D O C . 2 3 4 R E P O N S E T O A N D E R S O N 2 2 9
234. Response to a Comment by W. Anderson[1]
[Einstein 1924g]
Dated 15 April 1924
Published 30 June 1924
In: Astronomische Nachrichten 221, no. 5300 (1924): cols. 329–330.
It cannot be doubted that an electron gas would have to be optically equivalent
to a substance with a negative index of refraction, given the current state of our
knowledge, because it is equivalent to a substance of vanishingly small eigenfre-
quency.
For, from the equation of motion
of an electron of electric mass ε and ponderable mass , there follows for a sinu-
soidally oscillating process at frequency the equation
.
Taking into account that εx is the “moment” of an oscillating electron, one then ob-
tains for the polarization of an electron gas with n electrons per unit vol-
ume
.
From this it follows that the apparent dielectric constant is
.
is, in this case, the refractive index, consequently in any case smaller than 1.
Given this state of affairs, inquiring into the quantitative aspects is superfluous.
It should also be noted that a comparison between an electron gas and a metal is
impermissible because the “frictional force” at the basis of the elementary theory
of metals is lacking; the behavior of the latter is determined solely by the electric
field and by inertia.
Berlin, 15 April 1924. A.
Einstein.[2]
[col. 329]
εX μ
2x
dt2
d
=
μ
ν
εX 2πν)2μx –( =
p nεx =
p
ε2n
μ(
2πν)2]
[ ⁄ X ⋅ –= [col. 330]
D 1 4πp X ⁄ + 1
ε2n)
(
πμν2)
( ⁄ – = =
D