Symmetry, Antimatter, and Polarity
The abstract study of symmetry is the object of mathematical group theory, which, as its name implies, describes groups defined by the specific symmetry elements they contain and the specific symmetry operations they allow. Groups are also related to each other by symmetry transformations. Group theory provides physics with a powerful means for classifying "everything" in the universe and understanding the interdependence of physical processes based on symmetry transformations.
For example, many transformations in the physical world leave the laws of physics invariant, i.e. the laws of physics are the same everywhere in the universe. This is referred to as translational invariance, and it corresponds to the law of conservation of linear momentum; similarly, the symmetry that states the laws of physics are the same at all times is equivalent to the law of conservation of energy; and the rotational invariance of the laws of physics is equivalent to the law of conservation of angular momentum. Quantum theory fully describes atomic structure in terms of the symmetry properties of atoms, molecules, and orbitals. The symmetry of general relativity, much larger than any observed in physics before Albert Einstein, combines rotational invariance, translational invariance and Lorentz invariance to form the complete symmetry group of special relativity known as the Poincaré group, a 10-dimensional group (cf. the three-dimensional Euclidean or E(3) group generated by translations in the x direction, translations in the y direction, and rotations in the xy plane).
Particle physics describes elementary particle-antiparticle interactions as well as their associated wave fields entirely on the basis of symmetry considerations, embodied in gauge theory. This theory was formulated in 1918 by H.Weyl, and includes some infinite-dimensional groups. Symmetry or gauge transformations of the wave field variables are the means by which the basic quantum field laws remain valid, or gauge invariant, because they define general restrictions on the way a given field can interact with other fields and elementary particles.
In the 1960s physicists developed quantum field theories to explain the weak and strong nuclear interactions. They realized that gauge symmetry, termed the U(1) symmetry, could be generalized to gauge symmetries based on other continuous groups, such as the special orthogonal groups SO(N), the special unitary groups SU(N), the special symplectic groups Sp(N) and the exceptional groups G2, F4, E6, E7, and E8. A unified gauge symmetry could then be made up of combinations of these groups. The groups can combine using a direct product, denoted X, in which both groups are independent subgroups. From tables of particles, physicists were then able to propose, for example, that the strong nuclear interactions used the gauge group SU(3), termed color. The weak interaction was experimentally detected, and used SU(2) X U(1) symmetry, broken by a Higgs mechanism and a Higgs boson, whose vacuum state breaks the symmetry at low energies. With the use of these gauge symmetries, theoretical physicists were able to construct the complete standard model of particle physics by 1972, as well as its particle and corresponding antiparticle complement.
Antimatter is defined as any matter composed of antiparticles, which are the charge conjugates of ordinary protons, electrons, and neutrons, i.e., they have the same mass but opposite electrical charge and magnetic moment. The antiparticles also have properties exactly opposite to those of their corresponding particle due to a remarkable symmetry translation. Therefore, every known elementary particle has a counterpart with opposite charge and/or spin, or polarity. The existence of the first antiparticle was predicted by the theory of quantum mechanics by Paul Dirac in 1928. This was the positron, defined as an antielectron with positive charge and lepton number -1. It was experimentally observed in cosmic rays by Carl Anderson in 1932 at the California Institute of Technology. Since then, the full range of antiparticles has either been experimentally observed or predicted. In 1996, scientists at the European Organization for Nuclear Research in Switzerland, discovered the first antiatom, antihydrogen, in a spectacular breakthrough that will significantly contribute to our understanding of matter and antimatter.
Most of the antimatter of the universe is believed to have been canceled out during the initial big bang events through a parity symmetry violation, yielding an almost antimatter-free universe. Antimatter is now usually produced in particle accelerators. Its behavior is well described by gauge theory with the exception of its reaction to gravity because it has yet to be produced in sufficient quantities to study these interactions. When matter and antimatter are made to collide in accelerators, both may be annihilated, i.e., they disappear and their kinetic plus rest-mass energy is converted into other particles, such as photons and pions, according to the equation E = mc[sup2 ]. For example, when positrons and electrons collide they annihilate each other, and their energies are converted into gamma rays. If they are at rest and their spins are oppositely paired, the collision results in the production of two gamma rays, each with an energy of 511,002.7 electron volts. Antimatter is also produced during some radioactive decay processes. For example, when 14-carbon decays, a neutron decays to a proton plus an electron and an electron antineutrino. When 19-neon decays, a proton decays to a neutron plus a positron and an electron neutrino. The neutrino and electron are leptons while the antineutrino and positron are anti-leptons.
Leptons are defined as point-like particles that can interact with the electromagnetic, weak and gravitational forces, but not with the strong interactions. This is a result of their symmetry properties: the only massless particles known are the photon, the neutrinos, and the hypothetical graviton. These particles are symmetric under an even larger group than the Poincaré group, namely, the conformal group, which is 15-dimensional. Maxwell's equations are invariant under the conformal group and so are the Yang-Mills equations, which describe the weak and strong interactions. Thus, in each decay reaction, one lepton and one anti-lepton are produced, and this also illustrates a fundamental symmetry law of physics, i.e., for each new lepton that is produced there is a corresponding new antilepton.
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