9780192806727.pdf

248 RELATIVITY, THE GENERAL THEORY

of a wire. A fixed solenoid is placed coaxially around the cylinder. The iron is

magnetized by an alternating current run through the solenoid. The change AM

of the magnetic moment in the z direction induces a change A/ in the hidden

angular momentum due to the electron motions such that AM = —eg&J/2mc.

Angular momentum conservation demands that A/ be compensated for. Thus the

iron cylinder as a whole acquires an angular momentum — A/, since this body

may be considered rigid. The resulting angular velocity Aa would be given by

egQAa = 2mcAM if only the magnetic force were acting on the cylinder (Q being

the moment of inertia in the z direction). The true Aa results from the interplay

between the magnetic driving force and the restoring force due to the attachment

of the cylinder to the wire. It is clear that the experiment serves to determine g if

the various other magnetic and mechanical parameters are known.

There are many complications. The cylinder has to be hung precisely on its

axis; the magnetic field has to be symmetric with respect to the cylinder axis; it

also has to be uniform in order to give a simple meaning to AM; the effect of the

earth's magnetic field needs to be compensated for; there may be effects due to the

interaction of the alternating current with some remanent magnetization of the

cylinder. No wonder that the cylinder underwent 'the most adventurous motions'

[E33]. Einstein and de Haas showed that many of these difficulties could be over-

come by an ingenious trick, the resonance method. The cylinder is hung by means

of a rather rigid glass wire. The mechanical oscillation frequency of this system

is matched with the frequency of the alternating current. The resulting resonance

makes it much easier to separate the desired effect from perturbing influences.*

Einstein and de Haas took two sets of measurements. They managed to obtain

agreement with their calculated value g = 1 by singling out one of these two sets.

Six years later—after it was clear that g = 1 is not the right value—de Haas

described what they had done.** 'The numbers which we found [for g] are 1.45

and 1.02. The second value is nearly equal to the classical value [g = 1] so that

we thought that experimental errors had made the first value too large.... We

did not measure the field of the solenoid; we calculated it.... We did not measure

the magnetism of the cylinder, either; we calculated or estimated it. All this is

stated in our original memoir. These preliminary results seemed satisfactory to us,

and one can easily understand that we were led to consider the value 1.02 as the

better one ...' [Hla]. I am not aware of a similar confession by Einstein.

This section would not be complete without a few remarks about the transition

to the modern era. It is now known that ferromagnetism is almost purely a spin

* Additional information was obtained by measuring not only at resonance but also around resonance.

The many technical details of the measurement not discussed here can be found in Barnett's article

in the Reviews of Modern Physics [Bl].

**I express the answers in terms of g, thereby slightly changing the wording of de Haas.