.
An interesting non-mathematical discussion of the latest phases of the theory.
EDDINGTON, A. S.
Einstein’s Theory of Space and Time. _Contemporary_ _Review_, Dec, 1919.
Good popular article.
EDDINGTON, A. S.
Gravitation. _Scientific American Supplement_, July 6 and 13, 1918.
An excellent popular explanation by the leading British disciple of Einstein.
EINSTEIN, A.
Time, Space, and Gravitation. _Science_, Garrison, 1920, Jan. 3, n.s., vol. 51, p. 8-10.
My Theory. _Living Age._ Boston, 1920, vol. 304, p. 41-3, Jan. 3.
FLAMMARION, CAMILLE.
Lumen. New York: Dodd, Mead and Co., 1897.
Contains nothing about Einstein but presents the relativity of time in fantastic form. KEYSER, C. J.
Concerning the Figure and the Dimensions of the Universe of Space. _Science_, June 13, 1913.
LODGE, SIR OLIVER.
The New Theory of Gravity. _Nineteenth Century_, Dec., 1919.
The Ether versus Relativity. _Fortnightly Review_, Jan., 1920.
Admirable article by a courteous opponent.
POINCARÉ, HENRI.
Science and Method; also contained in The Foundations of Science. New York: The Science Press, 1913.
RUSSELL, BERTRAND.
The Relativity Theory of Gravitation. _English Review_, Dec., 1919.
A clear explanation by one of the foremost of British philosophers.
THOMSON, J.
Deflection of Light by Gravitation and the Einstein Theory of Relativity. _Scientific Monthly_, Garrison, N. Y., 1920, vol. 10, p. 79-85, Jan.
VARIOUS WRITERS.
The Fourth Dimension Simply Explained. New York: Munn and Co., 1910.
The essays submitted for a prize offered by the _Scientific_ _American_. Twenty-two mathematicians try their best to justify the title and if they do not succeed it is not their fault.
WETZEL, REINHARD A.
The New Relativity in Physics. _Science_, New York, 1913. New ser., vol. 38, pp. 466-474.
Explains the relativity of time with diagrams and references to the literature.
Other articles of general interest may be found in:
_Science_: July 16, 1909; May 20, 1910; June 20, 1913; April 24, 1914; Dec. 5, 1919.
_Scientific American Supplement_: April 7, 1917; Dec. 17, 1910.
London _Nation_: Nov. 14 and Dec. 27, 1919.
London _Times_: Nov. 8, 18, and 25, Dec. 4 and 19, 1919.
London _Nature_: Almost every number in Nov., Dec., 1919, Jan., Feb., 1920.
New York _Times_: Nov. 7 and 16, Dec. 21, 1919.
New York _Sun_: Nov. 10, 1919.
_The New Republic_: Jan. 21, 1920.
_For the mathematical reader_:
EINSTEIN, ALBERT.
Bases physiques d’une théorie de la gravitation. Société Astronomique de France. _Bulletin_, Paris, 1917, Tome 31, pp. 407-411.
Die formale Grundlage der allgemeinen Relativitätstheorie. Königlich Preussischen Akademie der Wissenschaften. _Sitzungsberichte_, Berlin, 1904 (Juli-Dez.), pp. 1030-1085.
Die Grundlagen der allgemeinen. Relativitätstheorie. _Annalen_ _der Physik_, Leipzig, 1916, Band 49, Folge 4, p. 769.
Ist die Trägheit eines Korpers von seinem Energieinhalt abhängig? _Annalen der Physik_, Leipzig, 1905, Band 18, Folge 4, pp. 639-644.
Lichtgeschwindigkeit und Statik des Gravitätionsfeldes. _Annalen der Physik_, Leipzig, 1912, Band 38, Folge 4, pp. 355-369.
Prinzipielles zur allgemeinen Relativitätstheorie. _Annalen_ _der Physik_, Leipzig, 1918, Band 55, Folge 4, pp. 241-244.
Uber das Relativitätsprinzip und die aus demselben gezogenen Folgerungen. _Jahrbuch der Radioaktivität und_ _Elektronik_, Leipzig, 1908, Band 4, pp. 411-462.
Uber den Einfluss der Schwerkraft auf die Ausbreitung des Lichtes. _Annalen der Physik_, Lypzig, 1911. Band 35, pp. 898-908.
Uber die Möglichkeit einer neuen Prüfung des Relativitätsprinzips. _Annalen der Physik_, Leipzig, 1907, Band 23, pp. 197-208.
Uber die vom Relativitätsprinzip geforderte Trägheit der Energie. _Annalen der Physik_, Leipzig, 1907, Band 23, Folge 4, pp. 371-384.
Uber einen die Erzeugung und Verwandlung des Lichtes betreffendes heuristischen Gesichtspunkt. _Annalen der_ _Physik_, Leipzig, 1905, Band 17, Folge 4, pp. 132-148.
Zum gegenwärtigen Stande des Gravitätionsproblems. _Physikalische Zeitschrift_, Leipzig, 1913, Band 14, pp. 1249-1266.
Zum Relativitäts Problem. _Scientia_, Bologna, 1914, vol. 15, pp. 337-48.
Zur Elektrodynamik bewegter Korper. _Annalen der_ _Physik_, Leipzig, 1905, Band 17, Folge 4, pp. 891-921.
Zur Theorie der Lichterzeugung und Lichtabsorption. _Annalen der Physik_, Leipzig, 1906, Band 20, Folge 4, pp. 199-206.
Spielen Gravitationsfelder im Aufbau der materiellen Elementarteilchen eine wesentliche Rolle? _Sitz. Preuss._ _Akad. Wiss._, April 10, 1919.
EINSTEIN, ALBERT, and MARCEL GROSSMAN.
Entwurf einer verallgemeinerten Relativitätstheorie und einer Theorie der Gravitation. _Zeitschrift für Mathematik_ _und Physik_, Leipzig, 1914, Band 62, pp. 225-261.
EINSTEIN, LORENTZ and MINKOWSKI.
Relativitätsprinzip, Das. Eine Sammlung von Abhandlungen. Mit Anmerkungen von A. Sommerfeld und Vorwort von O. Blumenthal. Leipzig: B. G. Teubner, 1913, 89 p. (_Fortschritte der mathematischen Wissenschaften in_ _Monographien_, Heft 2.)
A reprint of these three famous fundamental papers.
ABRAHAM, M.
Die neue Mechanik. _Scientia_, Bologna, 1914, vol. 15, pp. 8-27.
Nochmals Relativität und Gravitation. Bemerkungen zu A. Einsteins Erwiderung. _Annalen der Physik_, Leipzig, 1912, Folge 4, vol. 39, pp. 444-448.
BACKLUND, A. V.
Zusammenstellung einer Theorie der klassischen Dynamik und der neuen Gravitätionstheorie von Einstein. _Arkiv för_ _mathematik, astronomie, och fysik_, Stockholm, 1919, Band 14, no. 11, 64 seite.
BATEMAN, H.
General Relativity Theory. _Phil. Mag._, Feb., 1909, vol. 37.
Applies the theory to life and mind.
BRILLOUIN, MARCEL.
Propos Sceptiques au Sujet du Principe de Relativité. _Scientia_, Bologna, 1913, vol. 13, pp. 10-26.
BROSE, HENRY L.
Einstein’s Theory of Relativity (non-math. form). Lecture published in pamphlet by B. H. Blackwell. Noted in _English Mechanic_, Dec. 19, 1919.
CARMICHAEL, ROBERT DANIEL.
The Theory of Relativity. _Mathematical Monographs_, no. 12. New York: John Wiley, 1913.
COBB, CHARLES W.
Relativity. _Journal of Philosophy, Psychology, and Scientific_ _Method_, Jan. 18, 1917.
CONWAY, A. W.
Relativity. _Edin. Math. Tracts_, no. 3, London, 1913.
CROMMELIN, A. C. D.
Results of the Total Solar Eclipse of May 29 and the Relativity Theory. _Science_, vol. 50, pp. 518-520. _Sci. Amer._ _Supp._, Dec. 6, 1919.
CUNNINGHAM, E.
Report on the Relativity Theory of Gravitation. London, Green, 1915.
DEZUANI, ARMANDO.
Equilibrio relativo ed equazioni gravitazionali di Einstein nel caso stazionario. _Il nuovo cimento_, Pisa, 1919, vol. 18, pp. 5-25, July, 1919.
DONDER, T. DE.
Gravitational Tensors of Einstein’s Theory. _Science Abstracts_, April 30, 1919.
DROSTE, J.
The Field of Moving Centers in Einstein’s Theory of Gravitation. Koninklijke Akademie van Wetenschappen. _Proceedings_, Amsterdam, 1916, vol. 19, pp. 447-475.
The Field of a Single Center in Einstein’s Theory of Gravitation and the Motion of a Particle in that Field. Koninklijke Akademie van Wetenschappen. _Proceedings_, Amsterdam, 1916, vol. 19, pp. 197-218.
EDDINGTON, A. S.
Report on the Relativity Theory of Gravitation. London: Fleetway Press, 1918. 91 p.
The only account of Einstein’s latest theory in English.
EDDINGTON, A. S., and OTHERS.
The Deflection of Light by Gravitation and the Einstein Theory of Relativity. The Report of the British Eclipse Expedition to the Royal Society. _Scientific Monthly_, Jan., 1920.
GROSSMAN, MARCEL.
Définitions, méthodes et problèmes mathématiques relatifs à la théorie de la gravitation. _Archives des Sciences_ _Physiques et Naturelles_, Genève, Jan.-Juin, 1914, 4 période, Tome 37, pp. 13-19.
GUILLAUME, E.
Theory of Relativity. _Archives des Sciences_, Dec., 1918, vol. 46.
HUMM, R. J.
Energy Equations of General Theory of Relativity. _Annalen_ _der Physik_, 1919, vol. 58.
HUNTINGTON, EDWARD V.
A new approach to the theory of relativity. Festschrift Heinrich Weber. Leipzig, 1912, pp. 147-169.
ISHIWARA, JUN.
Zur relativistischen Theorie der Gravitation. Tohoku Imperial University. _Science_ reports, ser. 1, Sendai, Japan, vol. 4, pp. 111-160.
KAFKA, H.
Tensor Analysis. _Annalen der Physik_, 1919, vol. 58, pp. 1-54.
KOTTLER, FRIEDRICH.
Uber die physikalischen Grundlagen der einsteinschen Gravitätionstheorie. _Annalen der Physik_, Leipzig, 1918, Band 56, Folge 4, pp. 408-462. LARMOR, J.
Essence of Physical Relativity. _Nat. Acad. Sci. Proc._, vol. 4, Nov., 1918.
LAUE, RD. M.
Das Relativitätsprinzip. Braunschweig, 1911. 208 p.
LECORNU, LÉON.
La Mécanique. Paris: Flammarion, 1909.
LORENTZ, H. A.
Considerations élémentaires sur le principe de relativité. _Revue générale des sciences_, Paris, 1914. Tome 25, pp. 179-186.
La gravitation. _Scientia._ Bologna, 1914, vol. 6, pp. 28-59.
Das Relativitätsprinzip. 1914.
La Gravitation. _Scientia_, Bologna, 1914, vol. 16, pp. 28-59.
On Einstein’s theory of gravitation. Koninklijke Akademie van Wetenschappen. _Proceedings_, Amsterdam, 1917-18, vol. 19, pp. 1341-1369; vol. 20, pp. 2-34.
On Hamilton’s principle in Einstein’s theory of gravitation. Koninklijke Akademie van Wetenschappen. _Proceedings_, Amsterdam, 1917, vol. 19, pp. 751-765.
LUNN, ARTHUR C.