Concepts of mass in contemporary physics and philosophy

Concepts of Mass in Contemporary Physics and Philosophy

Volumn , Issue , 2009, Pages 1-180

  Jammer, Max ^a  

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References (459)

1. D. Lynden-Bell, "Inertia," in O. Lahav, E. Terlevich, and D. J. Terlevich, eds., Gravitational Dynamics (Cambridge, Mass.: Cambridge University Press, 1996), p. 235.
2. Harvard University Press, Cambridge, Mass., 1961; republished in 1997 by Dover Publications, Mineola, New York.
3. I. Newton, Philosophiae Naturalis Principia Mathematica (London: J. Streater, 1687, 1713, 1726), p. 1;
4. Isaac Newton's Mathematical Principles of Natural Philosophy and His System of the World (Berkeley: University of California Press, 1934), p. 1.
5. W. T. Padgett, "Problems with the Current Definitions of Mass," Physics Essays 3, 178-182 (1990).
6. H. A. Kramers, statement at the Princeton Bicentennial Conference on the Future of Nuclear Energy, 1946, in K. K. Darrow, ed., Physical Science and Human Values (Princeton: Princeton University Press, 1947), p. 196.
7. In Aristotelian physics the term "mechanics" or mhcanikh' (te' cnh), derived frommh'coV (contrivance), meant the application of an artificial device "to cheat nature," and was therefore not a branch of "physics," the science of nature. "When we have to produce an effect contrary to nature . . . we call it mechanical." Cf. the pseudo-Aristotelian treatise Mechanical Problems (847 a 10).
8. "C'est à cette science où les mouvements sont considérés en eux-m̂emes . . . j'ai donné le nom de cinématique, de ki'nhma, mouvement." A.-A. Ampère, Essai sur la philosophie des sciences (Paris: Bachelier, 1834), p. 52.
9. M. Jammer, "Cinematica e dinamica," in Saggi su Galileo Galilei (Florence: G. Barbèra Editore, 1967), pp. 1-12.
10. E. V. Huntington, "Bibliographical Note on the Use of the Word Mass in Current Textbooks," The American Mathematical Monthly 25, 1-15 (1918).
11. H. C. Ohanian, Gravitation and Spacetime (New York: Norton, 1973), p. 17.
12. For the history of the notion of "electromagnetic mass" see chapter 11 in M. Jammer, Concepts of Mass in Classical and Modern Physics (Cambridge, Mass.: Harvard University Press, 1961), referred to henceforth as COM.
13. See the beginning of chapter 4.
14. Chapters 2-6 of COM.
15. Beginning of chapter 5 of COM.
16. R. S.Westfall, "The Problem of Force in Galileo's Physics," in C. L. Golino, ed., Galileo Reappraised (Berkeley: University of California Press, 1966), pp. 67-95.
17. H. Weyl, "Philosophie der Mathematik und Naturwissenschaft," in R. Oldenbourg, ed., Handbuch der Philosophie (Munich: Oldenbourg, 1927). Philosophy of Mathematics and Natural Science (Princeton: Princeton University Press, 1949), p. 139.
18. Weyl, Philosophy of Mathematics and Natural Science, p. 139.
19. See, e.g., chapter 8 of COM.
20. See, e.g., chapter 5 in M. Jammer, Concepts of Space (Cambridge: Harvard University Press, 1954, 1969; enlarged edition, New York: Dover, 1993).
21. E. Mach, Die Mechanik in ihrer Entwicklung (Leipzig: Brockhaus, 1883, 1888, 1897, 1901, 1904, 1908, 1912, 1921, 1933); The Science of Mechanics (La Salle, Ill.: Open Court, 1893, 1902, 1919, 1942, 1960), chapter 2, section 3, paragraph 7. In his Die Principien der Wärmelehre (Leipzig: Barth, 1896, 1900, 1919) Mach called Newton's definition of mass "scholastisch."
22. For further details see chapter 8 in COM.
23. P.Volkmann, Erkenntnistheoretische Grundzüge der Naturwissenschaften (Leipzig: Teubner, 1910), p. 138.
24. R. Thiele, "Zur Charakteristik von Mach's Erkenntnislehre," in Abhandlungen zur Philosophie und ihrer Geschichte, vol. 45 (Halle: Niemeyer, 1914), p. 101.
25. P.W. Bridgman, The Logic of Modern Physics (New York: Macmillan, 1927, 1961), p. 25.
26. See chapter 8 of COM.
27. Bridgman, Logic of Modern Physics, pp. 102-103.
28. C. G. Pendse, "A Note on the Definition and Determination of Mass in Newtonian Mechanics," Philosophical Magazine 24, 1012-1022 (1937). See also References 27 and 28 in chapter 8 of COM.
29. V. V. Narlikar, "The Concept and Determination of Mass in Newtonian Mechanics," Philosophical Magazine 27, 33-36 (1938).
30. Mach, The Science of Mechanics, chapter 2, section 7, paragraph 5.
31. Mach, The Science of Mechanics, chapter 2, section 5, paragraph 6.
32. Mach, The Science of Mechanics, chapter 2, section 7, paragraph 5.
33. M. Bunge, "Mach's Critique of Newtonian Mechanics," American Journal of Physics 34, 585-596 (1966); reprinted in J. Blackmore, Ernst Mach-A Deeper Look (Dordrecht: Kluwer, 1992), pp. 243-261.
34. R. Wahsner and H.-H. von Borzeszkowski, epilogue to their new edition of Mach's Die Mechanik in ihrer Entwicklung (Berlin: Akademie Verlag, 1988), p. 600.
35. L. Boltzmann, "Über die Grundprinzipien und Grundgleichungen der Mechanik," in Populäre Schriften (Leipzig: J. A. Barth, 1905), p. 293.
36. A. Kamlah, "The Problem of Operational Definitions," inW. Salmon and G.Wolters, eds., Logic, Language, and the Structure of Scientific Theories (Konstanz: Universitätsverlag Konstanz, 1996), pp. 171-189.
37. A. Koslow, "Mach's Concept of Mass: Program and Definition," Synthese 18, 216-233 (1968).
38. P. A. Goodinson and B. L. Luffman, "On the Definition of Mass in Classical Physics," American Journal of Physics 53, 40-42 (1985).
39. R. Carnap, An Introduction to the Philosophy of Science (New York: Basic Books, 1966), pp. 103-104.
40. See chapter 9 of COM.
41. G.W. Mackey, Mathematical Foundations of Quantum Mechanics (New York: Benjamin, 1963), chapter 1.
42. J. D. Sneed, The Logical Structure of Mathematical Physics (Dordrecht: Reidel, 1971)
43. W. Stegmüller, Probleme und Resultate derWissenschaftstheorie und analytischen Philosophie (Vienna: Springer-Verlag, 1973), vol. 2, part 2.
44. F. P. Ramsey, The Foundations of Mathematics and Other Logical Essays, edited by R. B. Braithwaite (London: Kegan, Paul, Trench, Turner, 1931), pp. 260-261.
45. For details see, e.g., R. Tuomela, Theoretical Concepts (Vienna: Springer-Verlag, 1973), pp. 57-68.
46. See, e.g., Carnap, An Introduction to the Philosophy of Science, p. 249. Another example, soon to be discussed, is P. Lorenzen's protophysical definition of mass.
47. A. Kamlah, "Zur Systematik der Massendefinitionen," Conceptus 22, 69-82 (1988).
48. The only exception known to the present author is the (unpublished) study "Mechanik ohne Masse" (1985) by Rudolf Opelt of the Technische Hochschule in Bremen, Germany.
49. G. Kirchhoff, Vorlesungen über Mechanik (Leipzig: J. A. Barth, 1876, 1897).
50. H. Hertz, Die Prinzipien der Mechanik in neuem Zusammenhang dargestellt (Leipzig: J. A. Barth, 1894); The Principles of Mechanics Presented in a New Form (New York: Dover, 1956).
51. A. S. Sant'Anna, "An Axiomatic Framework for Classical Particle Mechanics without Force," Philosophia Naturalis 33, 187-203 (1996).
52. J.C.C. McKinsey, A. C. Sugar, and P. Suppes, "Axiomatic Foundations of Classical Particle Mechanics," Journal of Rational Mechanics and Analysis 2, 253-272 (1953).
53. P. Suppes, Introduction to Logic (New York: Van Nostrand, 1957), pp. 294-295.
54. J.C.C. McKinsey, "On the Independence of Undefined Ideas," Bulletin of the American Mathematical Society 41, 291-256 (135).
55. E.W. Beth, "On Padoa's Method in the Theory of Definition," Koninklijke Nederlandse Akademie van Wetenschappen, Proceedings of the Science Section 56, Series A, Mathematical Sciences, 330-339 (1953); Indagationes Mathematicae 15, 330-339 (1953).
56. A. Tarski, "Einige methodologische Untersuchungen über die Definierbarkeit der Begriffe," Erkenntnis 5, 80-100 (1936);
57. "Some Methodological Investigations on the Definability of Concepts," in A. Tarski, Logic, Semantics, Metamathematics (Oxford: Clarendon Press, 1956), pp. 296-319.
58. J. Dorling, "The Eliminability of Masses and Forces in Newtonian Particle Mechanics: Suppes Reconsidered," British Journal for the Philosophy of Science 28, 55-57 (1977).
59. H.-J. Schmidt, "A Definition of Mass in Newton-Lagrange Mechanics," Philosophia Naturalis 30, 189-207 (1993).
60. H. v. Helmholtz, "Über die physikalische Deutung des Princips der kleinsten Wirkung," Journal f ür die reine und angewandte Mathematik 100, 137-166, 213-222 (1886).
61. P. Havas, "The Range of Application of the Lagrange Formalism" Nuovo Cimento (Supp.) 5, 363-388 (1957).
62. See chapter 9 of COM.
63. A. Kamlah, "Two Kinds of Axiomatization of Mechanics," Philosophia Naturalis 32, 27-46 (1995).
64. G. Böhme, Protophysik (Frankfurt a.M.: Suhrkamp Verlag, 1976); P. Janich, ed., "Protophysik heute," Philosophia Naturalis 22, 3-156 (1985).
65. B.Thüring, Die Gravitation und die philosophischen Grundlagen der Physik (Berlin: Duncke & Humblot, 1967), chapter 3.
66. P. Janich, "Ist Masse ein 'theoretischer Begriff'?," Journal for General Philosophy of Science 8, 303-313 (1977);
67. "Newton ab omni naevo vindicatus," Philosophia Naturalis 18, 243-255 (1981);
68. "Die Eindeutigkeit der Massemessung und die Definition der Trägheit," Philosophia Naturalis 22, 87-103 (1985);
69. "The Concept of Mass," in R. E. Butts and J. R. Brown, eds., Constructivism and Science (Dordrecht: Kluwer, 1989), pp. 145-162.
70. Hence the title "Newton ab omni naevo vidicatus" of Janich's 1981 essay, in analogy to Gerolamo Saccheri's 1733 work "Euclides ab omni naevo vindicatus."
71. A. Kamlah, "Die Bedeutung des d'Alembertschen Prinzips f ür die Definition des Kraftbegriffes," in W. Balzer and A. Kamlah, Aspekte der physikalischen Begriffsbildung (Braunschweig: Vieweg, 1979), pp. 191-217.
72. A. Kamlah, "Methode oder Dogma," Journal for General Philosophy of Science 12, 138-162 (1981).
73. F. Steinle,"Was ist Masse? Newton's Begriff der Materiemenge," Philosophia Naturalis 29, 94-118 (1992).
74. G. G. Stokes, "On the Steady Motion of Incompressible Fluids," Transactions of the Cambridge Philosophical Society 7, 439-455 (1842); Mathematical and Physical Papers, vol. 1 (Cambridge, U.K.: The University Press, 1880), pp. 1-16.
75. C. G. Darwin, "Notes on Hydrodynamics," Proceedings of the Cambridge Philosophical Society 49, 342-354 (1953).
76. For a rigorous proof see, e.g., L. M. Milne-Thomson, Theoretical Hydrodynamics (London: Macmillan, 1968), pp. 246-247.
77. B. Stewart, "On the Temperature Equilibrium of an Enclosure in Which There Is a Body in Visible Motion," Reports of the British Association for the Advancement of Science, Edinburgh 187, 45-47 (1871).
78. See chapter 11 in COM.
79. J. J. Thomson,"Onthe Electric and Magnetic Effects Produced by Motion of Electrified Bodies," Philosophical Magazine 11, 229-249 (1881).
80. For a modern derivation of equation (1.31) see, e.g.,W.K.H. Panofsky and M. Phillips, Classical Electricity and Magnetism (Reading, Mass.: Addison-Wesley, 1956), pp. 314-317;
81. J. Vanderlinde, Classical Electromagnetic Theory (New York: JohnWiley and Sons 1993), pp. 317-319.
82. M. Abraham, "Die Dynamik des Elektrons," Göttinger Nachrichten 1902, 20-41.
83. Abraham, "Die Dynamik des Elektrons," p. 24.
84. H. A. Lorentz, "Über die scheinbare Masse der Ionen," Physikalische Zeitschrift 2, 78-79 (1901).
85. H. A. Lorentz, The Theory of Electrons (Leipzig: Teubner, 1909, 1916; New York: Dover, 1952), p. 43.
86. H. Poincaré, "Sur la dynamique de l'électron," Rendiconti del Circolo Matematico di Palermo 21, 129-176 (1906); Oeuvres de Henri Poincaré, vol. 9 (Paris: Gauthier-Villars, 1954), pp. 494-550.
87. For details see, e.g., C. Kittel, Introduction to Solid State Physics (New York: JohnWiley and Sons, 1953, 1986), chapter 8.
88. For details see M. Jammer, The Conceptual Development of Quantum Mechanics (New York: McGraw-Hill, 1966; enlarged and revised edition, New York: American Institute of Physics, 1989), chapter 3.
89. J. R. Oppenheimer, "Note on the Theory of the Interaction of Field and Matter," Physical Review 35, 461-477 (1930).
90. See in this context M. Dresden, H. A. Kramers-Between Tradition and Revolution (New York: Springer-Verlag, 1987), chapter 16.
91. H. Bethe, "The Electromagnetic Shift of Energy Levels," Physical Review 72, 329-341 (1947); reprinted in J. Schwinger, ed., Selected Papers on Quantum Electrodynamics (New York: Dover, 1958), pp. 139-141.
92. See, e.g., S. Weinberg, The Quantum Theory of Fields (Cambridge: Cambridge University Press, 1995), chapter 12;
93. M. E. Peskin and D. V. Schroeder, An Introduction to Quantum Field Theory (Reading, Mass.: Addison-Wesley, 1995).
94. J. Collins, Renormalization (Cambridge: Cambridge University Press, 1985).
95. O. Darrigol, Les Débuts de la Théorie Quantique des Champs (Ph.D. Thesis, Université de Paris I, 1982);
96. S. Aramaki, "Formation of the Normalization Theory in Quantum Electrodynamics," Historia Scientiarum 32, 1-42 (1987), 36, 97-116 (1989), 37, 91-112 (1989).
97. P. Teller, "Three Problems of Renormalization," in H. R. Brown and R. Harré, ed., Philosophical Foundations of Quantum Field Theory (Oxford: Clarendon Press, 1998), pp. 73-89;
98. "Infinite Renormalization," Philosophy of Science 56, 238-257 (1989).
99. A. Einstein, "Zur Elektrodynamik bewegter Körper," Annalen der Physik 17, 891-921 (1905);
100. The Collected Papers of Albert Einstein (Princeton: Princeton University Press, 1989), vol. 2, pp. 276-306. English translation in the Princeton translation project (Princeton University Press, 1989), pp. 140-171; also in
101. A. Einstein, H. A. Lorentz, H. Minkowski, and H. Weyl, The Principle of Relativity (New York: Dover, 1952), pp. 35-65.
102. See chapter 11 of COM.
103. See, e.g., H. A. Lorentz, "Electromagnetic Phenomena in a System Moving with Any Velocity Smaller Than That of Light," Proceedings of the Academy of Sciences of Amsterdam 6, 809-832 (1904); reprinted in Einstein et al., The Principle of Relativity, pp. 11-34.
104. M. Planck, "Das Prinzip der Relativität und die Grundgleichungen der Mechanik," Verhandlungen der Deutschen Physikalischen Gesellschaft 4, 136-141 (1906); reprinted in: M. Planck, Physikalische Abhandlungen und Vorträge (Braunschweig: E. Vieweg, 1958), vol. 2, pp. 115-120.
105. G. N. Lewis and R. C. Tolman, "The Principle of Relativity and Non-Newtonian Mechanics," Philosophical Magazine 18, 510-523 (1909).
106. For details see chapter 12 of COM.
107. R. C. Tolman, "Non-Newtonian Mechanics: The Mass of a Moving Body," Philosophical Magazine 23, 375-380 (1912).
108. Tolman, Philosophical Magazine 23, 376 (1912).
109. R. C. Tolman, Relativity, Thermodynamics, and Cosmology (Oxford: Clarendon Press, 1934), pp. 43-45.
110. B. V. Landau and S. Sampanthar, "ANew Derivation of the Lorentz Transformation," American Journal of Physics 40, 599-602 (1972).
111. Lewis died in 1946, and Tolman in 1948. Only a few years after their deaths W. Macke showed in a remarkable but little-known paper, "Begr ündung der speziellen Relativitätstheorie aus der Hamiltonschen Mechanik," Zeitschrift f ür Naturforschung 7a, 76-78 (1952), that the Hamiltonian canonical formalism, which includes energy and time, leads to a velocity-dependent mass and, provided that the limiting velocity is identified with the velocity of light, to the Lorentz transformations in compliance with Tolman's program.
112. L. B. Okun, "The Concept of Mass (Mass, Energy, Relativity)," Uspekhi Fisicevskikh Nauk 158, 511-530 (1989).
113. Soviet Physics Uspekhi 32, 629-638 (1989).
114. "The Concept of Mass," Physics Today 42, 31-36 (June 1989).
115. M. Born, Die Relativitätstheorie Einsteins und ihre physikalischen Grundlagen (Berlin: J. Springer, 1920, 1922, 1964); Einstein's Theory of Relativity (New York: Dover, 1962, 1965), p. 269.
116. See equations (15) and (16) in chapter 12 of COM.
117. V. L. Ginzburg,"WhoDeveloped the Theory of Relativity, and How?," inV. A. Ugarov (ed.), Special Theory of Relativity (Moscow: Mir, 1979), p. 352.
118. J. Aharoni, The Theory of Relativity (Oxford: Clarendon Press, 1959), p. 140.
119. R.W. Brehme, "The Advantage of Teaching Relativity with Four-Vectors," American Journal of Physics 36, 896-901 (1968).
120. M.A.B. Whitaker, "Definition of Mass in Special Relativity," Physics Education 11, 55-57 (January 1976).
121. C. G. Adler, "Does Mass Really Depend onVelocity, Dad?," American Journal of Physics 55, 739-743 (1987).
122. F.W. Sears and M.W. Zemansky, University Physics (Reading, Mass.:Addison-Wesley, 1963, 1970, 1976, 1980, 1982).
123. E. F. Taylor and J. A. Wheeler, Spacetime Physics (San Francisco: Freeman, 1963, 1966); see in particular Table 14: Uses and abuses of the concept of mass, pp. 134-137.
124. "Putting to Rest Mass Misconceptions," Physics Today 43, 13-15, 115-119 (May 1990).
125. T. R. Sandin, "In Defense of Relativistic Mass," American Journal of Physics 59, 1032-1036 (1991).
126. R. A. Mould, Basic Relativity (New York: Springer-Verlag, 1994), p. 119.
127. R. P. Bickerstaff and G. Patsakos, "Relativistic Generalization of Mass," European Journal of Physics 16, 63-68 (1995).
128. A. S. Eddington, The Mathematical Theory of Relativity (Cambridge: Cambridge University Press, 1924, 1965), p. 30.
129. T. S. Kuhn, The Structure of Scientific Revolutions (Chicago: University of Chicago Press, 1962, 1970).
130. P. K. Feyerabend, Problems of Empiricism-Philosophical Papers, vol. 2 Cambridge: Cambridge University Press, 1981).
131. According to Feyerabend, Problems of Empiricism, "two theories will be called incommensurable when the meanings of their main descriptive terms depend on mutually inconsistent principles."
132. P. K. Feyerabend, "Problems of Empiricism," in R. G. Colodny, Beyond the Edge of Certainty (Englewood Cliffs, N.J.: Prentice-Hall, 1965), p. 169.
133. E. Eriksen and K. Vøyenli, "The Classical and Relativistic Concepts of Mass," Foundations of Physics 6, 115-124 (February 1976).
134. Eriksen and Vøyenli consider not only ordinary particles, i.e., so-called tardyons (with velocity u < c), but also luxons (u D c) and tachyons (u > c). As is well known, whether a tachyon is an incoming or an outgoing particle depends on the reference frame. We confine our discussion to tardyons.
135. Eriksen and Vøyenli, Foundations of Physics 6, 123-124 (February 1976).
136. Okun, Physics Today 42, 31-36 (June 1989).
137. H. E. Ives, "Derivation of the Mass-Energy Relation," Journal of the Optical Society of America 42, 540-543 (1952).
138. See, e.g., H. Arzeliès, Études Relativistes: Rayonnement et Dynamique du corpuscule chargé fortement accéléré (Paris: Gauthier-Villars, 1966), pp. 74-79;
139. A. Miller, Albert Einstein's Special Theory of Relativity (Reading, Mass.: Addison-Wesley, 1981), p. 377;
140. U. E. Schröder, Spezielle Relativitätsthoerie (Thun: H. Deutsch, 1981), p. 118;
141. K. J. Köhler, "Die Aequivalenz von Materie und Energie," Philosophia Naturalis 19, 315-341 (1982);
142. C. A. Zapffe, A Reminder on E D mc2 (Baltimore: CAZLab, n.d.), p. 46.
143. A. F. Antippa, "Variations on a Photon-in-a-Box by Einstein," UQTR-TH-8 (Quebec: Université du Québec à Trois-Rivières, May 1975), pp. 1-52.
144. A. Einstein, "Ist die Trägheit eines Körpers von seinem Energieinhalt abhängig?," Annalen der Physik 18, 639-641 (1905);
145. "Does the Inertia of a Body Depend upon Its Energy Content?," in A. Einstein, H. A. Lorentz, H. Minkowski, and H. Weyl, The Principle of Relativity (New York: Dover, 1952), pp. 69-71. The original paper is reprinted in The Collected Papers of Albert Einstein (Princeton: Princeton University Press, 1989), vol. 2, pp. 312-314; English translation in the translation project, also published by Princeton University Press, pp. 172-175 (document 24).
146. A. Einstein, "Die Masse eines Körpers ist ein Mass f ür dessen Energieinhalt," Annalen der Physik 18, 641 (1905).
147. A. Einstein, Annalen der Physik 17, 891-921 (1905). Collected Papers, vol. 2, pp. 276-306 (English translation, pp. 140-171). English translation also in Einstein et al., The Principle of Relativity, pp. 35-65.
148. M. Planck, "Zur Dynamik bewegter Systeme," Berliner Sitzungsberichte 1907, pp. 542-570;
149. Annalen der Physik 26, 1-34 (1908);
150. Physikalische Abhandlungen und Vorträge (Braunschweig: F. Vieweg, 1958), vol. 2, pp. 176-209.
151. M. Sachs, "On the Meaning of E D mc2," International Journal of Theoretical Physics 8, 377-383 (1973).
152. J. Stachel and R. Torretti, "Einstein's First Derivation of Mass-Energy Equivalence," American Journal of Physics 50, 760-763 (1932).
153. W. L. Fadner, "Did Einstein Really Discover 'E D mc2'?," American Journal of Physics 56, 114-122 (1988).
154. It would be a psychologically and methodologically interesting research project to compare Einstein's various derivations of the mass-energy relation, which are listed here in chronological order: (1) "Ist die Trägheit eines Körpers von seinem Energieinhalt abhängig?," Annalen der Physik 18, 639-641 (1905); Collected Papers of Albert Einstein (Princeton: Princeton University Press, 1989), vol. 2, pp. 312-314;
155. "Does the Inertia of a Body Depend upon Its Energy Content?," A. Einstein, H. A. Lorentz, H. Minkowski, and H. Weyl, The Principle of Relativity (London: Methuen, 1923; New York: Dover, 1952), pp. 67-71;
156. Collected Papers (English translations), vol. 2, pp. 172-174. (2) "Prinzip von der Erhaltung der Schwerpunktsbewegung und die Trägheit der Energie," Annalen der Physik 20, 627-633 (1906);
157. Collected Papers, vol. 2, pp. 360-366; "The Principle of Conservation of Motion of the Center of Gravity and the Inertia of Energy,"
158. Collected Papers, vol. 2, pp. 413-427; "On the Inertia of Energy Required by the Relativity Principle,"Collected Papers (English translations), vol. 2, pp. 238-251. (4) Section 14 in
159. "Über das Relativitätsprinzip und die aus demselben gezogenen Folgerungen," Jahrbuch der Radioaktivität und Elektronik 4, 411-462 (1907);
160. Collected Papers, vol. 2, pp. 433-484; "On the Relativity Principle and the Conclusions Drawn from It,"
161. Collected Papers (English translations), vol. 2, pp. 252-311; "Einstein's Comprehensive 1907 Essay on Relativity, Part II" (translation by H. M. Schwartz), American Journal of Physics 45, 811-817 (1977).
162. (unpublished) "Manuscript on the Special Theory of Relativity (1912-1914)," Collected Papers (1995), vol. 4, pp. 9-101;
163. "Elementary Derivation of the Equivalence of Mass and Energy," Bulletin of the American Mathematical Society 41, 223-230 (1935).
164. "An Elementary Derivation of the Equivalence of Mass and Energy," Technion Yearbook 5, 16-17 (1946); Concise derivations can also be found in his books (7) Über die spezielle und die allgemeine Relativitätstheorie (Braunschweig: F. Vieweg, 1917 and numerous later editions), section 15, as well as in (8) The Meaning of Relativity (Princeton: Princeton University Press, 1921) (4th edition, p. 45).
165. Even in his (almost) group-theoretical derivation of the Lorentz transformations, which he presented in his lectures on relativity at the University of Berlin, Einstein had to refer to the velocity of light. See "RelativitätsvorlesungWinter 1914-1915" in his Notebook, Collected Papers, vol. 6 (document 7), pp. 44-66, especially pp. 49-51.
166. Einstein, according to T. F. Jordan, intended originally to make use of his proposed notion of "light quanta" or "photons," as they were later called, as early as March 1905 but changed hismindbecause he thought that the idea of "light quanta" is"more revolutionary and less finished than relativity."
167. T. F. Jordan, "Photons and Doppler Effect in Einstein's Derivation of Mass Energy," American Journal of Physics 50, 559-560 (1982).
168. D. J. Steck and F. Rioux, "An Elementary Development of Mass-Energy Equivalence," American Journal of Physics 51, 461-462 (1983).
169. P. Langevin, "L'inertie de l'énergie et ses conséquences," Journal de Physique théorique et appliquée 3, 553-591 (1913); reprinted in Oeuvres Scientifique de Paul Langevin (Paris: CNRS, 1950), pp. 397-426.
170. A. Shadowitz, Special Relativity (Philadelphia: W. B. Saunders, 1968), p. 90.
171. J. Perrin, Les Éléments de la Physique (Paris: Albin Michel, 1929), pp. 380-391.
172. Y. Simon and N. Husson, "Langevin's Derivation of the Relativistic Expressions for Energy," American Journal of Physics 59, 982-987 (1991).
173. V. P. Srivastava, "A Simple Derivation of E D mc2," Physics Education 26, 214 (1991).
174. R. Baierlein, "Teaching E D mc2," The Physics Teacher 29, 170-175 (1991).
175. G. Le Bon, L'Évolution de la Matière (Paris: Flammarion, 1905). Letter from Le Bon to Einstein, dated June 17, 1922. Einstein Archive reel 43-311.
176. F. Hasenöhrl, "Zur Theorie der Strahlung in bewegten Körpern," Annalen der Physik 15, 344-376 (1904);
177. Wiener Sitzungsberichte 113, 1039-1051 (1904). "Zur Theorie der Strahlung in bewegten Körpern," Annalen der Physik 16, 589-592 (1905), which contains the correction m D 4V"0=3c2.
178. F. Lenard, "Vorbemerkung zu J. Soldner, Über die Ablenkung eines Lichtstrahls von seiner geradlinigen Bewegung durch Attraktion eines Weltk örpers, an welchem er nahe vorbeigeht," Annalen der Physik 65, 593-604 (1921).
179. "Dass aber jede Energiestr ömung Impuls mit sich f ührt, und dass umgekehrt aller Impuls auf Energiestr ömung beruht, diesen Gedanken konnte erst die Relativitätstheorie folgerichtig durchf ühren; denn erst sie räumte mit der ihr widersprechenden Newtonschen Dynamik grundsätzlich auf." M. von Laue, "Erwiderung auf Hrn. LenardsVorbemerkung zur Soldnerschen Arbeit von 1801," Annalen der Physik 66, 283-284 (1921).
180. M. von Laue, "Inertia and Energy" in P. A. Schilpp, ed., Albert Einstein: Philosopher-Scientist (Evanston, Ill.: Library of Living Philsophers, 1949), p. 524.
181. M. J. Feigenbaum and N. D. Mermin, "E D mc2," American Journal of Physics 56, 18-21 (1988).
182. N. D. Mermin, "Relativistic Addition of Velocities Directly from the Constancy of the Velocity of Light," American Journal of Physics 51, 1130-1131 (1983).
183. B. V. Landau and S. Sampanthar, "ANew Derivation of the Lorentz Transformation," American Journal of Physics 40, 599-602 (1972).
184. For bibliographical references up to 1964 see H. Arzeliès, Relativistic Kinematics (Oxford: Pergamon, 1966), pp. 80-82.
185. Important more recent group-theoretical derivations of (generalized) Lorentz transformations are: G. Süssmann, "Begr ündung der Lorentz-Gruppe allein mit Symmetrie-und Relativitätsannahman," Zeitschrift f ür Naturforschung 24a, 495-498 (1969);
186. V. Gorini and A. Zecca, "Isotropy of Space," Journal of Mathematical Physics 11, 2226-2230 (1970);
187. A. R. Lee and T. M. Kalotas, "Lorentz Transformations from the First Postulate," American Journal of Physics 43, 434-437 (1975);
188. J.-M. Levy-Leblond, "One More Derivation of the Lorentz Transformation," American Journal of Physics 44, 271-277 (1976).
189. W. Pauli, The Theory of Relativity (New York: Pergamon, 1958), p. 11.
190. For more details and a simple group-theoretical derivation of the (general) Lorentz transformations see M. Jammer, "Some Foundational Problems in the Special Theory of Relativity," in G. Toraldo di Francia, ed., Problems in the Foundations of Physics, Proceedings of the International School of Physics 'Enrico Fermi', Course LXXII (Amsterdam: North-Holland, 1979), pp. 202-236.
191. For the history of this effect, which dates back to at least 1708, see E. Whittaker, A History of the Theories of Aether and Electricity (London: Thomas Nelson, 1910, 1951), vol. 1, pp. 273-276.
192. A. Einstein, "Prinzip von der Erhaltung der Schwerpunktsbewegung und die Trägheit der Energie," Annalen der Physik 20, 627-633 (1906).
193. R. T. Smith, "Classical Origins of 'E D mc2'," Physics Education 27, 248-250 (1992).
194. Van Laue in P. A. Schilpp, ed., Albert Einstein, pp. 524-527.
195. A.T. Antippa, "Variations on a Photon-in-a-Box by Einstein," UQTR-TH-8, Université du Québec à Trois-Rivières, pp. 1-48;
196. "Inertia of Energy and the Liberated Photon," American Journal of Physics 44, 841-844 (1976).
197. See also the earlier survey on some of Einstein's derivations by W. Kantor, "Inertia of Energy," American Journal of Physics 22, 528-541 (1954). A thorough analysis of Einstein's 1906 and 1907 derivations as well as their elaborations by Planck and von Laue has also been given by A. I. Miller in his Albert Einstein's Special Theory of Relativity (Reading, Mass.: Addison-Wesley, 1981), pp. 353-367.
198. Van Laue in P. A. Schilpp, ed., Albert Einstein, pp. 524-527.
199. E. Feenberg, "Inertia of Energy," American Journal of Physics 28, 565-566 (1960).
200. M. Born, Die Relativitätstheorie Einsteins und ihre physikalischen Grundlagen (Berlin: J. Springer, 1922).
201. M. Born, Einstein's Theory of Relativity (New York: Dover, 1962), pp. 283-286.
202. C. J. Rigney and R. H. Biser, "Note on a Famous Derivation of E D mc2," American Journal of Physics 34, 623 (1966).
203. A. P. French, Special Relativity (New York: Norton, 1966;Wokingham, Berkshire, U.K.: Van Nostrand-Reinhold, 1968, 1984), pp. 27-28.
204. Antippa, UQTR-TH-8 and American Journal of Physics 44.
205. Antippa, American Journal of Physics 44, 844.
206. Einstein, Jahrbuch der Radioaktivität und Elektronik 4, 411-462.
207. R. A. Mould, Basic Relativity (New York: Springer-Verlag, 1994). See also W. G. Holladay, "The Derivation of Relativistic Energy from the Lorentz γ," and the references listed therein, American Journal of Physics 60, 281 (1992).
208. A. Einstein, "Elementary Derivation of the Equivalence of Mass and Energy," Bulletin of the American Mathematical Society 41, 223-230 (1935).
209. See also F. Flores's instructive essay "Einstein's 1935 Derivation of E D mc2," Studies in History and Philosophy of Modern Physics 29, 223-243 (1998). Chapter 5 of this essay contains a detailed analysis of Einstein's 1935 derivation of the mass-energy relation.
210. This substratum was dubbed "massergy" in chapter 13 of COM.
211. C. R. Eddy, "A Relativistic Misconception," Science 104, 303-304 (1946).
212. "Comments on 'A Relativistic Misconception,' " Science 104, 400-401 (1946).
213. E. F. Barker, "Energy Transformations and the Conservation of Mass," American Journal of Physics 14, 309-310 (1946).
214. J. W. Warren, "The Mystery of Mass-Energy," Physics Education 11, 52-54 (January 1976).
215. H. Bondi and C. B. Spurgin, "Energy Has Mass," Physics Bulletin 38, 62-63 (February 1987).
216. R. Peierls, "Mass and Energy," Physics Bulletin 38, 128 (1987).
217. A. Einstein, Bulletin of the American Mathematical Society 41, 223-230 (1935).
218. M. A. Leonov, Očerk dialektičeskogo materializma (Essay on Dialectical Materialism) (Moscow: Gosizdat, 1948), p. 39.
219. N. F. Ovčinnikov, "Massa i Energia," Prioda 11, 7-16 (1951); Ponjatje Massy i Energii (Moscow: Nauk, 1957); see also his commentary (pp. 231-246) in the Russian edition of the present author's book Ponjatje Massy v Klassičeskoj i Sovremennoj Fizika (Moscow: Progress, 1967), pp. 231-246.
220. M.Jammer, "Mass and Energy," in C. D. Kernig, ed., Marxism,CommunismandWestern Society-A Comparative Encyclopedia (Freiburg: Herder, 1971), pp. 365-373.
221. É. Meyerson, Identité etRéalité (Paris: Alcan, 1908); Identity and Reality (London: George Allan and Unwin, 1930; New York: Dover, 1962), chapter 4.
222. Lord Kelvin and P. G. Tait, Elements of Natural Philosophy (London: Collier, 1872), paragraph 186.
223. "Les poids des corps sont rigoureusement proportionnels à leur masses. . . . Ce fait expérimental est connu depuis long temps. Il nous est devenu tellement familier que nous finissons presque par confondre la masse avec le poids." C. L. de Freycinet, Essais sur la Philosophie des Sciences (Paris: Gauthier-Villars, 1896), p. 181.
224. H. Poincaré, Science etMéthode (Paris: Flammarion, 1908); Science and Method (London: Nelson, n.d.; New York: Dover, 1952), p. 235.
225. H. Bondi, "Negative Mass in General Relativity," Reviews of Modern Physics 29, 423-428 (1957).
226. An exception is H. C. Ohanian's Gravitation and Spacetime (New York: Norton, 1976, 1994) and his essay "What Is the Principle of Equivalence?," American Journal of Physics 45, 903-909 (1977).
227. K. Nordtvedt Jr., "Equivalence Principle for Massive Bodies, II: Theory," Physical Review 169, 1017-1025 (1968).
228. C. M. Will, "Theoretical Framework for Testing Relativistic Gravity, II: Parametrized Post-Newtonian Hydrodynamics and the Nordtvedt Effect," Astrophysical Journal 163, 611-628 (1971).
229. For details see C. M.Will, Theory and Experiment in Gravitational Physics (Cambridge: Cambridge University Press, 1981, 1991).
230. I. Ciufolini and J. A. Wheeler, Gravitation and Inertia (Princeton: Princeton University Press, 1995), ppp. 163168.
231. R. H. Dicke, "New Research on Old Gravitation," Science 129, 621-624 (1959).
232. See also R. H. Dicke, "Experimental Relativity," in C. DeWitt andW. DeWitt, eds., Relativity Groups and Topology (New York: Gordon and Breach, 1964), pp. 168
233. See, e.g., the widely used text by C. W. Misner, K. S. Thorne, and J. A. Wheeler, Gravitation (San Francisco: Freeman, 1973), pp. 1050
234. P. von der Muehll, ed., Epicuri Epistulae Tres (Letter 1, 61.6) (Stuttgart: Teubner, 1975), pp. 16 See also T. Lucretius, De Rerum Natura Libri Sex, book 2, verse 238-239.
235. Ioannis Philoponi in Aristotelis Physicorum Libros Quinque Posteriores Commentaria (Berlin: Reimer, 1888), ppp. 676684.
236. English translation in M. R. Cohen and I. E. Drabkin, A Source Book in Greek Science (New York: McGraw-Hill, 1948), ppp. 217231.
237. G. Galilei, Discorsi e dimostrazioni matematiche intorno à due nuove scienze (Leiden: Elsevir, 1638), pp. 107 Dialogues Concerning Two New Sciences (New York: Macmillan, 1914; New York: Dover, 1954), pp. 62
238. A. Chalmers, "Did Democritus Ascribe Weight to Atoms?" Australian Journal of Philosophy 75, 279-287 (1997).
239. According to Edward Hussey, Aristotle could be credited with having conceived WEP, as he interprets Physics VII, 5 (250 a et seq.) as saying that there exists "an 'inertial resistance' to action which is proportional to weight." E. Hussey, Aristotle's Physics (Oxford: Clarendon Press, 1983), pp. 133
240. "Der gl ücklichste Gedanke meines Lebens," A. Einstein, Grundgedanken und Methoden der Relativitätstheorie in ihrer Entwicklung dargestellt," unpublished manuscript, Pierpont Morgan Library, New York City; Einstein Archive, reel 2-070.
241. "Dieselbe Qualität des Körpers äussert sich je nach Umständen als 'Trägheit' oder als 'Schwere.' " A. Einstein, Über die spezielle und die allgemeine Relativitätstheorie (Braun-schweig: Vieweg, 1920, 1965), pp. 45 Relativity-The Special and the General Theory (London: Methuen, 1920, 1988), pp. 65
242. D. E. Dugdale, "The Equivalence Principle and Spatial Curvature," European Journal of Physics 2, 43-51 (1981).
243. K. Hentschel, "Einstein's Attitude Toward Experiments: Testing Relativity Theory 1907-1927," Studies in History and Philosophy of Science 23, 593-624 (1992).
244. J. Illy, "Einstein und der Eötvös-Versuch," Annals of Science 46, 417-422 (1989).
245. Letter from Einstein to W. Wien, dated July 10, 1912. Einstein Archive, reel 23-566.
246. See, e.g., S. Weinberg, Gravitation and Cosmology (New York: John Wiley and Sons, 1972), pp. 69 or Ciufolini and Wheeler, Gravitation and Inertia, pp. 14
247. Atheory of gravitation is complete if it allows the calculation of the detailed behavior of atoms in a gravitational field. It is self-consistent if different methods of calculating the prediction of an experiment yield the same result.
248. L. I. Schiff, "On Experimental Tests of the General Theory of Relativity," American Journal of Physics 28, 340-343 (1960).
249. A. P. Lightman and D. L. Lee, "Restricted Proof that theWeak Equivalence Principle Implies the Einstein Equivalence Principle," Physical Review D 8, 364-376.
250. A. P. Lightman, "The Equivalence Principle as a Foundation for Gravitation Theories," in P. Barker and E. G. Shugart, eds., After Einstein (Memphis, Tenn.: Memphis State University Press, 1981), ppp. 5765.
251. W. Whewell, "Demonstration that All Matter Is Heavy," Essay III in his The Philosophy of the Inductive Sciences (London: Parker, 1847; New York: Johnson Reprints, 1967), vol. 2, ppp. 624634.
252. C. G. Hempel and P. Oppenheim, "Studies in the Logic of Explanation," Philosophy of Science 15, 125-175 (1948);
253. C. G. Hempel, Aspects of Scientific Explanation and Other Essays in the Philosophy of Science (New York: Free Press, 1965).
254. A. Einstein, "Einfluss der Schwerkraft auf die Ausbreitung des Lichtes," Annalen der Physik 35, 898-908 (1911);
255. Collected Papers, vol. 3, ppp. 485496; "On the Influence of Gravitation on the Propagation of Light," in A. Einstein, H. A. Lorentz, H. Minkowski,and H. Weyl, The Principle of Relativity (London: Methuen, 1923; New York: Dover, 1952), ppp. 99108. Collected Papers (English translations), vol. 3, ppp. 379387.
256. A. Einstein, "Lichtgeschwindigkeit und Statik des Gravitationsfeldes," Annalen der Physik 38, 355-369 (1912);
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258. A. Pais, 'Subtle Is the Lord . . .' The Science and the Life of Albert Einstein (Oxford: Oxford University Press, 1982), pp. 195.
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260. Although originally not intended as a null experiment, the Michelson-Morley experiment soon played such a role, as Loyd Swenson Jr., showed in his The Ethereal Aether (Austin: University of Texas Press, 1972).
261. Letter from Einstein to F. C. Davenport, dated February 2, 1954, Einstein Archive, reel 17-198.
262. Letter from Einstein to W. Wien, dated July 10, 1912. Einstein Archive, reel 28-56.
263. A. Einstein and M. Grommer, Entwurfeiner verallgemeinerten Relativitätstheorie (Leipzig: Teubner, 1913);
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265. P. G. Roll, R. Krotkov, and R. H. Dicke, "The Equivalence of Inertial and Passive Gravitational Mass," Annals of Physics 26, 442-517 (1964).
266. V. B. Braginski and V. I. Panov, "Verification of the Equivalence of Inertial and Gravitational Mass," Zhurnal Eksperimentalnoi i Teoreticheskoi Fisiki 61, 873-879 (1971); Soviet Physics JETP 34, 463-466 (1972).
267. G. Smith, E. G. Adelberger, B. R. Heckel, and Y. Su, "Test of the Equivalence Principle for Ordinary Matter Falling Toward Dark Matter," Physical Review Letters 70, 123-126 (1993).
268. P. K. Chapman and A. J. Hanson, "An Eötvös Experiment in Earth Orbit," paper read at the Conference on Experimental Tests of Gravitational Theories, held at the California Institute of Technology, November 1970.
269. P. W. Worden and C.W.F. Everitt, "Tests of the Equivalence of Gravitational and Inertial Mass Based on Cryogenic Techniques," in B. Bertotti, ed., Experimental Gravitation, Course LVI, International School of Physics 'Enrico Fermi' (New York: Academic, 1974), ppp. 381402.
270. D. Bramanti, A. M. Nobili, and G. Catastini, "Test of the Equivalence Principle in a Non-Drag-Free Spacecraft," Physics Letters A 164, 243-254 (1992).
271. For details see the supplementary issue of Classical and Quantum Gravity 13 (No. 11A, November 1996), pp. A33-A206.
272. E. Fischbach, D. Sudarsky, A. Szafer, C. Talmadge, and S. H. Aronson, "Reanalysis of the Eötvös Experiment," Physical Review Letters 56, 3-6 (1986).
273. For details see section 3 of the Resource Letter MNG-1, edited by G. T. Gillies, "Measurements of Newtonian Gravitation," American Journal of Physics 58, 525-534 (1990);
274. E. Fischbach and C. Talmadge, "Six Years of the Fifth Force," Nature 356, 207-215 (1992);
275. A. Franklin, The Rise and Fall of the Fifth Force (New York: American Institute of Physics, 1993).
276. For a recent Eöt-Wash torsion balance experiment for testing WEP see G. L. Smith, "New Test of the Equivalence Principle," in J. Tran Than Van, G. Fontaine, and E. Hinds, eds., Particle Astrophysics, Atomic Physics and Gravitation (France: Editions Frontiers, Gifsur-Yvette, 1994), ppp. 419425.
277. V. Cavasinni, E. Iacopini, E. Polacco, G. Stefanini, "Galileo's Experiment on Free-Falling Bodies Using Modern Optical Techniques," Physics Letters A 116, 157-161 (1986).
278. T.M.Niebauer,M.P.McHugh,J. E. Faller, "GalileanTest for the Fifth Force," Physical Review Letters 59, 609-612 (1987).
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280. S. Carusotto, V. Cavasinni, A. Mordacci, F. Ferrone, E. Polacco, E. Iacopini, G. Stefanini, "Test of g Universality with a Galileo-Type Experiment," Physical Review Letters 69, 1722-1725 (1992).
281. A. H. Wapstra and G. J. Nijgh, "The Ratio of Gravitational to Kinetic Mass for the Constituents of Matter," Physica 21, 796-798 (1955).
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283. M. Haugan and C. M. Will, "Weak Interactions and Eötvös Experiments," Physical Review Letters 37, 1-4 (1976).
284. R. H. Dicke, "Remarks on the Observational Basis of General Relativity," in H.-Y. Chiu andW. F. Hoffmann, eds., Gravitation and Relativity (New York: Benjamin, 1964), ppp. 116.
285. R. H. Dicke, "Mach's Principle and Equivalence," in C. Møller, ed., Evidence for Gravitational Theories, Course XX, Proceedings of the International School of Physics 'Enrico Fermi' (New York: Academic, 1962), ppp. 149.
286. R. Baierlein, "Testing General Relativity with Laser Ranging to the Moon," Physical Review 162, 1276-1288 (1967).
287. K. Nordtvedt Jr., "Testing Relativity with Lunar Ranging of the Moon," Physical Review 170, 1186-1187 (1968). "La lecture de cet article fut pour moi le déclic dont j'avais besoin.Enquelques jours je réalisai que la télémétrie laser-Lune pouvait mesurer le rapport entre la masse gravitationelle et la masse inertielle de la Terre."
288. K. Nordtvedt, "La Lune au secours d'Einstein," La Recherche 295, 70-76 (1997).
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290. I. I. Shapiro, C. C. Counselman III, and R. W. King, "Verification of the Principle of Equivalence for Massive Bodies," Physical Review Letters 36, 555-558 (1976) (η= 0.001±0.015).
291. E. G. Adelberger, B.R. Heckel, G. Smith, Y. Su, and H. E. Swanson, "Eötvös Experiments, Lunar Ranging and the Strong Equivalence Principle, Nature 347, 261-263 (1990).
292. J. Müller, M. Schneider, M. Soffel, and H. Ruder, "Testing Einstein's Theory of Gravity by Analyzing Lunar Laser Ranging Data," Astrophysical Journal 382, L101-L103 (1991).
293. J. O. Dickey et al., "Lunar Laser Ranging: A Continuing Legacy of the Apollo Program," Science 265, 482-490 (1994) (η=-0.0005 ±0.0011).
294. J. G.Williams, X. X. Newhall, and J. O. Dickey, "Relativity Parameters Determined from Lunar Laser Ranging," Physical Review D 53, 6730-6739 (1996).
295. C. Brans and R. H. Dicke, "Mach's Principle and a Relativistic Theory," Physical Review 124, 925-935 (1961).
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298. I. Newton, Mathematical Principles of Natural Philosophy (Berkeley: University of California Press, 1934, 1947), ppp. 2021.
299. Newton, Mathematical Principles, ppp. 411412.
300. Damour, "The Problem of Motion," pp. 143
301. Newton, Mathematical Principles, pp. 412
302. Newton, Mathematical Principles, pp. 413
303. P. S. de Laplace, Traité deMécanique Céleste (Paris: Bachelier, 1825; New York: Chelsea Publishing, 1969), book 16, chapter 4, quotation on pp. 447
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305. I. Estermann, O. C. Simpson, and O. Stern, "The Free Fall of Atoms and the Measurement of the Velocity Distribution in a Molecular Beam of Cesium Atoms," Physical Review 71, 238-249 (1947).
306. F. C.Witteborn andW. M. Fairbank, "Experimental Comparison of the Gravitational Force on Freely Falling Electrons and Metallic Electrons," Physical Review Letters 19, 1019-1052 (1967).
307. L. Koester, "Verification of the Equivalence of Gravitational and Inertial Mass for the Neutron," Physical Review D 14, 907-909 (1976).
308. V. F. Sears, "On the Verification of the Universality of Free Fall by Neutron Gravity Refractometry," Physical Review D 25, 2023-2029 (1982).
309. Aristotle, The Physics, book 2, chapter 4, 255 b 14-17.
310. A. L. Lavoisier, Traité Élémentaire de Chimie (Paris: Cuchet, 1789).
311. J. Atterley (G. Tucker), Voyage to the Moon (New York: E. Bliss, 1827).
312. J. Verne, De la Terre à la Lune (Paris: Hetzel, 1865).
313. J. C. Maxwell, "A Dynamical Theory of the Electromagnetic Field," Philosophical Transactions of the Royal Society London 155, 459-512 (1865).
314. A. Schuster, "Potential Matter-A Holiday Dream," Nature 58, 367 (1898).
315. P.A.M. Dirac, "Quantised Singularities in the Electromagnetic Field," Proceedings of the Royal Society London A 133, 60-72 (1931).
316. H. Bondi, "Negative Mass in General Relativity," Reviews of Modern Physics 29, 423-428 (1957).
317. F. C.Witteborn andW. M. Fairbank, "Experiments to Determine the Force of Gravity on Single Electrons and Positions," Nature 220, 436-440 (1968).
318. For comments on these experiments see J. Audretsch, "Gravitation and Quantenmechanik," in J. Nitsch, J. Pfarr, and E.-W. Stachow, Grundlagenprobleme der modernen Physik (Mannheim: Bibliographisches Institut, 1981), ppp. 939;
319. M. M. Nieto and T. Goldman, "The Arguments Against 'Antigravity' and the Gravitational Acceleration of Antimatter," Physics Reports 205, 221-281 (1991).
320. Letter from Professor Torleif Ericson of CERN to the author, dated October 31, 1995.
321. J. Eades, R. Hughes, and C. Zimmermann, "Antihydrogen," Physics World 6, 44-48 (July 1993);
322. R. J. Hughes, "Fundamental Symmetry Tests with Antihydrogen," NuclearPhysics A 558, 605c-624c (1993);
323. G. Baur et al., "Production of Antihydrogen," Physics Letters B 368, 251-258 (1996).
324. A. Einstein, "Einfluss der Schwerkraft auf die Ausbreitung des Lichtes," Annalen der Physik 35, 898-908 (1911);
325. "On the Influence of Gravitation on the Propagation of Light" in Einstein, The Principle of Relativity, ppp. 97108.
326. P. Morrison, "Approximate Nature of Physical Symmetries," American Journal of Physics 26, 358-368 (1958).
327. F.Winterberg, "Remark Concerning the Gravitational Interaction of Matter and Anti-Matter," Il Nuovo Cimento 19, 186 (1961).
328. P. Thieberger, "On the Gravitational Mass of Antiparticles, the Gravitational Energy Shift of Spectral Lines, and the Principle of Equivalence," Nuovo Cimento 25, 688-689 (1965).
329. J. S. Bell, "Gravity," in P. Bloch, P. Pavlopoulos and R. Klapisch, eds., Fundamental Symmetries (New York: Plenum, 1987), ppp. 139.
330. M. M. Nieto and T. Goldman, "The Argument Against 'Antigravity' and the Gravitational Acceleration of Antimatter," Physics Reports 205, 221-281 (1991).
331. See also R. J. Hughes, "The Equivalence Principle," Contemporary Physics 34, 177-191 (1993).
332. Schiff, Proceedings National Academy 45, 79. See also L. I. Schiff, "Size of the Gravitational Mass of a Positron," Physical Review Letters 1, 254-255 (1958).
333. M. L. Good, "K2 0 and the Equivalence Principle," Physical Review 121, 311-313, (1961).
334. H. Dehnen and D. Ebner, "Derivation of the Principle of Equivalence for Antimatter," Foundations of Physics 26, 105-115 (1996).
335. B. Hoffmann, "Negative Mass," Science Journal (April 1965), 74-78; Perspectives in Geometry and Relativity (Bloomington: Indiana University Press, 1966), ppp. 176183.
336. J. P. Terletsky, "Masses propres positives, négatives et imaginaires," Le Journal de Physique et le Radium 23, 910-920 (1962); Paradoxes in the Theory of Relativity (New York: Plenum, 1968), ppp. 83115.
337. A. P. Lightman, W. H. Press, R. H. Price, and S. A. Teukolsky, eds., Problem Book in Relativity and Gravitation (Princeton: Princeton University Press, 1975), ppp. 81 379-385.
338. R. Forward, "The Power of Negative Matter," New Scientist 125, 54-56 (1990).
339. R. H. Price, "Negative Mass Can Be Positively Amusing," American Journal of Physics 61, 216-217 (1993).
340. L. Tsai, "The Relation Between Gravitational Mass, Inertial Mass, and Velocity," American Journal of Physics 54, 340-342 (1986).
341. N. Gauthier, "Equality of Gravitational and Inertial Mass in Special Relativity," American Journal of Physics 54, 873 (1986).
342. L. B. Kreuzer, "Experimental Measurement of the Equivalence of Active and Passive Gravitational Mass," Physical Review 169, 1007-1012 (1968).
343. For critical comments on the Kreuzer experiment see J. J. Gilvarry and P. M. Muller, Physical Review Letters 28, 1665-1669 (1972), and D. Morrison and H. A. Hill, Physical Review D 8, 2731-2733 (1973). That the Kreuzer experiment can also be interpreted as imposing a limit on the strength of any supposed intermediate-range "fifth" force, associated with baryon number, has been pointed out by D. A. Neufeld, "Upper Limit on Any Intermediate Force Associated with Baryon Number" Physical Review Letters 56, 2344-2346 (1986).
344. D. F. Bartlett and D. van Buren, "Equivalence of Active and Passive Gravitational Mass Using the Moon," Physical Review Letters 57, 21-24 (1986);
345. "Asymmetry of the Moon and the Equivalence of Active and Passive Gravitational Mass," paper presented at the 11th International Conference on General Relativity and Gravitation, Stockholm, Sweden, July 6-12, 1986, Abstracts, vol. 2, pp. 608
346. W. B. Bonnor, "Active and Passive Gravitational Mass of a Schwarzschild Sphere," Classical and Quantum Gravity 9, 269-274 (1992).
347. N. Rosen and F. I. Cooperstock, "The Mass of a Body in General Relativity," Classical and Quantum Gravity 9, 2657-2663 (1992).
348. L. Herrera and J. Ibañez, "TheWork Required to Build up a Schwarzschild Sphere," Classical and Quantum Gravity 10, 535-542 (1993).
349. See, e.g., A. Lightman,W. Press, R. Price, and S. Teukolsky, Problem Book in Relativity and Gravitation (Princeton: Princeton University Press, 1975), pp. 73
350. A noteworthy exception is an investigation of the relation between mi and ma, presented by Hans Adolph Buchdahl in his Seventeen Simple Lectures on General Relativity Theory (NewYork: JohnWiley and Sons, 1981), ppp. 102107, where for a certain distribution of matter it is claimed that the ratio mi/ma can reach a value as high as 1.641.
351. C. Brans and R.H. Dicke, "Mach's Principleanda Relativistic Theory of Gravitation," Physical Review 124, 925-935 (1961).
352. C. Brans, "Mach's Principle and a Relativistic Theory of Gravitation, II," Physical Review 125, 2195-2201 (1962).
353. P. G. Bergmann, "Comments on the Scalar-Tensor Theory," International Journal of Theoretical Physics 1, 25-36 (1968).
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356. H. C. Ohanian, "Inertial and Gravitational Mass in the Brans-Dicke Theory," Annals of Physics 67, 648-661 (1971).
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368. J. F. Donoghue and B. R. Holstein, "Aristotle Was Right: Heavier Objects Fall Faster," European Journal of Physics 8, 105-112 (1987).
369. R. B. Partridge and D. T. Wilkinson, "Isotropy and Homogeneity of the Universe from Measurements of the Cosmic Microwave Background," Physical Review Letters 18, 557-559 (1967);
370. R. B. Partridge, "The Primeval Fireball Today," American Scientist 57, 32-74 (1969);
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377. J. Pantaleone, A. Halprin, and C. N. Leung, "Neutrino Mixing due to a Violation of the Equivalence Principle," Physical Review D 47, R 4199-R 4202 (1993).
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379. S. S. Gershtein, F. P. Kuznetsov, andV. A.Ryabov, "The Nature of Neutrino Mass and the Phenomenon of Neutrino Oscillations," Physics-Uspkhi 40, 773-806 (1997).
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382. M. Riordan, "Massive Attack," New Scientist 161, 32-35 (1999).
383. P. W. Bridgman, The Logic of Modern Physics (New York: Macmillan, 1927), pp. 5
384. There was an attempt made "to express absolute mass in terms of purely kinematic quantities" by means of the invariant periodicity associated with physical de Broglie waves by J.W.G. Wignall in his "De Broglie Waves and the Nature of Mass," Foundations of Physics 15, 207-227 (1985).
385. For details see chapter 11 of COM.
386. E. Mach, The Science of Mechanics (La Salle, Ill.: Open Court, 1960), chapter 2, section 5, paragraph 7.
387. Mach, The Science of Mechanics, pp. 284
388. J. B. Barbour, Absolute or Relative Motion? (Cambridge: Cambridge University Press, 1989);
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390. A. Einstein, "Gibt es eine Gravitationswirkung, die der elektrodynamischen Induktionswirkung analog ist?," Vierteljahrsschrift f ür gerichtliche Medizin und öffentliches Sanitätswesen 44, 37-40 (1912);
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392. A. Einstein, "Lichtgeschwindigkeit und Statik des Gravitationsfeldes," Annalen der Physik 38, 355-369 (1912);
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394. As H. Dehnen, H. Hönl, and K. Westpfahl in their paper "Ein heuristischer Zugang zur allgemeinen Relativitätstheorie," Annalen der Physik 7, 360-406 (1960) [see equation (3.9) on pp. 380
395. R. d'E. Atkinson, in "General Relativity in Euclidean Terms," Proceedings of the Royal Society A 272, 60-78 (1963), subsequently showed, the correct equation is m0 D m.1 C 318=c2 0/
396. A. Einstein, "Zum gegenwärtigen Stande des Gravitationsproblems," Physikalische Zeitschrift 14, 1249-1262 (1913);"On the Present State of the Problem of Gravitation," Collected Papers, vol. 4, ppp. 487500.
397. Letter from Einstein to Mie, dated February 8, 1917, Einstein Archive, reel 17-220.
398. Letter from Einstein to Mie, dated February 22, 1917, Einstein Archive, reel 17-221.
399. See, e.g., E. Nagel, The Structure of Science (New York: Harcourt and Brace, 1961), ppp. 175178.
400. "DasG-Feld ist restlos durch die Massen derKörper bestimmt." A. Einstein, "Prinzipielles zur allgemeinen Relativitätstheorie," Annalen der Physik 55, 241-244 (1918).
401. A. Einstein, "Feldgleichungen der Gravitation," Sitzungsberichte der Preussischen Akademie der Wissenschaften 1915, pt. 2, ppp. 844847. Collected Papers (1966), vol. 6, ppp. 245248.
402. A. Einstein, "Kosmologische Betrachtungen zur allgemeinen Relativitätstheorie, Sitzungsberichte der Preussischen Akademie der Wissenschaften 1917, pt. 1, ppp. 142152;
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404. A. Einstein, The Meaning of Relativity, 4th ed. (London: Methuen, 1950), ppp. 9596.
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406. H.-H. von Borzeszkowski and R. Wahsner, "Mach's Criticism of Newton and Einstein's Reading of Mach: The Stimulating Role of Two Misunderstandings," in J. B. Barbour and H. Pfister, eds., Mach's Principle (Boston: Birkhäuser, 1995), ppp. 5864.
407. C. H. Brans, "Mach's Principle and the Locally Measured Gravitational Constant," Physical Review 125, 388-396 (1962).
408. For details see, e.g., H. Goenner, "Mach's Principle and Einstein's Theory of Gravitation," in R. S. Cohen and R. J. Seeger, eds., Ernst Mach-Physicist and Philosopher (Dordrecht: Reidel, 1970), ppp. 200215.
409. M. Reinhardt, "Mach's Principle-A Critical Review," Zeitschrift f ür Naturforschung 28a, 529-537 (1973).
410. D. J. Raine, "Mach's Principle and Space-Time Structure," Reports on Progress in Physics 44, 1151-1195 (1981).
411. H. Dambmann, "Die Bedeutung des Machschen Prinzips in der Kosmologie," Philosophia Naturalis 27, 234-271 (1990).
412. J. B. Barbour and H. Pfister, eds., Mach's Principle (Boston: Birkhäuser, 1995).
413. D. W. Sciama, "On the Origin of Inertia," Monthly Notices of the Royal Astronomical Society 113, 34-42 (1953), "Inertia," Scientific American 196, 99-109 (February 1957); The Unity of the Universe (New York: Doubleday, 1961).
414. W. Weber, "Elektrodynamische Maassbestimmungen über ein allgemeines Grundgesetz der elektrischen Wirkung," Leipziger Berichte 1846, ppp. 211378;Wilhelm Weber's Werke (Berlin: J. Springer, 1893), vol. 3, pp. 157 vol. 4, ppp. 479632.
415. B. Riemann, Schwere, Elektrizität und Magnetismus, published posthumously by K. Hattendorff (Hannover: C. Rümpler, 1880), pp. 334 An interesting application of Riemann's law of gravitation in the context of Mach's principle can be found in Hans-J ürgen Treder's Die Relativität der Trägheit (Berlin: Akademie-Verlag, 1972).
416. G. Holzmüller, "Über die Anwendung der Jacobi-Hamiltonschen Methode auf den Fall der Anziehung nach dem elektrodynamischen Gesetze von Weber," Zeitschrift f ür Mathematik und Physik 15, 69-91 (1870).
417. F. F. Tisserand, "Sur le mouvement des planètes au tour du Soleil, d'après la loi électrodynamique de Weber," Comptes Rendus 75, 760-763 (1872);
418. "Sur les mouvements des planètes, en supposant l'attraction représentée par l'une des lois électrodynamiques de Gauss ou de Weber," Comptes Rendus 110, 313-315 (1890).
419. M. Lévy, "Sur l'application des lois électrodynamiques au mouvement des planètes," Comptes Rendus 110, 545-551 (1890).
420. For other derivations of this analogy see C. Møller, The Theory of Relativity (Oxford: Clarendon, 1952, 1972), chapter 8, section 92;
421. Appendix in J. D. Nightingale, "Specific Physical Consequences of Mach's Principle," American Journal of Physics 45, 376-379 (1977).
422. H. Weyl, "How Far Can One Get with a Linear Field Theory of Gravitation in Flat Space-Time?," American Journal of Mathematics 66, 591-604 (1944).
423. Such a separate paper on the origin of inertia seems never to have been published. But see D.W. Sciama, "Retarded Potentials and the Expansion of the Universe," Proceedings of the Royal Society A 273, 484-495 (1963)
424. "The Physical Structure of General Relativity," Reviews of Modern Physics 36, 463-469 (1964).
425. W. Davidson, "General Relativity and Mach's Principle," Monthly Notices of the Royal Astronomical Society 117, 212-224 (1958).
426. Einstein, The Meaning of Relativity, pp. 97
427. For a simple derivation of this equation see J. D. Nightingale, "Specific Physical Consequences of Mach's Principle," American Journal of Physics 45, 376-379 (1977).
428. J. D. Nightingale, American Journal of Physics 45, 377.
429. R. H. Dicke, "The Many Faces of Mach," in H.-Y. Chiu and W. F. Hoffmann, eds., Gravitation and Relativity (New York: Benjamin, 1964), ppp. 121141.
430. Some critical references to Sciama's approach can be found as early as in C. Brans and R. H. Dicke, "Mach's Principle and a Relativistic Theory of Gravitation," Physical Review 124, 925-935 (1961).
431. A.K.T. Assis, "On Mach's Principle," Foundations of Physics Letters 2, 301-318 (1989);
432. see also his "Deriving Gravitation from Electromagnetism," Canadian Journal of Physics 70, 320-340 (1992).
433. A.K.T. Assis, "Changing the Inertial Mass of a Charged Particle," Journal of the Physical Society of Japan 62, 1418-1422 (1993).
434. Reference 28 and Reference 31 of chapter 10 in COM.
435. N. Rosen, "Mach's Principle and Mass in an Expanding Universe," Annals of Physics 35, 426-436 (1965).
436. Reference 97 in chapter 4.
437. Reference 98 in chapter 4.
438. S. Malin, "Masses and Spins in Curved Space-Time," Physical Review D 9, 3228-3234 (1974).
439. J. D. Bekenstein, "Are Particle Rest Masses Variable? Theory and Constraints from Solar System Experiments," Physical Review D 15, 1458-1468 (1977).
440. J. D. Bekenstein and A. Meisels, "General Relativity Without General Relativity," Physical Review D 12, 4378-4386 (1978).
441. P. W. Higgs, "Broken Symmetry, Massless Particles and Gauge Fields," Physics Letters 12, 132-133 (1964);
442. "Spontaneous Symmetry Breakdown Without Massless Bosons," Physical Review 145, 1156-1163 (1966).
443. See, e.g., R. Castmore and C. Sutton, "The Origin of Mass," New Scientist 145, 35-39 (1992).
444. Y. Nambu, "A Matter of Symmetry: Elementary Particles and the Origin of Mass," The Sciences 32 (May/June), 37-43 (1992).
445. J. LaChapelle, "Generating Mass Without the Higgs Particle," Journal of Mathematical Physics 35, 2199-2209 (1994).
446. M.J.G.Veltman, "The Higgs Boson," Scientific American 255 (November), 88-94 (1986).
447. "Jegliche träge Masse ist als ein Vorrat von Energie aufzufassen." A. Einstein, "Über das Relativitätsprinzip und die aus demselben gezogenen Folgerungen," Jahrbuch der Radioaktivität und Elektronik 7, 411-462 (1907); quotation on pp. 442 Collected Papers, vol. 2, ppp. 432488.
448. H. Dehnen, F. Ghaboussi, and J. Schröder, "Gravitational Interaction by the Higgs Field," Wissenschaftliche Zeitschrift der Friedrich-Schiller Universität Jena 1990, ppp. 4145.
449. H. Dehnen, H. Frommert, and F. Ghaboussi, "Higgs Field Gravity," International Journal of Theoretical Physics 29, 537-546 (1990).
450. H. Dehnen and E. Hitzer, "Spin-Gauge Theory of Gravitation with Higgs Field Mechanism," International Journal of Theoretical Physics 33, 575-592 (1994).
451. H. Dehnen, "The Higgs Field and Mach's Principle of Relativity of Inertia," in J. B. Barbour and H. Pfister, eds., Mach's Principle (Boston: Birkhäuser, 1995), ppp. 479488.
452. B. Haisch, A. Rueda, and H. E. Puthoff, "Inertia as a Zero-Point-Field Lorentz Force," Physical Review A 49, 678-694 (1994).
453. The existence of such a zero-point field was anticipated as early as 1912 byMaxPlanck in his article "Über die Begründung des Gesetzes der schwarzen Strahlung," Annalen der Physik 37, 642-656 (1912).
454. P.C.W. Davies, "Scalar Particle Production in Schwarzschild and Rindler Metrics," Journal of Physics A 8, 609-616 (1975).
455. W. G. Unruh, "Notes on Black-Hole Evaporation," Physical Review D 14, 870-892 (1976).
456. A. D. Sakharov, "Vacuum Quantum Fluctuations in Curved Space and the Theory of Gravitation," Soviet Physics-Doklady 12, 1040-1041 (1968).
457. B. Haisch, A. Rueda, and H. E. Puthoff, "Beyond E D mc2," The Sciences 24 (November/December), 26-31 (1994).
458. A. Rueda and B. Haisch, "Contribution to Inertial Mass by Reaction of the Vacuum to Accelerated Motion," Foundations of Physics 28, 1057-1108 (1998).
459. A. Einstein, Foreword, in M. Jammer, Concepts of Space (Cambridge, Mass.: Harvard University Press, 1954; 3rd. ed., New York: Dover, 1993), p. xvii.