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
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-
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-
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.
εX 2πν)2μx –( =
p nεx =
[ ⁄ X ⋅ –= [col. 330]
D 1 4πp X ⁄ + 1
( ⁄ – = =