One of the most important conceptions of matter and energy to come out of this century, besides the fact that they are interchangeable states of the same thing (expressed in Einstein's famous equation, E=mc2) is the fact that either state can act as either a particle or a wave. This was a very perplexing problem, and still remains so if we try to visualize what matterenergy looks like at the elementary level. A particle is localized in spacetime -- it can be assigned very distinct coordinates, and even thought of as stationary and static. A wave is not localized and cannot be static.

The wave-particle duality is one of the best examples of the complementarity principle in quantum theory. An electron, for example, will either act like a particle or a wave, but never both at the same time. If we use a particle detector to see the electron, it will be a particle, and if we use a wave detector, it will be a wave. Somehow, we must think of the electron as being both, but in its ability to display both modes of mutually exclusive states of being, it is actually neither. The essence of what the electron really is must be something else entirely. Whatever that is, is quite impossible to visualize, and has been dubbed a wavicle.

Quantum Mechanics

CREDITS: Fermilab, images and text
Much of the work in particle physics is guided by the principles of quantum mechanics. Originally devised to explain the way the atom works, the theory underlies most of the ideas that define how scientists view the world of subatomic physics.

The basic postulates of quantum mechanics:

•Particles actually have a wave nature and can be described as a wave function of any of their coordinates (position, momentum, angle, energy) so that if the wave function is squared, it represents a probability function of that coordinate.

•If you prepare two samples, each having a wave function that demands the probability of a certain outcome, then if the samples are totally identical in every way, the wave functions must be added first, and then squared. Because part of the wave function is imaginary, any phase difference between the two functions (regardless of the amplitude) will result in an effect on the result whereas if one squares and then adds, the phase difference is washed out. This is the principle of interference and is common to all wave phenomena. In quantum mechanics however, the square of the wave function represents a probability as opposed to an actual distribution of some quantity.

The wave function of a particle must satisfy boundary conditions. The diagram at left shows three simple functions which fit exactly an integer number of wavelengths between the two walls.

Since there are usually conditions at boundaries that the wave function must obey, a string being tied at both ends for example, the wave function is constrained. This will allow only certain wavelengths to exist. The walls in quantum mechanics are actually potential energy wells. The probability of a particle to exist outside of its potential well boundary must drop to zero in some way. This is the principal of quantization.

This is true for all quantum systems. Interesting phenomena arise when we introduce special relativity into quantum mechanics. One of these is spin. Particles revolving around one another can have what is known as angular momentum, and particles with a size can spin like a top. Although the spin in quantum mechanics can be described similarly, it is not the same as ordinary spin. For example, the electron has no size, it is a point particle, but it has a quantity known as spin which is different from the classical notion of spin. Spin is important in classifying the various particles and in how they interact with each other.


The ElectroWeak Force

CREDITS: Fermilab
One of the major goals of elementary particle science is showing that even though particles may interact in somewhat different ways, they are utterly controlled by the same guiding principles. During the early part of the 20th century, as the first particles were discovered, the forces acting on them were eventually classified as electromagnetic, weak nuclear, and strong nuclear. As time went on, scientists realized that the electromagnetic and weak nuclear forces were really one and the same force. The electroweak force fully explains the interactions (very well) of all the known leptons at the energy scales attainable so far.

It is hard to detect this at small energies, but as accelerators allowed the scientists to use more energetic interactions, the evidence became clear that forces would unify at a larger energy. On the other hand, a difficulty arose in that the gauge bosons or force carrying particles of the weak nuclear force have large masses. The force carrying particle of the electromagnetic force is the photon which is massless. Since it is massless, two bare electric charges can interact over an infinite distance (if they are the only charges around). The weak nuclear force can only act over a distance on the order of magnitude of the nuclear size.

Both the electromagnetic and weak force arise from gauge theories. This means the particles are "representations of a group" - or they define a mathematical structure whose elements interact in a definite way governed by the transformations of the group. When two different groups are combined together, they don't always form a composite group. In the electroweak case, fortunately, they do.

One of the interesting phenomenon about this force is CP violation. This is one of the spacetime symmetries which is violated at the energies seen in the lab and has been experimentally observed but is postulated to be recovered as very high energies are attained. The mechanism by which the violation is though to occur is by a Goldstone boson known as the Higgs particle. Through the process, both the weak force carriers (W+,W-,Z), and the Higgs boson itself acquire a large mass.


Quantum Chromodynamics

CREDITS: Fermilab, images and text
The color force, also known as the strong nuclear force, gets its name not from any real color that we can see, but because scientists could not think of what to call it. The force itself is real though. It is a property of quarks and gluons, responsible for binding quarks together to form protons and neutrons and binding quark-antiquark pairs to form mesons.

An interesting property of particles with color is their confinement within the proton. Quarks come in three shades, (call them red, blue, green for convenience). If you combine a red quark and an anti-red anti-quark, the net object is colorless. If you combine red, blue, and green together, the net object (proton for example) is also colorless. A bare quark or gluon (with a net color) has never been observed. The interaction of bare partons (quarks or gluons) with incoming projectiles such as electrons has been inferred through.

The color force is an example of a gauge theory, a theory using relativistic quantum mechanics and principles of symmetry to summarize how particles with a charge interact. Particles with color charge interact via the color force although they may have other charges such as an electric charge. Therefore there may be multiple forces acting on the particle. Electromagnetism can be formulated as a U(1) type gauge theory under the banner of Quantum Electrodynamics. The color force is an SU(3) type gauge theory. The U(1) and SU(3) correspond to the symmetry governing the interactions.