MOTION MOUNTAIN

what is light? 137
An object moving along the path A 1 B 2 C 3 D that is always oriented
perpendicular to the path (thus undergoing parallel transport) acquires a
rotation if the path is three-dimensional: the geometric phase.
The same happens with polarized light.
2
z
B
Challenge 146 ny
Ref. 98
Vol. I, page 228
3
initial position
and initial
orientation
C
A
D
1
B
final position
and final
orientation
x
C
2
Ω
3
1
A, D
y
initial
and
final
orientation
F I G U R E 87 Left: a three-dimensional path traced by a pointed object that behaves like the polarization
of light. The bends 1, 2 and 3 could be induced by mirrors. Right: the rotation angle of the polarization
is given by the solid angleΩ, the geometric phase, enclosed by the path.
phase turns out to be the solid angle enclosed by the path. In short, the geometric phase
angle is given by the enclosed solid angle. With this result, the geometric phase has no
mysteries any more. (For paths that are not closed on the sphere of directions, the calculationcanstillbecarriedoutbysuitablyclosingthepathonthesphere.)Aprettycase
is the experiment in which polarized light is fed into a helically coiled optical fibre. In
this case, the geometric phase is fixed by the length of the fibre and the pitch length of
thehelix.Effectsofthegeometricphasehave also been observed in molecules, in nuclei,
neutron beams, in interferometers of all kind, in particle accelerators, in gyroscopes, in
general relativity and in many other settings.
Historically, the geometric phase has been discovered independently by many people
in different fields of physics. The researcher who understood its general importance in
quantum physics was Michael Berry in 1983, but the phase was known in quantum physics,opticsandmechanicslongbefore,amongothersthroughtheworkinnuclearphysics
by Christopher Longuet-Higgins in the 1950s, through the work on light by the young
genius Shivaramakrishnan Pancharatnam also in the 1950s, through the work on molecules
by Alden Mead in the 1970s, and, of course, through the mentioned Foucault
pendulumfrom1851.But alsotheerrorsinthesouth-pointingcarriage,whichwemen-
Motion Mountain – The Adventure of Physics copyright © Christoph Schiller June 1990–November 2015 free pdf file available at www.motionmountain.net