The mass-energy relation is, according to Einstein, the most important result of the special theory of relativity.1 Many educators have called for the inclusion of more such “modern” (post-1900) physics in our introductory courses.2 Although we frequently treat as a simple numerical relation, useful for solving nuclear physics problems, it is more important to discuss what this equation means. What can it tell us about the nature of energy and matter? Does rest mass arise purely from the energy of force fields? It seems not to be widely recognized that the answer to this last question is now known, at least for 90% of the mass of ordinary matter, to be “yes.”
REFERENCES
1.
Albert Einstein, “What is the theory of relativity?” The London Times, Nov. 28, 1919, reprinted in The Collected Papers of Albert Einstein, Vol. 7, The Berlin Years: 1918–1921, English translation (Princeton University Press, Princeton, 2002), p. 100; see p. 103.
2.
Ruth
Howes
, “Modern physics—Guest editorial
,” Phys. Teach.
38
, 73
(Feb. 2000
);Rainer
Mueller
and Hartmut
Wiesner
, “Teaching quantum mechanics on an introductory level
,” Am J. Phys.
70
, 200
–209
(March 2002
);Dean A.
Zollman
, N. Sanjay
Rebello
, Kirsten
Hogg
, “Quantum mechanics for everyone
,” Am. J. Phys.
70
, 252
–259
(March 2002
);Jay M.
Pasachoff
, “What should students learn?
” Phys. Teach.
39
, 381
–382
(Sept. 2001
);Conor
Henderson
, “Putting the fizz back into physics
,” Phys. World
11
(9
), 15
–16
(Sept. 1998
);C. H.
Holbrow
et al., “Modernizing introductory physics
,” Am. J. Phys.
63
, 1078
–1090
(Dec. 1995
);Robert Resnick, “Retrospective and prospective,” in Conference on the Introductory Physics Course, edited by Jack Wilson (Wiley, New York, 1997), p. 3;
Art
Hobson
, “Enlivening introductory physics with SETI
,” Phys. Teach.
39
, 436
–441
(Oct. 2001
);Art
Hobson
, “Teaching quantum theory in the introductory course
,” Phys. Teach.
34
, 202
–209
(April 1996
).3.
For an especially clear discussion of other aspects of the mass-energy relation, see
Ralph
Baierlein
, “Teaching An exploration of some issues
,” Phys. Teach.
29
, 170
–175
(March 1991
).4.
Eric Mazur, Peer Instruction (Prentice Hall, Upper Saddle River, NJ, 1997).
5.
Einstein insisted that fields are real. See Albert Einstein and Leopold Infeld, “The reality of the field,” in The Evolution of Physics (Simon and Schuster, New York, 1938), pp. 148–156; on p. 151 we find: “The electric and magnetic field, or in short, the electromagnetic field is, in Maxwell's theory, something real. The electric field is produced by a changing magnetic field, quite independently, whether or not there is a wire to test its existence; a magnetic field is produced by a changing electric field, whether or not there is a magnetic pole to test its existence.”
6.
Much of the information in this section comes from
Frank
Wilczek
's article “Mass without mass I: Most of matter
,” Phys. Today
52
, 11
(Nov. 1999
).7.
John A. Wheeler, Geometrodynamics (Academic Press, New York, 1962), p. 25.
8.
H.A. Lorentz, reprinted in A. Einstein et al., The Principle of Relativity (Dover, New York, 1952), p. 24.
9.
The Standard Model of Fundamental Particles and Interactions Chart (Contemporary Physics Education Project, 1999).
10.
See Ref. 6.
11.
Steven Weinberg, quoted in Heinz Pagels' The Cosmic Code (Bantam Books, New York, 1983), p. 239.
12.
Further discussion can be found in the author's textbook, Physics: Concepts and Connections, 3rd ed. (Prentice Hall, Upper Saddle River, NJ, 2003).
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