Particle-antiparticle pairs arise from pure energy and will annihilate one another to give pure energy, usually in the form of photons. Antiparticles are produced by nuclear reactions and cosmic rays. Antimatter is a collection of antiparticles, in particular antiprotons, antineutrons and positrons (anti-electrons) in a similar composition as matter.

The existence of antiparticles was predicted by Dirac a few years before the first one, the antielectron or positron, was found. The idea stemmed from the existence of negative energy states, which in a relativistic universe can not be discarded *a priori*. Since electrons normally seek the lowest possible energy state, Dirac posited that these extra states must all be filled with what are called virtual particles. In that case, a virtual particle could be promoted to a positive energy state, creating a real particle and leaving a hole that would behave exactly the same, but with opposite charge.

However, nobody (including Dirac) was very satisfied with the idea that the universe was completely filled with a sea of negative electrons, particularly because bosons have antiparticles, though hole theory doesn't work for them. Richard Feynman, however, shortly afterwards, showed that negative energy forward in time and positive energy backwards in time solutions are not allowed to the energy equation. A negative energy running backwards in time would appear to be exactly the same as a positive energy particle running forward in time except for its polarization, which would cause two particles of the same charge travelling in different directions through time to attract electromagnetically.

So, how does this fit into the idea of anti-matter?

Say you have an electron, travelling forward through time, and it emits a photon with enough energy and in the right direction to send it hurling back in time. It continues along for a while, then emits another photon, which sends it hurling forward through time once again.

t5 ----*------/ t4 ----/\\----/ t3 ---/--\\--/ t2 --/----\\/ t1 -/-----*The Y axis is time and the X axis is position. The "*" are places where photons are emitted, the "/" and "\\" trace out the path of the particle, from left to right, and the "-" designate a specific point in time, labeled as t1, t2, t3, t4, and t5.

To us, observing this reaction travelling only forward in time, at T1 we see a photon split up into two particles, a positron and an electron. The electron travelling off to the right while the positron moves to the left, colliding with a regular electron at T5 and releasing energy.

In "reality" the electron starting at the left end, moves forward in time until T5 when it emits enough energy to slip into a negative energy state. It can only do so if the photon is emitted in a way that will send it back in time, however, which is a very low probability. It continues backwards in time with negative energy but since it is travelling backwards in time the negative energy, from the viewpoint of something moving forwards in time, appears to be acting like a positive energy particle.

The intristic parity is unchanged, since C, P, and T all commute, thus [P,CPT]=0.

Since the hamiltonian and the energy are CPT invariant, if the original particle was possible, the result is possible as well. Thus there is no reason applying the CPT operation to a particle will not produce another particle(this is the modern theoretical argument for the existence of antiparticles).

In summary here are the properties of antiparticles(only those that distinguish particle species are considered here):

particle | antiparticle | |||
---|---|---|---|---|

mass | m | m | ||

spin quantum number | s | s | ||

electric charge | q | -q | ||

color charge | {r,g,b} | {-r,-g,-b} | ||

intristic parity |