In 1928, British physicist Paul Dirac wrote down an equation that combined quantum theory and special relativity to describe the behaviour of an electron moving at a relativistic speed. The equation would allow whole atoms to be treated in a manner consistent with Einstein's relativity theory. Dirac's equation appeared in his paper The quantum theory of the electron, received by the journal Proceedings of the Royal Society A on 2 January 1928. It won Dirac the Nobel prize in physics in 1933. But the equation posed a problem: just as the equation x2=4 can have two possible solutions (x=2 or x=-2), so Dirac's equation could have two solutions, one for an electron with positive energy, and one for an electron with negative energy. But classical physics (and common sense) dictated that the energy of a particle must always be a positive number. Dirac interpreted the equation to mean that for every particle there exists a corresponding antiparticle, exactly matching the particle but with opposite charge. For the electron there should be an "antielectron" identical in every way but with a positive electric charge. In his 1933 Nobel lecture, Dirac explained how he arrived at this conclusion and speculated on the existence of a completely new universe made out of antimatter: 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.

While studying cosmic rays in a Wilson cloud chamber, the Soviet academic Dimitri Skobeltsyn noticed something unexpected among the tracks left by high-energy charged particles. Some particles would act like electrons but curve the opposite way in a magnetic field. In an independent experiment that same year, Caltech graduate student Chung-Yao Chao observed the same phenomenon. The results were inconclusive, and both scientists disregarded the anomaly. 

Paul Dirac published a paper mathematically predicting the existence of an antielectron that would have the same mass as an electron but the opposite charge. The two particles would mutually annihilate upon interaction. “This new development requires no change whatever in the formalism when expressed in terms of abstract symbols denoting states and observables, but is merely a generalization of the possibilities of representation of these abstract symbols by wave functions and matrices. Under these circumstances one would be surprised if Nature had made no use of it,” he wrote.

  The discovery was confirmed soon after by Occhialini and Blacket, who published Some photographs of the tracks of penetrating radiation in the journal Proceedings of the Royal Society A. Anderson's observations proved the existence of the antiparticles predicted by Dirac. For discovering the positron, Anderson shared the 1936 Nobel prize in physics with Victor Hess. For years to come, cosmic rays remained the only source of high-energy particles. The next antiparticle physicists were looking for was the antiproton. Much heavier than the positron, the antiproton is the antiparticle of the proton. It would not be confirmed experimentally for another 22 years.

William H. Sweet and Gordon L. Brownell at Massachusetts General Hospital in Boston suggested using the radiation emitted by positron annihilation to improve the quality of brain images by increasing sensitivity and resolution. They published a description of the first positron-imaging device to record three-dimensional data of the brain in their 1953 paper Localization of brain tumors with positron emitters in Nucleonics XI. This was the beginning of positron emission tomography.