Abstract
The November lectures, published in the Proceedings of the Prussian Academy of Sciences, exposed the struggles and breakthroughs of the last days of “searching in the dark.” What was needed next was a logically organized and comprehensive summary of the theory for theoretical physicists – and perhaps, posterity – to devour and digest. This Einstein published 3 months later, in March 1916, producing one of the greatest papers in the history of science.
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- 1.
Sitzungsberichte, Prussische Akademie der Wissenschaften; Reports of Proceedings of the Prussian Academy of Sciences, in Einstein Papers, Vol. 6, Docs., 21, 22, 24, and 25.
- 2.
Einstein Papers, Vol. 6, Doc 30. The document published in the English translation volume is a reprint of the translation in the book Einstein et al. [57], pp. 109–164, except for the first page, which was missing in the book and is reproduced in the Papers. Otherwise, I am using the book for my citations of this paper.
- 3.
Einstein Papers, Vol. 6, Doc. 30, p.146 ET.
- 4.
Einstein et al. [57] [1916], pp. 112–113.
- 5.
Einstein et al. [57] [1916], p. 114.
- 6.
Einstein et al. [57] [1916], pp. 114–115.
- 7.
Einstein et al. [57] [1916], pp. 142–145.
- 8.
See, for example, Einstein and Infeld [59] [1938].
- 9.
Einstein et al. [57] [1916], p. 157. Einstein Papers, Vol. 6, Doc. 30: “Eine der Wirklichkeit näher liegende Approximation erhalten wir….”
- 10.
Einstein et al. [57] [1916], pp. 160–164.
- 11.
Einstein et al. [57] [1916], p. 162.
- 12.
Einstein et al. [57] [1916], p. 162n.
- 13.
I think that the gravitational redshift may, alternatively, be deduced from the bending of light by gravity using the wave model of light. Since gravity bends light, then gravity attracts light; thus a wave of light being emitted from the center of the Sun would be attracted back towards the Sun as it traveled outward, so when it reached the surface of the Sun the light would be stretched to a longer wavelength, that is, it would be shifted toward the red. I do not know if Einstein ever conceived of this.
- 14.
Einstein Papers, Vol. 8, Doc. 178. Letter of January 3, 1916.
- 15.
Einstein Papers, Vol. 8, Doc. 178, “…so einfach sie im Grunde nun ist.”
- 16.
- 17.
Einstein [49] [1917].
- 18.
Pais [162], p. 525; Fölsing [65], p. 855.
- 19.
A blunt overview of the triangle among Albert, Elsa, and Mileva, based on recent sources, is in Levenson [132], pp. 141–157.
- 20.
We wrote Newton’s Law (I.4) as a proportion: F α (m × M)/D 2. This was essentially how Newton expressed it. Not until the late-nineteenth century was it written as an equation, which entailed a constant (G): hence, F = G (m × M)/D 2. For some details, see Topper [198], pp. 162–163.
- 21.
In some ways this problem is a non-problem in the following sense. Geometry and arithmetic had separate histories. Briefly, and very simply put: Geometry came from the Greeks. Arithmetic was ubiquitous (every culture eventually counts things), but one important branch began in India and coming through Islam evolved into algebra (note the Arabic name). In the seventeenth century, they were put together in what became known as analytical geometry (note the title). A simple example is the equation,x 2 + y 2 = r 2, which a circle (geometry) with radius r. Tensor calculus later evolved from these roots.
References
Einstein, Albert. 1960. Relativity: the special and the general theory. Fifteenth Edition. (trans: Robert W. Lawson in 1920.). London: Methuen & Co. This popular account was first published in German in 1917. This edition has five appendices, the last (1952) is titled “Relativity and the Problem of Space.”
Einstein, Albert, H. A. Lorentz, H. Weyl, and H. Minkowski. 1923. The principle of relativity. New York: Dover Publications. This book contains the first English transitions of essential papers on relativity. The translations of Einstein’s papers in The Collected Papers of Albert Einstein have supplanted some of these; in other cases the Einstein Papers merely reprint these translations of 1923.
Einstein, Albert, and Leopold Infeld. 1961. The evolution of physics: the growth of ideas from early concepts to relativity and quanta. New York: Simon & Schuster. This was first published in 1938. In the preface to the 1961 edition, Infeld acknowledges Einstein as the “chief author” of the book.
Fölsing, Albrecht. 1997. Albert Einstein: a biography (trans: Ewald Osers.). New York: Viking. Originally published in German in 1993.
Galilei, Galileo. 1967. Dialogue concerning the two chief world systems (trans Stillman Drake.). Berkeley: University of California Press. The Dialogue was published in 1632.
Levenson, Thomas. 2003. Einstein in Berlin. New York: Bantam Books.
Newton, Isaac. 1969. De mundi systemate (A Treatise on the System of the World). English translation. London: Dawsons. Published posthumously in 1727. Intro by I. Bernard Cohen.
Topper, David R. 2007. Quirky sides of scientists: true tales of ingenuity and error in physics and astronomy. New York: Springer.
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Topper, D.R. (2013). 1916: The Great Summation Paper on General Relativity. In: How Einstein Created Relativity out of Physics and Astronomy. Astrophysics and Space Science Library, vol 394. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-4782-5_15
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