By maintaining the relativity of all motion, especially rotational motion, Mach denied the existence of absolute motion and of absolute space. Accordingly, he maintained the equivalence of the Ptolemaic and the Copernican systems and the equivalence of rotating-system/fixed-universe and universe-rotating/fixed-system situations. An analysis of the Foucault pendulum shows that Mach’s relativity principle implies that there cannot be a fixed bucket in a rotating universe. Also, Mach’s views violate the physics that he espoused: noninertial experiments, for example stellar aberration and electromagnetic effects, distinguish between a rotating bucket in a fixed universe and a fixed bucket in a rotating universe, between a Copernican universe and a Brahean or Ptolemaic universe, and establish that one cannot ascribe all pertinent observations solely to relative motion between a system and the universe.
REFERENCES
1.
Mach’s Principle: From Newton’s Bucket to Quantum Gravity, edited by Julian Barbour and Herbert Pfister (Birkhauser, Boston, MA, 1995), p. 530 where 21 different formulations are listed.
2.
Denis W. Sciama, The Unity of the Universe (Anchor Books, New York, 1961).
3.
Ernst Mach, The Science of Mechanics (Open Court, LaSalle, IL, 1960), 6th ed. Originally published as Die Mechanik in ihrer Entwicklung Historisch-kritisch Darstellt, 9th ed.
4.
Isaac Newton, The Mathematical Principles of Natural Philosophy (University of California Press, Berkeley, CA, 1960), pp. 10–11.
5.
Reference 3, p. xxviii.
6.
Reference 3, p. 279.
7.
Reference 3, p. 341, emphasis in the original.
8.
Max Jammer, Concepts of Space (Harper Torchbooks, New York, 1954), p. 141, quotes the 4th German edition of Ref. 3 wherein Mach states that “…for me, above all, there is only relative motion, and in this respect I cannot make any difference between rotation and translation” (our translation).
9.
John Norton, “Mach’s principle before Einstein,” in Ref. 1, pp. 9–55.
10.
The Einstein Myth and the Ives Papers, edited by Richard Hazelett and Dean Turner (Devin-Adair, Old Grenwich, CT, 1979), pp. 247–255, contains a translation of Georges Sagnac, “The lumineferous ether demonstrated by the effect of the relative motion of the ether in an interferometer in uniform motion,” Comptes Rendus de l’Academie des Sciences (Paris) 157, 708–710, 1410–1413 (1913) and a reprint of
Albert A.
Michelson
, “The effects of the Earth’s rotation on the velocity of light
,” Philos. Mag.
8
, 716
–719
(1904
).11.
Robert Wood, Physical Optics (Dover, New York, 1967), 3rd ed., p. 29.
12.
Richard P. Feynman, Robert B. Leighton, and Matthew Sands, The Feynman Lectures in Physics (Addison–Wesley, Reading, MA, 1964), Vol. II, p. 14-7.
13.
The rotation of the pendulum bob is not usually discussed in mechanics texts because earth-bound pendula partake of the rotation of the earth.
14.
Albert Einstein, Ideas and Opinions (Bonanza Books, New York, 1954), p. 286.
16.
Reference 3, p. 393.
17.
Reference 3, p. 187.
18.
Thomas S. Kuhn, The Copernican Revolution (Vintage Books, New York, 1959), p. 187.
19.
Robert W.
Brehme
, “New look at the Ptolemaic system
,” Am. J. Phys.
44
, 506
–514
(1976
).20.
Reference 3, p. 280 (emphasis in the original). See also p. 271.
21.
Reference 3, p. 160.
22.
Mario
Bunge
, “Mach’s critique of Newtonian mechanics
,” Am. J. Phys.
34
, 585
–596
(1966
).23.
Albert Einstein, “Autobiographical notes,” in Albert Einstein Philosopher Scientist, edited by Paul Schilpp (Tudor, New York, 1949), p. 21.
24.
John Earman, World Enough and Space-Time, Absolute Versus Relational Theories of Space and Time (MIT, Cambridge, MA, 1989).
25.
Reference 23, p. 69.
26.
Reference 22, p. 589. Bunge lists Duhem, Pearson, Le Roy, Goodman, Reichenbach, and Frank as authorities who agree with Statement 2.
27.
Reference 3, p. 284.
28.
Joseph Norwood, Jr., Intermediate Classical Mechanics (Prentice–Hall, Englewood Cliffs, NJ, 1979), p. 274.
29.
Hans Reichenbach, The Philosophy of Space and Time (Dover, New York, 1957), p. 254, and From Copernicus to Einstein (Dover, New York, 1980), p. 84.
30.
Ronald Adler, Maurice Bazin, and Menahem Schiffer, Introduction to General Relativity (McGraw-Hill, New York, 1975), 2nd ed., pp. 437–448.
31.
Carl Hoefer, “Einstein’s formulation of Mach’s principle,” in Ref. 1, pp. 67–90, 80.
32.
Clifford Will, “Testing Machian effects in laboratory and space experiments,” in Ref. 1, pp. 365–386.
33.
Reference 24.
This content is only available via PDF.
© 2003 American Association of Physics Teachers.
2003
American Association of Physics Teachers
AAPT members receive access to the American Journal of Physics and The Physics Teacher as a member benefit. To learn more about this member benefit and becoming an AAPT member, visit the Joining AAPT page.
