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.
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Das Relativitätsprinzip. Braunschweig, 1911. 208 p.
LECORNU, LÉON.
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La gravitation. _Scientia._ Bologna, 1914, vol. 6, pp. 28-59.
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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.
Some functional equations in the theory of relativity.
American Mathematical Society. _Bulletin_, Lancaster, Pa.,
1919, vol. 26, pp. 26-34.
MICHELSON, A. A., and MORLEY, E. W.
The Relative Motion of the Earth and the Luminiferous
Ether. _American Journal of Science_, 1887, vol. 34, p. 333.
See also: _Astro-Physical Journal_, vol. 37, pp. 100-193.
The report of the crucial experiments that upset the idea
of a stationary ether.
MINKOWSKI, HERMANN.
Relativitätsprinzip. _Jahresbericht der Deutschen Mathematiker-Vereinigung._
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NORDSTRÖM, GUNNAR.
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PALATINI, A.
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PLANCK, MAX.
Zur Dynamik bewegter Systeme. Königlich Preussischen
Akademie der Wissenschaften. _Sitzungberichte_, Berlin, 1907,
pp. 542-570.
His theory.
PETZOLDT, J.
Does the Relativity Theory Exclude the Reality of Space
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La gravitation. _Scientia_, Bologna, 1909, vol. 5, pp. 152-165.
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92 p.
SITTER, W. DE.
On Einstein’s theory of gravitation, and its astronomical
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WILSON, WILLIAM.
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THANKS
Most of the mathematical references cited above have been borrowed
bodily from the book list prepared by Miss Mary E. Todd of the Science
Room of the New York Public Library and published in the _Library
Journal_. As soon as the Einstein craze struck New York these books
were placed on a long table and it has been difficult to find a seat
at this table, day or evening, ever since. At Cambridge University
when Professor Eddington lectured on the Einstein theory the students
waiting for the opening of the hall doors formed a cue extending
half-way across Trinity Great Court. It is unusual in any university to
have “standing room only” at a lecture on mathematical physics.
About half of the present volume appeared in _The Independent_
of November 29, December 7, 13, and 20, 1919, and I am indebted to
Hamilton Holt, the editor, and to Karl V. S. Howland, the publisher
of that magazine, for the privilege of reprinting them in book form.
I am further grateful to several professors of physics, mathematics,
astronomy and philosophy who have been kind enough to criticize and
correct this material, but since it would not be fair to hold them
responsible for my personal views and unconventional language I shall
have to express my thanks to them in private.
INDEX
Bergson, Henri, 47, 51, 52
Carlyle, iv
Curvature of space, 26, 35, 38, 96
Eclipse observations, 2, 65, 72
Einstein, Albert
Postulates of, 13, 83, 111
Theory of time, 109
Theory of gravitation, 39, 58, 76, 80, 86, 93, 96, 109
Life of, 78
Works of, 116, 117
Equivalence, principle of, 14, 83, 86
Ether, 8, 11, 88, 106
Flammarion, Camille, 40
Flatland, 35, 57
Fourth dimension, 24, 34, 49
Gravitation, 68, 74, 77, 80, 86, 90
Laws, natural, 102, 109
Light, deflection of ray, 11, 62, 79, 85
Light, pressure of, 67, 93
Lodge, Sir Oliver, 2, 68, 75, 87, 88
Lorentz, 22, 111, 112, 118
Macdonald, George, 34
Maxwell, Clerk, 67, 111, 112
Mercury, orbit of, 14, 66
Michelson and Morley experiment, 11, 21, 22, 85
Minkowski, iv, 18
Mirror, images, 18
Motion picture illustrations, 31, 44, 46, 50, 53
Newton, 15, 23, 39, 66, 76, 79, 87, 90, 95
Non-Euclidean geometry, 30, 48, 57, 112
Planck, 98, 121
Poincaré, H., 88, 107
Relativity of measurements, 15, 20, 26
Relativity of motion, 4, 8, 15, 23
Relativity of time, 15, 24, 47, 51
Slade, 58, 60
Spectrum, shifting of lines of, 14, 77, 85
Theories, reception of new, 98, 101
Theory of relativity, 2, 15
Thomson, Sir Joseph, 3, 93, 94, 95
Time as fourth dimension, 30, 32, 49
Time, reversal of, 41, 44
Wells, H. G., 32, 34, 40, 52
Zöllner, 58, 60
=TRANSCRIBER’S NOTES=