The Gyromagnetic Ratio (a synopsis of part II of Peter Galison’s book How Experiments
End)
Galison’s depiction of the Gyromagnetic ratio experiments illustrates well some of the
historical and philosophical issues which were raised by the shift from macrophysics to
microphysics. As Jed Buchwald has written many English physicists of the mid 19th
century believed in a macrophysical approach which tried to avoid models and theories of
the inner workings of matter as far as possible (or perhaps rather tried to avoid being tied
down to any particular model). In particular they were suspicious of the atomic model of
matter precisely because it obliged the physicist to depend for his analysis of his
experiments on interpretations of the behavior of microscopic entities which he could not
see or interact with directly. Those who favored an atomic or microscopic approach, on
the other hand, valued it because it permitted them, so they claimed, to apply the same
Newtonian laws of physics to all natural phenomena. Ultimately the macroscopic
physicists lost out, as we know, but they were proved right in one important respect. The
rules of the macroscopic world turned out not to be the Newtonian rules of mechanics
after all. Thus as physics became more and more an examination of the microscopic
world of atoms and sub-atomic particles it obliged physicists to examine entities which
they could not see, guided by theories which they knew might give out on them at any
moment.
A classic example of the tension between microscopic and macroscopic approaches is the
subject of ferromagnetism. When, in the early 19th century, it was shown that electric
current generated magnetic fields, Andre-Marie Ampere proposed that magnetized
materials must contain some form of electric current, small charges of some kind which
were circulating in the material. Thus all magnetic phenomena could be unified under the
theory that they were all the products of electric currents. The discovery of the electron in
the late 19th century, and the subsequent development of an atomic model which
hypothesized orbiting electrons with the atom, naturally encouraged early 20th century
physicists to wonder if these electronic orbits were the very current loops Ampere had
imagined.
How could one hope to demonstrate the existence of these current loops? Maxwell had
already pointed out in the mid-19th century that if such current loops existed, and if the
charged particles moving in them were ponderable, that is to say had gravitational mass,
or weight, then there must be some angular momentum associated with their motion.
Thus it was possible to imagine that if one magnetized a material, but presumably getting
all of the electron orbits to line up in the same way so that each tiny magnetic field added
up to create a macroscopic field, that this was creating an angular momentum associated
with a specific direction of rotation of this tiny particles (the electrons) within the
material. The principle of conservation of angular momentum demanded that the total
angular momentum of the iron (or other) material remain zero, so the iron itself must
being to rotate in the opposite direction to the rotation of the electrons. The effect would
be tiny, because of the small mass of the electrons, but by the 1910s it was possible on
theoretical grounds to estimate the size of the expected effect and to believe that the
technology existed to measure it.
Theoretical calculations suggested that if L was the angular momentum associated with
the electron orbit generating the magnetic field, and M was the associated magnetic
moment of the current loop, then L/M = 2 m/e where m was the mass of the orbiting
electron and e its charge. The aim of the various experiments described was the show the
existence of the electronic current loops by showing that this equation actually held good,
which was accomplished by measurements which would yield determinations of L and M
(the ratio e/m having been established by prior experiments). The fly in the ointment
arose primarily because of the following two discoveries:
1. It is not actually the orbit of the electron which generates the current loop. It is now
believed that the magnetic fields themselves encourage this orbits to line up so as to
oppose each other, not so as to reinforce each other. Instead the phenomenon of
ferromagnetism is believed to be due to the spin or rotation of the electrons which can,
because of subtle quantum mechanical effects, line up to reinforce each other.
2. The spin of the electron turns out to ½. This unexpected result demanded a new way of
writing the above formula. One now writes g L/M = 2 m/e where g is believed to be close
to 2 (g is equal to the inverse of the spin of the particle producing the magnetic field).
Thus these experiments became determinations of g, which ultimately confounded the
original theoretical prediction that g=1.
This spin has no classical analogue. Classically one expects spin, so defined, to be an
integer number. An object with a spin of 1 has no symmetry so that one has to rotate it
through a full 360 degrees before it has the same appearance as one began with. Objects
with higher symmetry than this can be rotated through 180 degrees, or 90, or some other
value less than 360 and resume their initial appearance. An object with spin ½, like an
electron, has less symmetry than this! When one rotates it through 360 degrees it does not
resume its original appearance. One must rotate it through 720 degrees to achieve this.
Note how these experiments began with the expectation that one could use the
microscopic picture of matter to explain macroscopic phenomena (ferromagnetism) in
terms of the basic laws of Newtonian mechanics applies to microscopic particles, and
ended by overthrowing those same Newtonian laws, in so far as they applied to
microscopic particles. For instance a classical claim that the electron was possessed of
spin would naturally lead one to ask the question, what is the physical size of the
electron, its radius, which would determine how fast it would have to be rotating to
generate the observed angular momentum. But physicists today still treat the electron as a
point mass and do not inquire as to its physical size. Thus a research program, the
microscopic world view, which began as an attempt to use the established Newtonian
laws of physics as a window through which to observe and describe the underlying
structure of matter, has ended with the overthrow of those Newtonian laws, and the
ultimate abandoning of the effort to visualize the microscopic world.
Galison’s story follows physicists such as Einstein through a series of experiments which
are carried out at the frontier of measurability for the technology available to them. As
Galison emphasizes their objective is to screen out various effects which might disguise
the phenomenon they are looking for. To do so it would be nice to be able determine
when the experiment is working properly by checking if it measuring the desired quantity
correctly. But if one does not know the answer in advance, how does one know when this
has occurred? The problem is compounded by theoretical uncertainty. The Einstein-De
Haas experiments are considered a classic explain of stopping the experiment when the
theoretical expectation had been met. Galison shows that the actual practice of
experiment is much messier and less tractable than normative theories of how science is
done would tend to portray it.
Without going into the gory detail of the struggles of the experimenters, there efforts can
be described as for the most part concerned with the difficulty that if they magnetized
their iron it was likely to interact with nearby fields, such as the Earth’s magnetic field to
produce forces greater than those there were trying to measure. The solution, which
became increasingly common as 20th century physics progressed was to operate “near
zero” by preventing the magnetization of the iron bar as they went. Thus they would hope
that the unwanted external interactions would remain small, enabling them to detect the
torque on the rod produced by the spinning electron within.