14
R. N. Mohapatra
Thus if a particle has spin half, two times half plus one is two and hence two
orientations for spin half particles. There can be particles which have three
spin orientations—they are supposed to have spin one, etc. A particle can have
no spin—that will be said to have spin zero. This idea of spin was suggested
by George Uhlenbeck and Samuel Goudsmit in 1925 at Leiden University to
explain certain properties of atomic spectra. Atomic spectra indeed played a
crucial role in unraveling the mysteries of the atomic world. The mathematical
theory of spin was worked out by Wolfgang Pauli in 1927.
There were found to be two kinds of particles in the universe: particles that
had spin 1/2, 3/2, etc. (half odd integral) and particles that had spin zero, 1, 2,
…(integral). These two classes of particles were fundamentally different—the
former set were called fermions and the latter bosons. When more of them are
together, the fermions behave very differently from bosons. As already noted, at
a given point, there cannot be two identical fermions by the principle called the
exclusion principle. This explains the stability of matter and also stars made out
of neutrons and other massive objects in astronomy. The bosons on the other
hand have no such restrictions and can congregate together at one place in large
numbers. This is called a Bose condensate, named after Satyendra Nath Bose
who suggested how the bosons behave when they are in large numbers. This
was discovered experimentally by Eric Cornell, Carl Wieman, and co-workers
at JILA on 5 June 1995, and Wolfgang Ketterle at MIT in 1996. Cornell,
Weiman, and Ketterle were awarded Nobel Prize for this discovery in 2001.
2.4 Particle Helicity
Closely associated with spin of a particle is the concept of particle helicity. As
we just discussed, spin comes in discrete orientations—spin half comes in 2
orientations, spin one comes in three orientations, etc. To understand helicity,
imagine a clock. We describe clockwise or anti-clockwise movement of the
hands, depending on which way the hands are moving, as we are looking at
the face of the clock. If we look at the clock from its back, what was clockwise
would be anti-clockwise and vice versa. Thus, to define clockwise, you need
to know from which side you are looking. The same way, to define helicity,
we need a direction. It is chosen as the direction of motion of the particle.
Thus if a particle is moving in some direction and its spin is pointed along
the same direction, the particle is defined to have right-handed helicity (i.e.,
looking along the direction of motion, if the particle is spinning clockwise,
it is a right-handed helicity) and left handed if it is aligned the opposite way
to its motion direction. These two helicity states become more distinct if the
R. N. Mohapatra
Thus if a particle has spin half, two times half plus one is two and hence two
orientations for spin half particles. There can be particles which have three
spin orientations—they are supposed to have spin one, etc. A particle can have
no spin—that will be said to have spin zero. This idea of spin was suggested
by George Uhlenbeck and Samuel Goudsmit in 1925 at Leiden University to
explain certain properties of atomic spectra. Atomic spectra indeed played a
crucial role in unraveling the mysteries of the atomic world. The mathematical
theory of spin was worked out by Wolfgang Pauli in 1927.
There were found to be two kinds of particles in the universe: particles that
had spin 1/2, 3/2, etc. (half odd integral) and particles that had spin zero, 1, 2,
…(integral). These two classes of particles were fundamentally different—the
former set were called fermions and the latter bosons. When more of them are
together, the fermions behave very differently from bosons. As already noted, at
a given point, there cannot be two identical fermions by the principle called the
exclusion principle. This explains the stability of matter and also stars made out
of neutrons and other massive objects in astronomy. The bosons on the other
hand have no such restrictions and can congregate together at one place in large
numbers. This is called a Bose condensate, named after Satyendra Nath Bose
who suggested how the bosons behave when they are in large numbers. This
was discovered experimentally by Eric Cornell, Carl Wieman, and co-workers
at JILA on 5 June 1995, and Wolfgang Ketterle at MIT in 1996. Cornell,
Weiman, and Ketterle were awarded Nobel Prize for this discovery in 2001.
2.4 Particle Helicity
Closely associated with spin of a particle is the concept of particle helicity. As
we just discussed, spin comes in discrete orientations—spin half comes in 2
orientations, spin one comes in three orientations, etc. To understand helicity,
imagine a clock. We describe clockwise or anti-clockwise movement of the
hands, depending on which way the hands are moving, as we are looking at
the face of the clock. If we look at the clock from its back, what was clockwise
would be anti-clockwise and vice versa. Thus, to define clockwise, you need
to know from which side you are looking. The same way, to define helicity,
we need a direction. It is chosen as the direction of motion of the particle.
Thus if a particle is moving in some direction and its spin is pointed along
the same direction, the particle is defined to have right-handed helicity (i.e.,
looking along the direction of motion, if the particle is spinning clockwise,
it is a right-handed helicity) and left handed if it is aligned the opposite way
to its motion direction. These two helicity states become more distinct if the