Genesis of Eden
Left: Signature of the Zo particle. The Zo, W+
and W- bosons transmit the weak force; their existence was predicted
by the unified theory of the weak and the electromagnetic interactions,
and their discovery vindicated the theory. The tracks depicted
correspond to particles detected following the high-energy collision
of a proton and antiproton. The two tracks in white above and
below are an electron and a positron, the decay products of the
Zo, which disintegrated soon after it materialized in the collision.
Right: Top quark candidate at Fermilab 1989. This is the sole
piece of the standard model yet to be fully confirmed.
Symmetry and local symmetries are believed to
underlie the fundamental forces. Top left: 60 degree rotational
geometric symmetry of a snowflake, charge symmetry of electromagnetism
and isotopic spin symmetry between a neurton and a proton illustrate
symmetries in nature. Right: The electromagnetic force can be
conceived of as an effect required to make the global symmetry
of phase change local. A global phase shift does not alter the
two-slit interference of electron waves (which usually have one
light band in the centre), but a phase filter which locally shifts
the phase through one slit has precisely the same effect as applying
a magnetic field between the slits. The local phase shift causes
the centre peak to become split in both cases. Gravitation can
likewise be conceived as a symmetry of the Lorenz transformations
of relativity, usually referred to as Poincare invariance.
The Four Fundamental Forces and Symmetry-breaking
Four distinct force fields have been discovered in nature. Two are familiar, gravity on the one hand and electromagnetism, comprising many effects including electricity, magnetism, light and the electromagnetic spectrum, and the indirect effects seen in chemical reactions. The other two are distinct forces which occur in the nucleus of the atom.
The nucleus consists of protons and neutrons. These are bound together tightly by the strong nuclear force. This force is responsible for the great energy of nuclear fusion and fission. It is a secondary product of a more inaccessible force which comes in threes, called the colour force which binds the constituent quarks of protons and neutrons.
(a) Unificationof the strong and weak nuclear
forces with electromagnetism is suggested by the convergence of
the strength of the three non-gravitational forces at high energy
(b) The four forces of nature appear to differentiate from a common
super-force. (c) Broken electro-weak symmetry has a lower energy
than the symmetrical state. This explains how nature has become
asymmetric with positive and neutral charges in the nucleus and
negative electrons outside. The universe is like a ferromagnetic
material which is magnetised in its lowest energy state. The energy
released by cosmic symmetry-breaking may represent the hot shower
of particles in the big bang. Just as a magnet can be polarised
in many directions in space, so symmetry break may be. This could
result in anomalies such as cosmic strings, domain walls or magnetic
monopoles. Below: The four particles of the unified electro-weak
force. The photon, the two charged W particles and the Z0. While
the photon is massless the others all inherit a lage mass from
symmetry-breaking causing the weak force to be very short-range.
The four particles of the unified electro-weak force. (d) The
stable nuclei and radioactive decay of the neutron. The balance
between neutrons and protons is mediated by the weak force. Too
many protons and the electromagnetic repulsion becomes unstable.
Too many of either kind and the nuclear energy levels likewise
become unstable. Notably the weak force is chiral. The emitted
electron is left-spinning.
A second, quite different force, the weak nuclear force, is responsible for radioactive decay. If a nucleus has too many neutrons, one neutron can decay into a proton, an electron and an antineutrino [above figure] This reaction and its reverse act to keep the balance of protons and neutrons, which is roughly 50-50 to keep each nuclear particle in the lowest possible energy states under the strong force, but becomes biased toward neutrons in heavier elements, because of instability caused by the accumulated repulsive positive charges of the protons. Significantly, the reaction does not preserve mirror symmetry, as it gives rise only to left-handed electrons, the anti-neutrino involved in beta decay also has a spefic handedness.
Scalar and vector fields illustrate the classical
behaviour or potential functions and electrostatic fields and
fluid flows. A scalar is a single quantity wheras a vecotr field
in 3 dimensions has 3-dimensional vectors as well. Quantum fields
likewise can have differing dimension depending on their spin.
Spin-0 fields have one degree of freedom and are scalar. Spin-1
fields have three degrees of freedom and are vectors. Photons,
because they are massless have lost the longitudinal mode and
have only two degrees of freedom (polarisation). The one additional
degree of freedom contributed by the Higg's boson gives back to
the weak bosons the degree of freedom they need to be massive
and have a varying velocity. Spin 1/2 fermions have two-component
wave functions which turn inside out upon a 360 degree revolution
leading to the Pauli exclusion principle.
Weak neutral currents mediated
by the Z0 can resutl in interactions between uncharged neutrinos
and other form of matter.
The weak force is mediated by three types of particle, the charged W+, W-, and the neutral Zo, each of which has a very high rest mass, but otherwise behaves very much as a photon. The heaviest of these was predicted by Stephen Weinberg in a theory which unites electromagnetism and the weak force in a single super-force in which three of the particles have gained a large rest mass by a process called symmetry-breaking, but are otherwise sister particles of the photon. This is basically extending quantum electrodynamics to the weak force.
The very short range of the weak force is immediately explained by this high rest mass. The exchanged virtual particle has to gain at least the energy of the rest mass to exist at all, so there is a very short time and a very small distance beyond which the force cannot occur through uncertainty. By contrast, the photon, which has zero rest mass has only to deal with its energy of transmission and thus can occur with decreasing probability over larger and larger distances. Electromagnetism and gravity are thus long-range forces which fall off gradually with distance.
This new mass is explained through an additional filed the Higgs field which has a scalar particle the Higgs boson contributing an extra degree of freedom to the wave function to make it able to change velocity and behave as a non-zero rest mass particle.
Evidence for quarks and gluons: Left: two narrow
jets of particles emerge from the collision and mutual annihilation
of an electron and an anti-electron, or positron. The detected
particles have a variety of masses, charges and spins. If the
particles arose directly from the annihilation, they would be
expected to follow widely divergent paths. The focused character
of the nets suggests instead that each jet developed from a single
precursor: a quark or an antiquark. Centre: Three-jet event confirms
the existence of the gluon, the mediating particle of the color
force. An electron and a positron collided at high energy, creating
a quark and an antiquark, as in the previous event. In this case
one of the quarks radiated a gluon. The quarks and the gluon diverged;
each promptly gave rise to a shower of particles, which preserved
the trajectory of the original entity. The event reveals the asymptotic
freedom of quarks and gluons: their ability to move independently
within a very small region in spite of the enormous strength of
the color force across larger distances.
Resonances in particle collision
experiments suggest there are three families of fermions.
An important feature of such theories is that a given force can be identified with a local symmetry possessed by the universe. In the case of electromagnetism this is the phase of the wave and in gravity it is the relativistic transformations of space-time. Changing the phase of all wave-particles in the universe has no net effect, but changing the phase of some results in an electromagnetic interaction which makes up the difference by applying a force which changes the phase of only those particles involved. When the larger symmetry between the weak and electromagnetic forces is broken, by some of the particles gaining a non-zero rest mass, the two forces gain their distinctive character. Because the broken-symmetry state has lower energy the universe is no longer in the symmetrical state.
The Particle Menagerie:
Fermions (spin = 1/2):
| lepton | mass | symbol | charge | quark | mass | symbol | charge |
| electron neutrino | < 16 eV |  |
0 | up | 310 MeV | u u u | 2/3 |
| electron | 0.5 MeV | e | 1 | down | 310 MeV | d d d | -1/3 |
| muon neutrino | < 65 eV |  |
0 | charm | 1500 MeV | c c c | 2/3 |
| muon | 106.6 MeV |  |
1 | strange | 505 MeV | s s s | -1/3 |
| tau neutrino | < 65 eV |  |
0 | truth | >89 GeV | t t t | 2/3 |
| tau | 1784 MeV |  |
1 | beauty | 5000 MeV | b b b | -1/3 |
Neutrino masses and family numbers
Neutrinos may have a small mass. This is consistent with the idea that the neutrino types may be able to interconvert by a resonance similar to that of the Ko meson (see below). This would explain the small observed flux of neutrinos from the sun which is only about 1/3 what it should be for the nuclear energy required to keep it at current luminosity.
In the early universe there was a sea of protons and neutrons constantly interacting with electrons, neutrinos of every type and their anti-particles through weak interactions. Because neutrons are slightly more massive (939.5 MeV) than the proton (938.2 MeV), there are fewer of them. As the expansion separates, these the weak interactions cease, leaving about a 1:5 n:p ratio at 1 second. The neutrons begin to decay with a half-life of 15 minutes. After 3 minutes deuterium becomes stable and is rapidly converted to helium. At this point neutron decay has reduced the n:p ratio to 1:8. These flush out another 1/8 of the particles (protons) leaving a 1:4 ratio of helium to hydrogen. More families of neutrinos than four would cause a faster the expansion rate, and the faster reaction would produce more helium than observed.
Experiments on the supernova 1987A limits electron neutrino mass to less than 16 eV. All neutrinos must have a mas less than 65 eV or the universe will be closed and collapse and moreover the expansion rate would be slower than observed. The observed mass is only 10 to 20 percent of the closing mass. Neutrinos cannot be too massive. There are even more than photons, several billion for every proton, electron and neutron.
Bosons:
| force | range | strength at 10^ -13 cm | particle | mass | spin | charge | status |
| gravity | infinite | 10^ 38 | graviton | 0 | 2 | 0 | conjectured |
| electromagnetism | infinite | 10^ 2 | photon |
0 | 1 | 0 | observed |
| weak | < 10^ 16 cm | 10^ 13 | W+ | 81 GeV | 1 | +1 | observed |
| W | 81 GeV | 1 | 1 | observed | |||
| Zo | 93 GeV | 1 | 0 | observed | |||
| strong | < 10^ 13 cm | 1 | gluons | 0 | 1 | 0 | confined |
The electroweak unification occurs at around 10^11 eV. Current limits on collider energy are around 10^13 - 10^14 eV. The hypothetical targets for unification with the colour force have ranged upward from 10^15 to 10^24 eV. Complete unification with gravity requires the Planck scale requires energies of 10^28 eV, requiring a collider 1000 light years around to probe. This makes it difficult for supercolliders to push our knowledge of unification further. It is likely we will have to develop theoretical insight more deeply and use indirect evidence from the universe at large.
The standard model of particle physics: Particles are divided into half-integer spin fermions
which obey the Pauli exclusion principle and can only exist in
a single wave-function in pairs, thus becoming matter, and integer-spin
particles called bosons, which can clump in any number (lasing)
and thus form the radiation and force fields. The fermions form
two types, leptons which are light and do not experience the colour
force ( electrons and their neutrino partners) and the quarks
which make up protons and neutrons. Each quark comes in three
colours (red, green, blue) and two flavours (up and down). Decay
of the neutron into a proton, electron, and anti-neutrino is mediated
by the weak nuclear force. This force also mediates flavour in
the nucleus. The strong nuclear force, which binds the protons
and neutrons together, is a secondary effect of the coulour force
which binds quarks together inside these particles. By exchanging
the three colours, just as the electromagnetic field mediates
charge, gluons bind the quarks together with a force which is
relaxed at close distances but becomes stronger as they are pulled
apart. This causes quarks to be confined within nuclei and protons
and neutrons. The antiquarks are also shown top left to illustrate
their anti-colours. There are likewise anti-particles of the leptons
such as the anti-electron (positron). Both quarks and leptons
come in three (or possibly four) series of rapidly increasing
mass. The bosons mediate each of the forces. The photon and graviton
are the only massles bosons. The other three electro-weak W and
Z particles have inherited a large rest mass (and an extra degree
fo freedom) by coupling to a hypothetical spin-0 particle called
the Higg's boson, as shown. The photon is exchanged only between
charged particles, but the Zo interacts even between neutral particles.
The W particles are themselves charged, so emit and absorm photons.
There are 8 independent degrees of freedom in the colour field
mediate by gluons. Like the quarks these remain confined.
A similar mechanism is believed to unify these two forces with the strong nuclear force. Every proton and neutron is itself believed to consist of three subparticles called quarks as follows: n=udd, p+=uud. Neutron decay is thus actually the transformation of a down quark into an up [see fig above]. The three quarks are bound together by a force, called the colour force because each quark comes in one of three colours, just as electric charges come in two types, positive and negative. Each neutron has one up and two down quarks and each proton two up and one down. To balance the charges each up must have charge 2/3 and each down -1/3. However, regardless of their up or down flavour, there is always one of each colour, so that the proton and neutron are colourless.
Top left: Mesons (quark-antiquark0 and baryons
(three quarks) mediate their color by exchanging gluons of appropriate
color-anticolour combinations. Top right: The electromagnetic
field reduces effective charge by forming virtual electron-antielectron
pairs. The colour force also does this by forming quark-antiquark
pairs, but in addition the gluons have a colour charge (unlike
the uncharged photon) which increases the effective charge towards
infinity at great distances, while remaining relaxed at short
distances, allowing the quarks to move freelywithin a confined
space. This phenomenon, which is known as camoflage is also illustrated
in the lower series of diagrams where electromagnetism has only
shielding while colour has shielding and camoflage. The effect
of quark and gluon confinement is that individual particles cannot
be isolated. When they are drive apart in a very energetic collision,
a shower of particles results which eventually neutralizes the
colour charge.
The colour force is mediated by particles called gluons, which like the electroweak family are vector particles of spin 1. The colour force and its secondary effect, the strong nuclear force, are believed to be unified with the weak and electromagnetic forces in a similar manner. In fact the strengths of these three forces converge to the same value at a high temperature called the unification temperature for this reason. Because the colour force generates quark-antiquark pairs as any quark is pulled apart from the rest, a quark cannot simply escape, but instead generates a whole jet of excited particles.
Decay of the Ko meson is a parallel to photon
polarization. The K1 component (see below) by decay is similar
to vertical polarization removing the horizontal component from
circularly polarized light. However there is a small amplitude
for the K2 to go into resonance back into the K1 form, just as
dextrose rotates the polarization of light, allowing it to subsequently
decay again, similarly to detecting horizontal polarization in
the rotated light. Lower left Feynman diagram for quark flavour
mixing. Just as classical chirality requires three dimensions,
CP-violation of the Ko requires at least three families of fermions.
Recent investigations of the B meson containing a b (beauty) quark
indicate flavour mixing suggesting a fourth family is possible.
Then can be no more than four or the extra neutrino types would
cause an unrealistic expansion rate of the universe.
The weak force is known to be chiral (see above), but the asymmetry
of nature runs even deeper. In 1964 the principle of charge-parity
conservation was oveerthrown by the neutral K meson, which usually
decayed into 3 pions but once in 500 times was found after a strange
delay to decay into only two. The neutral Ko meson, and its antiparticle
both decay into a pair of mesons
The rapid decay
of the component 
into pi-mesons, subsequently leaves the remaining
component 
which does not follow the same decay. However
subsequently there is a small amplitude for conversion of some
of the K2 back to K1
resulting in a KL which is not matter-antimatter
symmetric, since it contains differing components of Ko and its
anti-particle. Thus the reaction 
is preferred over
the mirror-image Since the Ko has quark constituents (d, anti-s)
and its anti-particle (anti-d,s), this implies that the reaction
should be directed in time. Similar considerations are used to
explain the preponderance of matter over anti-matter. It is suggested
that the one part in 10^8 of matter to radiation could have come
from a similar process resulting in a slight differential in the
stability of matter an anti-matter with respect to time.
Right: The SU5 theory, an attempt to make an immediate
extention of the ideas of the electroweak unification to unification
with the colour force. The principal difficulty with this theory
is that its prediction that the proton should also be unstable,
like the neutron, has not proven to be validated, despite major
experimental efforts of underground scintillation detectors. Right:
Proton decay. The diagram shows one of several proposed decay
routes of quarks into leptons. The proton's constituent u quarks
combine to form an X particle, which disintegrates into a d antiquark
and a positron (a lepton). The d antiquark combines with the remaining
quark of the proton, a d quark, to form a neutral pion. Because
pions are composed of matter and antimatter, they are short-lived;
the mutual annihilation of their constituents will release energy
in the form of two photons. The failure to detect proton decay
has pushed up the energy of possible unification by orders of
magnitude. A more fundamental symmetry proposed is supersymmetry,
a hypothetical symmetry between fermions and bosons which identifies
each with a partner of one half spin less. The spin-2 gravitonwould
thus have a series of partners, as shown as left. Supersymmetric
theories are usually developed in higher dimensional spaces in
the form of string theories, in which particles become harmonically
excitable strings of perhaps 10 to 12 dimensions at very small
distance scales.