Fermions and Bosons
Advanced chemistry students are familiar with the Pauli-Exclusion Principle,
which states that
no two particles may occupy all the same quantum states, such as energy and
position. But does this
apply to all particles? When the derivation of the principle is studied, one
finds that it applies
only to particles with fractional spin.
Spin is not analogous to any real-world action. The spin of an
electron is not exactly
its rotation about an axis. Electrons do not rotate about the nucleus as the
earth revolves around
the sun; the earth rotates around its axis. Particle spin is not fully
understood yet. It's defined
as "internal angular momentum" and measured in terms of h/2pi, that is Planck's
constant over two times pi.
For conciseness, it is written h'.
Individual leptons and quarks have 1/2 h' spin. Such particles with fractional
spins of h' are termed fermions. Force-carriers: photons, gluons, gravitons, W-, W+, Z0 have
spins of 1 h'. They
are called bosons. Bosons, having integral multiples spins of h', do not obey
the Pauli-Exclusion
Principle. As a result, many bosons may occupy the same quantum states.
Position, being a quantum
state, is no longer a barrier to bosons. Two bosons may coexist at the same
place. This is how supercooled
helium has no viscosity. The nucleus is made of 4 nucleons, each with 3 quarks.
Because all the quarks
are bonded to each other, the apparent spin is 12 * 1/2 h', equivalent to 6h'.
The nucleus has
integral spin and is a boson. As a result, the helium nuclei may pass through
each other with no apparent
resistance.
Strong Colors
No, we're not talking about Paige Fox's chicken soup. In electromagnetism,
there were two charges:
positive and negative. Gell-Man and Zweig, in their quark models, found that
the strong force has
three "charges". For easy communication, the charges were called red, blue, and
green. Each color
attracts the others. When two quarks interact, gluons are exchanged, but gluons
also have a color
(contrary to the neutrally charged photon).
It is a necessary law, as shall be explained below, that systems of quarks must
have an overall
"white" color. In baryons, at a particular time, one quark should be red, one
blue, one green. The
"sum" of the charges is representatively white, which is neutral. In mesons,
anti-quarks have
anti-colors. For example, blue and anti-blue combine to form neutral white.
When a gluon is emitted
from a quark, the quark switches color. When the gluon is received, the
receiver also switches
color. This way, whiteness is maintained.
Antimatter
As mentioned before, anti-particles and particles differ only by the sign of the
electric charge
(or color/anticolor). The anti-electron is called a positron, and has +1
charge. An anti-proton
has the corresponding anti-quarks. The proton is made of two ups and one down.
The anti-proton
would be composed of two anti-ups and one anti-down, and would have a total -1
charge. The reader
might be wondering how anti-neutrons may exist. A neutron is made of two downs
and one up. The
counterpart would have two anti-downs and one anti-up. The total charge would
still be 0, but the
componential quarks would be opposite.
Paul Dirac took Einstein's relativistic equation E^2 = m^2 * c^4 + m^2 * p^2 and
noticed that negative
energy values were allowable, ie. if a particle had negative E, the equation
would still be satisfied
if mass and momentum remained the same. He came to the prediction for
antimatter, and soon the positron
was discovered in cosmic rays.
There are several models for the explanation of antimatter. The most popular
one is as follows:
Space is filled with infinite amounts of invisible particles. They begin with 0
energy.
When enough energy is imparted to one such particle, it "jumps up" in energy
levels. After attaining
a positive energy, the particle becomes visible and real. But there is a "hole"
left where the
particle jumped out from. That hole is the anti-particle. Hence, particles and
their anti-twins
accompany each other.
When particles and their counterparts meet together, the holes are "filled up"
again. The particle
returns to 0 energy, releasing the amount of energy required to pluck it out..
Experimentally, this
system seems to be accurate. When electrons and anti-electrons meet, they
combine and form an
energetic photon. This process is called annihilation and is what
powers the Enterprise
around the universe. An energetic photon seems to be able to transform into a
electron/positron pair.
These interactions may be interpreted: the photon is able to donate enough
energy to pull
an electron into existence; when an electron returns to its hole, the energy
(photon) comes back.
The invisible particles that are the parents of all real particles are called
"virtual particles".
They have another use in quantum mechanics related to the Heisenberg Uncertainty
Principle, but it
will not be explained here. Space is thus filled with an infinite number of
virtual particles.
Scientists occasionally mention the "inattainability of a true vacuum"; this
results from the all
"empty" space being overflowing with invisible virtual particles.
Vacuum Polarization
There are virtual photons and gluons, corresponding the types of particles
associated with it;
photons produce or form from lepton annihilations; gluons produce or form from
quark annihilations.
Virtual photons, as real photons, are neutrally charged. Hence, a electron in
space does not attract
any of the infinite virtual photons toward itself. On the other hand, virtual
gluons and gluons
both have color charges. If there were a lone quark of a particular color, the
virtual gluons around it
would be attracted towards it. But more gluons means only a stronger color
charge. Then even
more virtual gluons would zip towards the bunch of gluons about the quark.
Eventually, all the virtual
gluons in the universe would be attracted to the single quark; the universe may
collapse, chaos may
plague eternity. Anyways, it would not be a good thing if such vacuum
polarization were able to
exist.
The way to avoid this would be to have quarks in "white" groups. Gluons would
not be attracted to
the neutral white and the space would remain stable. Hence quarks may not exist
alone.
