We trace the historical appearance of Planck's constant in physics, and we note that initially the constant did not appear in connection with quanta. Furthermore, we emphasize that Planck's constant can appear in both classical and quantum theories. In both theories, Planck's constant sets the scale of atomic phenomena. However, the roles played in the foundations of the theories are sharply different. In quantum theory, Planck's constant is crucial to the structure of the theory. On the other hand, in classical electrodynamics, Planck's constant is optional, since it appears only as the scale factor for the (homogeneous) source-free contribution to the general solution of Maxwell's equations. Since classical electrodynamics can be solved while taking the homogenous source-free contribution in the solution as zero or non-zero, there are naturally two different theories of classical electrodynamics, one in which Planck's constant is taken as zero and one where it is taken as non-zero. The textbooks of classical electromagnetism present only the version in which Planck's constant is taken to vanish.

1.
M.
Planck
,
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, translated by
F.
Gaynor
(
Philosophical Library
,
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,
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), p.
35
.
2.
The historical information is taken from the following sources:
T. S.
Kuhn
,
Black-Body Theory and the Quantum Discontinuity 1894-1912
(
Oxford U.P.
,
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,
1978
);
A.
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, translated by C. W. Nash (
MIT Press
,
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,
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);
M. J.
Klein
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,”
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(
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108
;
M. J.
Klein
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Thermodynamics and quanta in Planck's work
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S. R.
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and
M.
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(
AIP
,
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,
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), pp.
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302
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3.
See, for example, Ref. 2,
M.
Klein
, History, p.
297
.
4.
M.
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,
S.-B.
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,
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(
1899
).
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See, for example, Ref. 2,
A.
Hermann
, p.
13
.
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See, for example, Ref. 2.
A.
Hermann
, p.
14
.
7.
M.
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2
,
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(
1900
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See, for example, Ref. 2,
T.
Kuhn
, pp.
34
36
.
9.
See, for example, Ref. 2,
A.
Hermann
, p.
17
.
10.
See, for example, Ref. 2,
M.
Klein
, Philosopher, pp.
91
92
.
11.

We are using Gaussian units.

12.
See, for example,
D. J.
Griffiths
,
Introduction to Electrodynamics
, 4th ed. (
Pearson
,
New York
,
2013
), Sec. 10.2.1, Eq. (10.26); or
L.
Eyges
,
The Classical Electrodynamic Field
(
Cambridge U.P.
,
New York
,
1972
), p.
186
, Eqs. (11.45) and (11.46); or
J. D.
Jackson
,
Classical Electrodynamics
, 3rd ed. (
John Wiley & Sons
,
New York
,
1999
), p.
246
, Eq. (6.48); or
A.
Zangwill
,
Modern Electrodynamics
(
Cambridge U.P.
,
2013
), pp.
724
725
, Eqs. (20.57) and (20.58); or
A.
Garg
,
Classical Electromagnetism in a Nutshell
(
Princeton U.P.
,
Princeton, NJ
,
2012
), p.
204
, Eqs. (54.16) and (54.17).
13.
H. B. G.
Casimir
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51
,
793
795
(
1948
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14.
M. J.
Sparnaay
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Measurement of the attractive forces between flat plates
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Physica (Amsterdam)
24
,
751
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(
1958
);
S. K.
Lamoreaux
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Demonstration of the Casimir force in the 0.6 to 6μm range
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Phys. Rev. Lett.
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,
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4549
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H. B.
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V. A.
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R. N.
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D. J.
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F.
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Quantum mechanical actuation of microelectromechanical systems by the Casimir force
,”
Science
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1941
1944
(
2001
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[PubMed]
G.
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G.
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[PubMed]
15.
T. H.
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,”
Phys. Rev. D
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790
808
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T. H.
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Any classical description of nature requires classical electromagnetic zero-point radiation
,”
Am. J. Phys.
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1163
1167
(
2011
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See also
D. C.
Cole
and
Y.
Zou
, “
Quantum mechanical ground state of hydrogen obtained from classical electrodynamics
,”
Phys. Lett. A
317
,
14
20
(
2003
);
A review of the work on classical electromagnetic zero-point radiation up to 1996 is provided by
L.
de la Pena
and
A. M.
Cetto
,
The Quantum Dice—An Introduction to Stochastic Electrodynamics
(
Kluwer Academic
,
Dordrecht
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).
17.
T. W.
Marshall
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Random electrodynamics
,”
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T. W.
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,”
Proc. Camb. Phil. Soc.
61
,
537
546
(
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).
18.

Author's personal correspondence with the American Journal of Physics.

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