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 –=