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R. N. Mohapatra
the principles of quantum mechanics require that certain other mathematical
conditions be satisfied for oscillations to occur. One of the conditions is that
the two states (or particles) must have their energies (or masses) close to each
other, so that the states can get “confused” about their “identity.” According
to Heisenberg’s uncertainty principle, energy and momentum cannot be
measured precisely in quantum mechanics. As a result, if two particles have
masses or energies so close to each other that they cannot be separated by a
measurement, they can get confused as the same particle (the same swing) and
particle oscillations can take place. The same thing can happen to neutrinos if
they have mass and the states of the neutrinos (say ν e and ν μ ) mix. In other
words, the neutrinos mix through their mass. If they are without mass, as is
the case in the standard model, then neutrinos cannot oscillate since two states
cannot mix with each other. Thus mass mixes one state of the neutrino with
another state of the neutrino and oscillations of particles happens if there is a
mixing mass.
13.2 Quantum Mechanics and Neutrino
Oscillations
Although the swing analogy broadly captures some essential aspects of the
phenomenon of neutrino oscillation, the basic reason for neutrino oscillation
has to do with the quantum nature of sub-atomic particles and not the
classical nature of the swing. To understand how quantum mechanics is at
the root of neutrino oscillation phenomenon, we note what broad quantum
mechanics entails. In physics, there are two classes of descriptions for physical
phenomena: one classical and the other quantum mechanical. Classical physics
was a well-developed (almost thought to be complete) description of natural
phenomena prior to the beginning of the twentieth century. In classical
physics, one can use both particles and waves. The first describes motions of
solid objects and the second describes motions of sound waves, water waves,
etc. There is no overlap between the two. Once we move to atomic and subatomic distances, the two descriptions overlap, i.e. the same phenomenon can
be described by waves as well as particles. This is called wave–particle duality
and is the basis of quantum mechanics.
Two major revolutions in our thinking took place as the twentieth century
was unfolding. The first was the theory of relativity, mentioned earlier, which
is independent of whether the description is quantum or classical. The second
was quantum mechanics. The first as noted earlier referred to situations when
R. N. Mohapatra
the principles of quantum mechanics require that certain other mathematical
conditions be satisfied for oscillations to occur. One of the conditions is that
the two states (or particles) must have their energies (or masses) close to each
other, so that the states can get “confused” about their “identity.” According
to Heisenberg’s uncertainty principle, energy and momentum cannot be
measured precisely in quantum mechanics. As a result, if two particles have
masses or energies so close to each other that they cannot be separated by a
measurement, they can get confused as the same particle (the same swing) and
particle oscillations can take place. The same thing can happen to neutrinos if
they have mass and the states of the neutrinos (say ν e and ν μ ) mix. In other
words, the neutrinos mix through their mass. If they are without mass, as is
the case in the standard model, then neutrinos cannot oscillate since two states
cannot mix with each other. Thus mass mixes one state of the neutrino with
another state of the neutrino and oscillations of particles happens if there is a
mixing mass.
13.2 Quantum Mechanics and Neutrino
Oscillations
Although the swing analogy broadly captures some essential aspects of the
phenomenon of neutrino oscillation, the basic reason for neutrino oscillation
has to do with the quantum nature of sub-atomic particles and not the
classical nature of the swing. To understand how quantum mechanics is at
the root of neutrino oscillation phenomenon, we note what broad quantum
mechanics entails. In physics, there are two classes of descriptions for physical
phenomena: one classical and the other quantum mechanical. Classical physics
was a well-developed (almost thought to be complete) description of natural
phenomena prior to the beginning of the twentieth century. In classical
physics, one can use both particles and waves. The first describes motions of
solid objects and the second describes motions of sound waves, water waves,
etc. There is no overlap between the two. Once we move to atomic and subatomic distances, the two descriptions overlap, i.e. the same phenomenon can
be described by waves as well as particles. This is called wave–particle duality
and is the basis of quantum mechanics.
Two major revolutions in our thinking took place as the twentieth century
was unfolding. The first was the theory of relativity, mentioned earlier, which
is independent of whether the description is quantum or classical. The second
was quantum mechanics. The first as noted earlier referred to situations when