Abstract
Sometime during Einstein’s student years, his friend Besso introduced him to the widely-read book The Science of Mechanics, by Mach. In perhaps the most famous section of the book, Mach put forward a critique of Newton’s concept of absolute motion and the corresponding idea of absolute space. Einstein was enamored by this argument and pondered it for many years. The argument from Newton, however, first must be understood before considering Mach’s challenge. So we return to Newton and yet another famous thought experiment – this one is called Newton’s bucket experiment.
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Notes
- 1.
Die Mechanik in Inrer Entwicklung, Historisch-Kritisch Dargestellet, the first edition published in 1883. Available in English as The Science of Mechanics: A Critical and Historical Account of Its Development. See Mach [134]. Notice how the title of Einstein’s important 1920 document, “Fundamental Ideas and Methods of the Theory of Relativity, Presented in Their Development,” discussed above, echoes the title of Mach’s book. Stachel [192], pp. 262–263.
- 2.
The most comprehensive study of this topic is by Hoefer [95, 96]. It has been pointed out that there are at least ten different interpretations of what constitutes Mach’s principle. See, for example, Bondi and Samuel [11], and the list in Barbour and Pfister [6], on p. 530. This more general problem is not of concern here, since we are only interested in how Einstein interpreted it.
- 3.
Newton [151] [1726], p. 415.
- 4.
Centrifugal, is from the Latin words for a force away from the center; it was coined by the Dutch mathematician-physicist Christiaan Huygens, a contemporary of Newton. Incidentally, Newton subsequently coined the term, centripetal force, for a force toward the center.
- 5.
I am avoiding the challenges from the German mathematician-philosopher Gottfried Leibniz and others, since it is not relevant here, and the topic is far beyond the scope of this book. In some ways, Mach later picked up where Leibniz left off.
- 6.
Actually the ball does minimally rotate, due to the friction of the water, but it is clear that without friction there would be no rotational motion, just was without air resistance all falling bodies would fall at the same rate. I recommend the reader perform this simple experiment; it is quite astonishing.
- 7.
Galileo [71] [1632], pp. 389–399.
- 8.
Mach [134] [1883, preface to the first edition], p. xxii.
- 9.
Mach [134] [1912, from the Preface to seventh edition], p. xxviii.
- 10.
Einstein first used the term “Mach’s principle” in 1918. Einstein Papers, Vol. 7, Doc. 4, “On the Foundations of the General Theory of Relativity.” But the idea appears much earlier in his work.
- 11.
Einstein Papers, Vol. 4, Doc. 7.
- 12.
Letter to Mach, 25 June 1913, Einstein Papers, Vol. 5, Doc. 448.
References
Barbour, Julian, and Herbert Pfister (eds.). 1995. Mach’s principle: from Newton’s bucket to quantum gravity, Einstein Studies, vol. 6. Boston/Basel/Berlin: Birkhäuser.
Bondi, Hermann, and Joseph Samuel. 1996. The lense–thirring effect and Mach’s principle. Available online at: arXiv:gr-qc/96070-09v1 4 July 1996.
Galilei, Galileo. 1967. Dialogue concerning the two chief world systems (trans Stillman Drake.). Berkeley: University of California Press. The Dialogue was published in 1632.
Hoefer, Carl. 1994. Einstein’s struggle for a Machian gravitation theory. Studies in History and Philosophy of Science 25(3): 287–335.
Hoefer, Carl. 1995. Einstein’s formulation of Mach’s principle. In Barbour, J., and Pfister H. (eds.), 1995, above, 67–90.
Mach, Ernst. 1960. The science of mechanics: a critical and historical account of its development. Sixth Edition. (trans: Thomas J. McCormack.). New York: Open Court. The original German edition, Die Mechanik in Inrer Entwicklung, Historisch-Kritisch Dargestellet, was published in 1883. The German edition went through nine revisions.
Newton, Isaac. 1999. The principia (trans: I. Bernard Cohen and Anne Whitman.). Berkeley: University of California Press. This is a translation of the third edition of 1726, from which, using the footnotes, one is able to reconstruct the first (1687) and second (1713) editions.
Stachel, John. 2002. Einstein from ‘B’ to ‘Z’. Boston/Basel/Berlin: Birkhäuser. This is Volume Nine in the Einstein Studies series.
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Topper, D.R. (2013). Enter, Mach’s Principle; or, Seduced by an Idea. 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_13
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