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