During much of the 20th century it was widely believed that one of the significant insights of special relativity was “relativistic mass.” Today there are two schools on that issue: the traditional view that embraces speed-dependent “relativistic mass,” and the more modern position that rejects it, maintaining that there is only one mass and it's speed-independent. This paper explores the history of “relativistic mass,” emphasizing Einstein's public role and private thoughts. We show how the concept of speed-dependent mass mistakenly evolved out of a tangle of ideas despite Einstein's prescient reluctance. Along the way there will be previously unrevealed surprises (e.g., Einstein never derived the expression for “relativistic mass,” and privately disapproved of it).
REFERENCES
1.
L.H. Greenberg, Physics with Modern Applications (W.B. Saunders Co., Philadelphia, 1978), p. 456. Similarly, Marshall Burns, Modern Physics for Science and Engineering (Harcourt Brace Javanovich Publishers, New York, 1988), p. 103 calls Eq. (1) “Einstein's mass equation.”
2.
H. Semat, Introduction to Atomic and Nuclear Physics (Rinehart & Co., New York, 1958), p. 46.
3.
Typical of the many articles that erroneously claim that Einstein derived the expression for is
Ling
Tsai
, “The relation between gravitational mass, inertial mass, and velocity
,” Am.J Phys.
54
, 340
–342
(April 1986
).4.
Walter Isaacson, Einstein (Simon & Schuster, New York, 2007), p. 130. Ronald Clark, Einstein: The Life and Times (The World Pub. Co., New York, 1971), p. 100.
5.
Max Jammer, Concepts of Mass in Contemporary Physics and Philosophy (Princeton University Press, Princeton, 2000), p. 42 states that Einstein's first paper “introduced the notion of relativistic mass,” which Jammer earlier defined as ; it certainly did not do that. This is misleading even though Jammer goes on to point out that the expression is “not in its later accepted form.”
6.
For a translation of Kaufmann's 1901 paper, see Henry Boorse and Lloyd Motz, The World of the Atom (Basic Books, New York, 1966), Vol. I, p. 502.
7.
Max Jammer, Concepts of Mass in Classical and Modern Physics (Dover Publications, New York, 1997), p. 136.
8.
Edmund Whittaker, A History of the Theories of Aether & Electricity Vol. 2 (Dover Publications, New York, 1989), p. 53, footnote 1. Lorentz's “transverse mass” is expressible as , but that's a far cry from being a statement of the direction-independent relativistic mass. That these two different ideas have the same mathematical form is no coincidence; the former helped convince people to accept the latter.
9.
We should not overlook that these early electron theories all had significant flaws. The analyses of both Abraham and Lorentz incorporated the aether. Both treated the electron as having a significant size and a particular charge distribution.
10.
P. S.
Faragó
and L.
Jánossy
, “Review of the experimental evidence for the law of variation of the electron mass with velocity
,” Nuovo cimento
5
, 1411
–1436
(1957
).11.
G.N.
Lewis
, “A revision of the fundamental laws of matter and energy
,” Phil. Mag.
16
, 705
–717
(LIX Nov. 1908
).G. N.
Lewis
and R. C.
Tolman
, “The principle of relativity, and non-Newtonian mechanics
,” Phil. Mag.
18
, 510
–523
(LVII 1909
).R.C.
Tolman
, “Note on the derivation from the principle of relativity of the fifth equation of the Maxwell-Lorentz theory
,” Phil. Mag.
21
, 296
(1911
).R.C.
Tolman
, “Non-Newtonian mechanics, the mass of a moving body
,” Phil. Mag.
23
, 375
–380
(XXXIII 1912
).12.
Max Born, Einstein's Theory of Relativity (Dover Publications, New York, 1962).
13.
Wolfgang Pauli, Theory of Relativity (Pergamon Press, New York, 1958).
14.
The only public place where it might appear Einstein came close to articulating anything resembling “relativistic mass” is in The Evolution of Physics by A. Einstein and L. Infeld (Simon and Schuster, New York, 1938), p. 205. This popularization was undertaken to make some money for Infeld, who was one of Einstein's near-destitute European protégés working at Princeton. The book was conceived by Infeld, who knew that it would surely succeed if Einstein's name was on it. It was written (in English) exclusively by Infeld, though he did discuss it periodically with Einstein (in German). Infeld, like most physicists of the day, seems to have embraced “relativistic mass“; nonetheless, that term is never used in the book. The exposition very cautiously tiptoes around the idea of inertia as if Einstein was watching over Infeld's shoulder as he wrote it. According to Infeld's autobiography, Einstein probably never even read the book.
15.
Lev B.
Okun
, “The concept of mass
,” Phys. Today
42
(6
), 31
–36
(1989
). See p. 32 for a photograph of Einstein's handwritten letter to Lincoln Bennett, 19 June 1948.
This content is only available via PDF.
© 2009 American Association of Physics Teachers.
2009
American Association of Physics Teachers
AAPT members receive access to The Physics Teacher and the American Journal of Physics as a member benefit. To learn more about this member benefit and becoming an AAPT member, visit the Joining AAPT page.