The equivalence of mass m and rest-energy E0 is one of the great discoveries of all time. Despite the current wisdom, Einstein did not derive this relation from first principles. Having conceived the idea in the summer of 1905 he spent more than 40 years trying to prove it. We briefly examine all of Einstein’s conceptual demonstrations of E0=mc2, focusing on their limitations and his awareness of their shortcomings. Although he repeatedly confirmed the efficacy of E0=mc2, he never constructed a general proof. Leaving aside that it continues to be affirmed experimentally, a rigorous proof of the mass-energy equivalence is probably beyond the purview of the special theory.

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1912
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20.
Reference 3. See also
A. P.
French
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311
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Reference 13,
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54
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On the special theory of relativity
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1912
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) and “rest-mass” (p.
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32.
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David
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705
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,
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(
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For a different approach, see
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53.
W.
Pauli
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;
Max
Born
,
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(
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,
New York
,
1962
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1920
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54.
Francisco
Flores
, “
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(
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Also see Ref. 13,
Wallace
Kantor
, and Ref. 51,
David
Topper
and
Dwight
Vincent
.
55.
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A.
Einstein
, p.
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.
56.
Reference 28,
A.
Einstein
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228
.
57.
Reference 28,
A.
Einstein
, p.
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.
58.
“The notion of ‘material point’ is fundamental for mechanics. If now we seek the mechanics of a bodily object which itself cannot be treated as a material point—and strictly speaking every object ‘perceptible to our senses’ is of this category….”
Albert
Einstein
,
Out of My Later Years
(
Philosophical Library
,
New York
,
1950
) p.
72
. Also see p.
100
where he discusses “mass points with invariable mass” as fundamental to Newtonian mechanics.
59.
This expression as written appeared on the blackboard during Einstein’s talk (see Ref. 51,
David
Topper
and
Dwight
Vincent
) but not in his paper.
60.
Ruth W.
Chabay
and
Bruce A.
Sherwood
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Modern mechanics
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Am. J. Phys.
72
(
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439
445
(
2004
) (These authors write, “consider a positron and electron each of mass m initially at rest far from each other. The (relativistic) energy of the two-particle system is 2mc2, with no additive constant possible (otherwise the four-momentum would not transform properly).”
61.
Albert
Einstein
, “
An elementary derivation of the equivalence of mass and energy
,”
Technion Yearbook
5
,
16
17
(
1946
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62.
Einstein used the phrase “light complex” in the June
1905
paper (Ref. 2). There he was considering electromagnetic plane waves. Here the term seems to correspond to a narrow pulse or localized wave train that could be absorbed completely by a finite object, something that could not happen with plane waves that have unlimited wavefronts.
63.
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
);
Also see
Saul
Dushman
, “
Mass-energy relation
,” G. E. Review, 6–13 October
1944
, reproduced in
Special Relativity Theory, Selected Reprints
(
AIP
,
New York
,
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), pp.
20
25
.
64.
S.
Rainville
,
J. K.
Thompson
,
E. G.
Myers
,
J. M.
Brown
,
M. S.
Dewey
,
E. G.
Kessler
, and
D. E.
Pritchard
, “
A direct test of E=mc2
,”
Nature (London)
438
,
1096
1097
(
2005
). Their experiment established that E0=mc2 “holds to a level of at least 0.00004%.”
65.
G. J.
Aubrecht
 II
, “
Comment on ‘Apparatus to measure relativistic mass increase’
,”
Am. J. Phys.
72
(
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),
970
971
(
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);
L. B.
Okun
, “
Putting to rest mass misconceptions
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Phys. Today
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(
5
),
14
, 115, 117 (
1990
).
66.
“[I]t appears to be outside the scope of special relativity to prove that c2mγ is the available (as distinct from conventional) energy of a mass m.”
J.
Ehlers
,
W.
Rindler
, and
R.
Penrose
, “
Energy conservation as the basis of relativistic mechanics II
,”
Am. J. Phys.
35
,
995
997
(
1965
).
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