Space is filled everywhere with fields. The electromagnetic field is one example. The electron field is another example. A field is any quantity that has a value everywhere in space. The value of the electromagentic field in a region of pure and utter darkness is zero. When a photon passes by, the electromagnetic field stops being zero wherever the photon is located at that particular instant. Likewise, the value of the electron field in empty space is zero. Where there are electrons, the electron field has a positive numerical value. Where there are positrons (antielectrons), the electron field has a negative value. When a positive number is added to a negative number, the sum is zero. When an electron and a positron meet, they both cease to exist or annihilate. The loss of mass excites the electromagnetic field producing two photons that zip away at the speed of light.
We can also visualize fields as a surface whose height at a location corresponds to its value. As far as the electron field is concerned, empty space is flat. Where there are no electrons, there is no height or depth. A bump in the electron field is an electron and a pit to a positron. When an electron and an positron meet, the bump falls into the pit and the electron field flattens out. No height or depth means no electron or positron. The particles cease to exist, but the field continues on for eternity. This transition generates a pair of photons, which are bumps on the normally flat electromagnetic field.
Every particle has its own antiparticle. Two major discoveries helped physicists to establish this fundamental principle:
- positron (e+)
Examining cosmic-ray data, Anderson discovers the positively charged electron later named the positron. He receives the 1936 Nobel Prize.
- antiproton (p−)
Using an accelerator at Berkeley University, Segre and Chamberlain discover the antiproton. They receive the 1959 Nobel Prize. (Later, physicists learn that a proton contains quarks and an antiproton consists of antiquarks.)
Paraphrase needed …
Carl David Anderson (1905-91) received Nobel prize in 1936 for the discovery of the positron. In 1936, with Seth Neddermeyer, Anderson also discovered the positive and negative "mesotron", now called the muon. Thus he added three new particles to physics and pointed the way to the existence of antimatter. To obtain more intense, higher energy cosmic rays, the pair transported their magnet cloud chamber to the summit of Pike's Peak, colorado. Analyzing the cloud chamber photos after the summer at the Peak, they found positive and negative tracks that were different from electrons and protons and appeared to have intermediate mass.
interesting (but wrong) idea
As a by-product of this same view, I received a telephone call one day at the graduate college at Princeton from Professor Wheeler, in which he said, "Feynman, I know why all electrons have the same charge and the same mass" "Why?" "Because, they are all the same electron!" And, then he explained on the telephone, "suppose that the world lines which we were ordinarily considering before in time and space — instead of only going up in time were a tremendous knot, and then, when we cut through the knot, by the plane corresponding to a fixed time, we would see many, many world lines and that would represent many electrons, except for one thing. If in one section this is an ordinary electron world line, in the section in which it reversed itself and is coming back from the future we have the wrong sign to the proper time — to the proper four velocities — and that's equivalent to changing the sign of the charge, and, therefore, that part of a path would act like a positron." "But, Professor", I said, "there aren't as many positrons as electrons." "Well, maybe they are hidden in the protons or something", he said. I did not take the idea that all the electrons were the same one from him as seriously as I took the observation that positrons could simply be represented as electrons going from the future to the past in a back section of their world lines. That, I stole!
Richard Feynman, 1965
Paul Dirac, usually cited by his inititial P.A.M. Dirac (for Paul Adrien Maurice).
- 1928 invents the relativistic Schödinger equation now called the Dirac equation and applied it to the electron. Realizes it allows the electron to have either negative or positive charge and positive or negative kinetic energy. "The second difficulty in Gordon's interpretation arises from the fact that if one takes the conjugate imaginary of equation (1), one gets
which is the same as one would get if one put −e for e. The wave equation (1) thus refers equally well to an electron with charge e as to one with charge −e. If one considers for definiteness the limiting case of large quantum numbers one would find that some of the solutions of the wave equation are wave packets moving in the way a particle of charge −e would move on the classical theory, while others are wave packets moving in the way a particle of charge e would move classically. For this second class of solutions W has a negative value. One gets over the difficulty on the classical theory by arbitrarily excluding those solutions that have a negative W. One cannot do this on the quantum theory, since in general a perturbation will cause transitions from states with W positive to states with W negative. Such a transition would appear experimentally as the electron suddenly changing its charge from −e to e, a phenomenon which has not been observed. The true relativity wave equation should thus be such that its solutions split up into two non-combining sets, referring respectively to the charge −e and the charge e." The quantum theory of the electron
− W + e A0 ⎞2
− p + e A ⎞2
+ m2c2 ⎤
ψ = 0 c c c
- 1930 solves the problem of negative energy by imagining those particles as holes. When an ordinary electron meets its negative energy sister, the two particles annihilate and electromagnetic radiation is released. "An electron, according to relativity quantum theory, has two different kinds of states of motion, those for which the kinetic energy is positive and those for which it is negative. Only the former, of course, can correspond to actual electrons as observed in the laboratory. The latter, however, must also have a physical meaning, since the theory predicts that transitions will take place from one kind to the other. It has recently been proposed that one should assume that nearly all the possible states of negative energy are occupied, with just one electron in each state in accordance with Pauli's exclusion principle, and that the unoccupied states or 'holes' in the negative-energy distribution should be regarded as protons. According to these ideas, when an electron of positive energy makes a transition into one of the unoccupied negative-energy states, we have an electron and proton disappearing simultaneously, their energy being emitted in the form of electromagnetic radiation. The object of the present paper is to calculate the frequency of occurrence of these processes of annihilation of electrons and protons." On the annihilation of electrons and protons
- 1933 Quote that should be condensed. "It thus appears that we must abandon the identification of the holes with protons and must find some other interpretation for them. Following Oppenheimer, we can assume that in the world as we know it, all, and not merely nearly all, of the negative-energy states for electrons are occupied. A hole, if there were one, would be a new kind of particle, unknown to experimental physics, having the same mass and opposite charge to an electron. We may call such a particle an anti-electron. We should not expect to find any of them in nature, on account of their rapid rate of recombination with electrons, but if they could be produced experimentally in high vacuum they would be quite stable and amenable to observation. An encounter between two hard y-rays (of energy at least half a million volts) could lead to the creation simul taneously of an electron and anti-electron, the probability of occurrence of this process being of the same order of magnitude as that of the collision of the two y-rays on the assumption that they are spheres of the same size as classical electrons. This probability is negligible, however, with the intensities of y-rays at present available." Quantised singularities in the electromagnetic field.
- 1933 Nobel prize. Speculates on the possibility of anti-other-stuff "If we accept the view of complete symmetry between positive and negative electric charge so far as concerns the fundamental laws of Nature, we must regard it rather as an accident that the Earth (and presumably the whole solar system), contains a preponderance of negative electrons and positive protons. It is quite possible that for some of the stars it is the other way about, these stars being built up mainly of positrons and negative protons. In fact, there may be half the stars of each kind. The two kinds of stars would both show exactly the same spectra, and there would be no way of distinguishing them by present astronomical methods."
|βmc2 + c||⎛
|ψ(x,t) = iℏ||
iℏγμ∂μψ − mcψ = 0
(i∂̸ − m)ψ = 0