First I provide some history of how the equation $E=mc2$ arose, establish what “mass” means in the context of this relation, and present some aspects of how the relation can be understood. Then I address the question, Does $E=mc2$ mean that one can “convert mass into energy” and vice versa?

1.
The Collected Papers of Albert Einstein
, edited by
John Stachel
,
David C.
Cassidy
,
Jürgen Renn
, and
Robert Schulmann
(
Princeton U. P.
, Princeton, NJ,
1989
), Vol.
2
, “
The Swiss Years: Writings, 1900–1909
,” pp.
311
314
.
2.
Reference 1, pp.
275
306
.
3.

The word inertia denotes an object’s (or a system’s) reluctance to undergo a change in velocity. Inertia is distinct from momentum. For example, a golf ball exhibits a “reluctance to undergo a change in velocity” even when at rest on the tee. That’s why one has to whack it with a golf club to send it down the fairway.

4.

Inertia can be given an operational definition. For example, if a mass spectrometer uses a “velocity filter” in the sense that only particles of a specific velocity make it through a region of crossed electric and magnetic fields and then magnetic deflection at low speed, the outcome is a measurement of the particle’s rest mass, that is, its inertia when it is accelerated from rest. Thus inertia can be given an operational meaning and one that is independent of the notion of energy.

5.
In the most fundamental physics—quantum field theory—the expression for energy is derived from a Lagrangian for fields and is expressed in terms of those fields. Thus, I maintain, energy is a property—an attribute—of fields (and particles). To be sure, other views exist. In his
Concepts of Mass in Classical and Modern Physics
(
Harvard U. P.
, Cambridge, MA,
1961
), Max Jammer writes of inertial mass and energy as “the same physical substratum” (p.
188
) and writes of the “reification of energy” (p. 173).
6.
Reference 1, pp.
413
427
.
7.
Reference 1, p.
425
.
8.
Ralph
Baierlein
, “
Teaching $E=mc2$: An exploration of some issues
,”
Phys. Teach.
29
,
170
175
(
1991
). The derivation uses the notion of relativistic mass, but the limit of vanishing speed yields Eq. (4).
9.
Ralph
Baierlein
,
Newton to Einstein: The Trail of Light
(
Cambridge U. P.
, New York,
1992
), pp.
236
269
, and
Ralph
Baierlein
,
Newton to Einstein: The Trail of Light
(
Cambridge U. P.
, New York),pp.
319
325
.
10.
Reference 1, p.
428
.
11.
For example,
Wolfgang
Pauli
,
Theory of Relativity
(
Pergamon
, New York,
1958
), p.
125
(in conjunction with note 146 on p. 86).
12.
Albert
Einstein
, “
Autobiographical Notes
,” in
Albert Einstein: Philosopher-Scientist
, edited by
Paul
Arthur Schilpp
(
Tudor
, New York,
1949
), p.
60
.
13.
The Collected Papers of Albert Einstein
, edited by
Martin J.
Klein
,
A. J.
Kox
,
Jürgen
Renn
, and
Robert
Schulmann
(
Princeton U. P.
, Princeton, NJ,
1995
), Vol.
4
, “
The Swiss Years: Writings, 1912–1914
,” pp.
97
98
.
14.

A calculation that one person views as showing that inertia and energy are necessarily proportional another person may view as indicating that inertia and energy are identical. The difference in viewpoints may not be as great as it seems. The two camps would agree, I believe, that—most fundamentally—the connection between inertia and energy follows from the stress-energy tensor.

15.

Rest energies figure prominently in the discussion that follows, and so a detailed example is in order. Consider a hydrogen atom whose center of mass is at rest. The atom’s rest energy consists of the electrostatic potential energy (of the electron-proton interaction), the kinetic energy of motions relative to the center of mass (primarily the electron’s kinetic energy), and the rest energies of the electron and proton. According to the standard model, the electron’s rest energy cannot be dissected into distinct contributions. The proton’s rest energy could be described in terms of the rest energies of the constituent quarks, their motion (internal to the proton), and their interaction energy.

16.
J. D.
Cockcroft
and
E. T. S.
Walton
, “
Experiments with high velocity positive ions. II. The disintegration of elements by high velocity protons
,”
Proc. R. Soc. London, Ser. A
137
,
229
242
(
1932
).
17.
Roger H.
Stuewer
, “
Mass-energy and the neutron in the early thirties
,”
Sci. Context
6
,
195
238
(
1993
).
Stuewer points out that Cockcroft and Walton intended their comparison to support their inferred value of the kinetic energy, not to test Einstein’s relation (whose validity they assumed). Kenneth T. Bainbridge published a test based on their experiment in “The equivalence of mass and energy,”
Phys. Rev.
44
,
123
(
1933
), and found agreement within the probable error, which was approximately 3%.
18.
This Month in Physics History: Energy and mass are equivalent
,”
APS News
14
(
4
),
2
(
2005
). The anonymous author writes, “Meanwhile, in Cambridge, England, the reverse process was seen in 1932: the conversion of mass into energy. With their apparatus, John Cockcroft and E. T. S. Walton ….” Such statements are common in books and articles; in Sec. III D, I cite some other instances.
19.
Simon
Rainville
et al, “
A direct test of $E=mc2$
,”
Nature (London)
438
,
1096
1097
(
2005
). Despite the title, a careful reading shows that the authors tested the increment equation $ΔE0=Δm0c2$. Their impressive accuracy is the best yet achieved: a few parts in ten million.
20.
Because the number of protons and neutrons remains constant in nuclear fission, one can understand the energy release in terms of changes in potential energy, kinetic energy, and the energy of electromagnetic radiation. There is no need to invoke $E=mc2$. The analysis for nuclear fission is developed in an elementary fashion in Ref. 9, pp.
248
252
and 256–260.
21.
Reference 18. The author writes, “
…Iréne and Frédéric Joliot-Curie obtained direct photographic evidence of the conversion of energy into mass
.”
22.

The relativistic mass $mrel$ is defined as the proportionality factor between momentum $p$ and velocity $v:p=mrelv$. The relativistic mass may depend on the object’s speed.

23.
Max
Jammer
,
Concepts of Mass in Contemporary Physics and Philosophy
(
Princeton U. P.
, Princeton, NJ,
2000
), pp.
77
82
.
24.
Max
von Laue
, “
Inertia and energy
,” in
Albert Einstein: Philosopher-Scientist
, edited by
Paul
Arthur Schilpp
(
Tudor
, New York,
1949
), pp.
503
533
.
25.
Reference 11, p.
217
.
26.
Edwin F.
Taylor
and
John
Archibald Wheeler
,
Spacetime Physics
, 2nd ed. (
Freeman
, New York,
1992
), pp.
237
243
, and
Edwin F.
Taylor
and
John
Archibald Wheeler
,
Spacetime Physics
, 2nd ed., (
Freeman
, New York,
248
249
.
27.
Julian
Schwinger
,
Einstein’s Legacy: The Unity of Space and Time
(
Scientific American Books
, New York,
1986
), pp.
98
111
.
28.
Reference 1, p. 465.
The New Quotable Einstein
, edited by
Alice
Calaprice
(
Princeton U. P.
, Princeton, NJ,
2005
), p.
245
. Also at $⟨$www.aip.org/history/einstein/voice1.htm$⟩$.
29.
Reference 27 provides an illuminating example. Schwinger starts with “rest energy” (p.
98
), slips to “rest-mass energy” (p. 99), and then converts “rest mass” to kinetic energy (pp. 105, 108, and 110–111).
30.
Der Grosse Brockhaus, Brockhaus’ Konversations-Lexikon
(
Eberhard Brockhaus
1952
), Vol.
1
, p.
352
.
31.
Reference 13, p.
482
.
32.
Reference 13, p.
575
.
33.
The seven different characterizations that I display in this paragraph come from Ref. 13, pp.
304
305
(twice),
322
488
, and
585
, respectively.