It is shown that the correct expressions for the momentum and kinetic energy of a particle moving at high speed were already implicit in physics going back to Maxwell. The demonstration begins with a thought experiment of Einstein by which he derived the inertial equivalence of energy, independently of the relativity postulates. A simple modification of the same experiment does the rest.

1.
Feynman gave an extremely concise pedagogical derivation of the momentum of light:
Richard P.
Feynman
,
Robert
Leighton
, and
Matthew
Sands
,
The Feynman Lectures on Physics
(
Addison-Wesley
,
Reading, MA
,
1963
), Vol.
1
, Chap. 34, pp.
10
11
.
2.
Albert
Einstein
, “
The principle of conservation of motion of the center of gravity and the inertia of energy
,”
Ann. Phys. (ser. 4)
20
,
627
633
(
1906
).
English translation in
The Collected Papers of Albert Einstein, The Swiss Years: Writings, 1900–1909
, translated by Anna Beck (
Princeton U.P.
,
Princeton, NJ
,
1989
), Vol.
2
, pp.
200
206
.
3.
A 1905 thought experiment of Einstein, involving the emission of oppositely directed pulses of light from a free body, also apparently establishes the mass equivalent of energy independently of the relativity postulates. Feigenbaum and Mermin offer a purely mechanical version in which the light pulses are replaced by particles:
Mitchell J.
Feigenbaum
and
N.
David Mermin
, “
E = mc2
,”
Am. J. Phys.
56
(
1
),
18
21
(
1988
). Their version relies on the relativistic velocity addition formula, which does derive from the relativity postulates.
4.
A. P.
French
,
Special Relativity
(
Norton
,
New York
,
1968
), pp.
16
29
.
5.
More rigorously, the recoil speed and light travel time are V=E/(Mδm)c,t=(Lδs)/c where δs=Vt, so the condition of stationary center of mass, (Mδm)δs=δm(LVt), can be written as (Mδm)Vt=δmct. Dividing through by t and substituting for V, we find δm = E/c2 as before.
6.
Max
Von Laue
, “
Inertia and energy
,” in
Albert Einstein: Philosopher-Scientist
, 3rd ed., edited by
P. A.
Schilpp
(
Open Court
,
London
,
1970
), pp.
503
533
.
7.
Reference 3, pp.
20
22
.
8.
William C.
Davidon
, “
Consequences of the inertial equivalence of energy
,”
Found. Phys.
5
(
3
),
525
541
(
1975
).
9.
J. M.
Levy Leblond
, “
What is so special about relativity?
,” in
Group Theoretical Methods in Physics
, edited by
A.
Janner
 et al, Lecture Notes in Physics 50 (
Springer
,
Verlag
,
1976
);
J. M.
Levy Leblond
What if Einstein had not been there? A Gedankenexperiment in science history
,” in
Proceedings of the 24th International Colloquium on Group Theoretical Methods in Physics
, Paris, July, 2002, edited by
J. P.
Gazeau
, et al
(
Institute of Physics
,
London
,
2003
), pp.
173
182
.
10.
Adel F.
Antippa
, “
Inertia of energy and the liberated photon
,”
Am. J. Phys.
44
(
9
),
841
844
(
1976
).
11.
Eugene
Feenberg
, “
Inertia of energy
,”
Am. J. Phys.
28
(
6
),
565
566
(
1960
).
12.
Reference 3, pp.
27
28
.
13.
Examples: Ref. 1, Chap. 16, pp. 6–7; Ref. 3, pp. 169–175;
Edwin F.
Taylor
and
John
Archibald Wheeler
,
Spacetime Physics
(
W. H. Freeman
,
New York
,
1966
), pp.
103
109
;
See also
P. C.
Peters
, “
An alternate derivation of relativistic momentum
,”
Am. J. Phys.
54
(
9
),
804
808
(
1986
) for a variant of the approach.
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