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R. N. Mohapatra
have a symmetry, then practical systems which are based on those force laws
will have that symmetry reflected in their properties. For instance, laws of
electricity are symmetric under reflection in a mirror, as well as rotation around
an electric charge. This is reflected in the value of the electric field which is
same on both sides of a charge (mirror symmetry) and all around the charge
(rotation symmetry). Similar rules apply to gravitational force. By the same
token, if we do not know the basic nature of a force, its symmetries can be
guessed from the way the processes governed by the force behave. When not
much is known about the force, symmetries provide a clue to determine the
exact nature of the force.
20.2 Mirror Symmetry and Weak Force
Let us delve a bit into mirror symmetry which is connected to neutrino mass.
It is a symmetry like one of the above symmetries, which had always been
thought to be a fundamental symmetry of nature before the 1956 Lee–Yang
revolution. The meaning of mirror symmetry is that all physical processes look
the same when reflected in a mirror. This is obeyed by electric forces, which
look the same in a mirror, as just stated. The atomic light emission lines obey
that symmetry, a fact which was known since Otto Laporte enunciated it in
1925. As noted in Sect. 5.5, it was also known to be valid in nuclear forces and
the force of gravity and thus it was thought that every kind of force in nature
would have mirror symmetry; but as we now know, the weak force is the odd
one out and does not obey the mirror symmetry.
20.3 Mirror Symmetry and Neutrinos
How is the mirror symmetry breakdown (parity violation) connected to
neutrinos? Again, it all comes from experiment. To repeat some of the earlier
discussion, parity violation was confirmed by Wu et al, in the decay of
cobalt to nickel, an electron, and an anti-neutrino. From this experiment,
one could not tell if mirror symmetry breaking had anything specific to do
with neutrinos. But a major understanding came the following year when
Goldhaber, Grodzins, and Sunyar carried out an experiment involving the
europium atom. This atom decays by capturing one of its own electrons and
emitting a neutrino and a photon. This is also a weak force mediated processes.
Since total spin in this situation must remain same, both in the beginning
and at the end, and the initial total spin is zero, the measurement of the
R. N. Mohapatra
have a symmetry, then practical systems which are based on those force laws
will have that symmetry reflected in their properties. For instance, laws of
electricity are symmetric under reflection in a mirror, as well as rotation around
an electric charge. This is reflected in the value of the electric field which is
same on both sides of a charge (mirror symmetry) and all around the charge
(rotation symmetry). Similar rules apply to gravitational force. By the same
token, if we do not know the basic nature of a force, its symmetries can be
guessed from the way the processes governed by the force behave. When not
much is known about the force, symmetries provide a clue to determine the
exact nature of the force.
20.2 Mirror Symmetry and Weak Force
Let us delve a bit into mirror symmetry which is connected to neutrino mass.
It is a symmetry like one of the above symmetries, which had always been
thought to be a fundamental symmetry of nature before the 1956 Lee–Yang
revolution. The meaning of mirror symmetry is that all physical processes look
the same when reflected in a mirror. This is obeyed by electric forces, which
look the same in a mirror, as just stated. The atomic light emission lines obey
that symmetry, a fact which was known since Otto Laporte enunciated it in
1925. As noted in Sect. 5.5, it was also known to be valid in nuclear forces and
the force of gravity and thus it was thought that every kind of force in nature
would have mirror symmetry; but as we now know, the weak force is the odd
one out and does not obey the mirror symmetry.
20.3 Mirror Symmetry and Neutrinos
How is the mirror symmetry breakdown (parity violation) connected to
neutrinos? Again, it all comes from experiment. To repeat some of the earlier
discussion, parity violation was confirmed by Wu et al, in the decay of
cobalt to nickel, an electron, and an anti-neutrino. From this experiment,
one could not tell if mirror symmetry breaking had anything specific to do
with neutrinos. But a major understanding came the following year when
Goldhaber, Grodzins, and Sunyar carried out an experiment involving the
europium atom. This atom decays by capturing one of its own electrons and
emitting a neutrino and a photon. This is also a weak force mediated processes.
Since total spin in this situation must remain same, both in the beginning
and at the end, and the initial total spin is zero, the measurement of the