1 4 8 D O C . 1 5 2 O R I G I N O F G E O M A G N E T I C F I E L D

152. “On an Obvious Hypothesis about the Origin of the

Geomagnetic Field and Its Experimental Refutation”[1]

[Berlin, before 15 November

1923][2]

Attempts arising out of relativity theory to understand gravitation and electricity

as essentially alike lead to the suspicion that direct physical meaning is attached to

electromagnetic

potentials.[3]

Cf., e.g., H. Weyl, Space Time Matter, 5th edition,

§40, eq. (86). A. Einstein, Proc. of the Pruss. Acad. of S[ciences], XVII, 1923, eqs.

(6) and (15). Neglecting the influence of gravitation, field equations for an elec-

tron-free space of the

form[4]

… (1)

result, where fν are the components of

the[5]

electromagnetic four-potential. β is a

constant of unknown quantity, which, according to Maxwell’s theory, vanishes. Ac-

cording to the theory, in empty space there is, hence, an apparent charge and current

density that is proportional to the negatively taken scalar, i.e., vector potential. This

consequence, given the present state of our physical knowledge, does not exactly

inspire great confidence in the theory’s physical significance. Equations (1), how-

ever, lead to a simple explanatory possibility for that part of the Earth’s magnetic

field whose axis coincides with the Earth’s rotational axis.

In order to examine this, we supplement equations (1) with a phenomenological

term ρν that expresses the mean ion and ion-current density at the given place, such

that they take the form

…(2).

We thus have to distinguish between corpuscular spatial-charge density and

current density, embodied by the electrons or ions, and an (apparent) continuous

“spatial-charge density”[6]

fν βfν =

fν βfν ρν –=