Much of modern physics is founded on Quantum Physics and Einstein's Theories of Relativity - this is evidenced by a large number of Nobel Prizes related to the development and testing of the predictions of Special and General Relativity.
I give a brief description of the important ones: More detailed information is available in the website of the Nobel Prize Organisation.
I shall put a list of Nobel Prizes for work in Quatum Physics to coincide with my talks on Quantum Mechanics sometime in 2011. Watch this space.
1921 - Albert Einstein
Ironically, while relativity has led to so many Nobel prizes, it only played a minor role in Einstein's own. The Nobel committee's brief prize announcement refers to Einstein's "services to Theoretical Physics" with explicit mention given only to his finding the law of the photoelectric effect.
1933 - Paul Dirac
Dirac's prize was the first of many given for work on the connection between special relativity and quantum theory.
Dirac was the pioneer of relativistic quantum mechanics and formulated the Dirac equation, the first equation for the quantum behaviour of relativistic matter particles. He discovered a fundamental relativistic quantum phenomenon: for every species of relativistic particle, there must be a kind of mirror image, a species of corresponding antiparticles. In a world in which electrons exist, which carry negative electric charge, Dirac's equation demands the existence of anti-electrons, particles with the same mass as electrons, but a positive electric charge.
1936 - Carl D. Anderson
What, at first sight, appeared to be a stumbling stone for Dirac's theory - where were those anti-electrons he postulated? - later turned into a triumph. Among the particles of cosmic rays, a highly energetic particle radiation reaching the earth's surface from space, Carl Anderson discovered traces of anti-electrons. Diracs anti-particles, with the same mass as electrons but the opposite electric charge, really do exist! Anti-electrons are now called positrons.
1949 - Hideki Yukawa
The force that bonds protons and neutrons together to form atomic nuclei has a strictly limited range: of the order of a trillionth of a metre. Yukawa found an explanation for the short-range nuclear force that is directly linked to the fact that the carrier particle of nuclear force has a non-zero (rest) mass. He derived this directly from a relativistic quantum equation for massive particles.
1951 - John Cockcroft and Ernest T. S. Walton
Cockcroft and Walton bombarded atomic nuclei of the element Lithium with fast protons, thus creating helium nuclei in the first controlled transmutation of one species of nucleus to another. Summing up the energies before and after the transmutation, they tested directly the equivalence of mass and energy postulated by Einstein: the helium nuclei that result have a slightly lower mass than that of proton and lithium nucleus combined, and this difference in mass leads to a kinetic energy of the resulting nuclei that is higher than expected by non-relativistic physics, exactly following Einstein's prediction.
1955 - Willis Eugene Lamb and Polykarp Kusch
Lamb and Kusch performed precision measurements, establishing the reality of two effects: called the Lamb shift and the electron's magnetic properties that Dirac's equation could not correctly predict. These measurements contributed to the eventual development of relativistic quantum feld theories: of quantum electrodynamics, the relativistic quantum theory of the electromagnetic field.
1959 - Emilio Segrè and Owen Chamberlain
In relativistic quantum theories, for every species of particle, there is a species of antiparticles. Segrè and Chamberlain received their prize for the discovery of anti-protons, the antiparticles of protons.
1963 - Eugene Wigner
The relativity principle states that observers that are in motion relative to each other are on equal footing; the physical laws are exactly the same for each of them. In physics, such equality is called a symmetry. Whether or not a physical theory, be it a model of electromagnetic phenomena, fluid dynamics or a theory of heat, is consistent with the relativity principle can be examined in a general framework that analyzes the theory's symmetries. Wigner was the first to apply this framework to quantum theory, and laid the foundation of modern relativistic quantum feld theories.
1965 - Shin-Itiro Tomonaga, Julian Schwinger, Richard P. Feynman
In quantum field theories, not only the matter particles, but also the forces acting between them follow quantum laws. The distinction between matter and forces becomes blurred: The action of a force is represented by the exchange of particles - the carrier particles.
Tomonaga, Schwinger and Feynman formulated a theory of relativistic quantum forces for the simplest case, that of the electromagnetic force, creating what is known as quantum electrodynamics.
This was the starting point leading to the formulation of the more general quantum field theories of the standard model of particle physics.
1974 - Antony Hewish
The discovery that won Hewish his prize, although not a consequence of relativity, is nonetheless an important step for relativistic astrophysics.
Together with his graduate student Jocelyn Bell-Burnell, Hewish discovered the first pulsar, opening up the field of observational astronomy of neutron stars.
1978 - Arno Penzias and Robert Wilson
Penzias and Wilson won their Nobel prize for the first detection of the cosmic background radiation, an afterglow from the early, hot days of the universe. With their discovery, they confirmed a prediction made by Ralph Alpher and Robert Herman in 1948 on the basis of the relativistic big bang models.
1983 - Subramanyan Chandrasekhar and William A. Fowler
The Chandrasekhar mass is the maximal mass for which the inner pressure of the White Dwarf can resist further collaps. For remnants with higher mass the collapse continues, forming a neutron star or even a black hole.
Fowler won the prize for his research on the origin of the chemical elements in the universe. Part of that work concerned another prediction of the big bang models of relativistic cosmology, namely that of the formation of light elements in the early universe.
1993 - Russell A. Hulse and Joseph H. Taylor
Hulse and Taylor discovered the first binary pulsar: a binary in which a pulsar and a companion neutron star orbit each other. Their observations of this binary pulsar, called PSR1913+16, led to the first indirect detection of gravitational waves and provided some sensitive tests of the General theory of Relativity.
2002 - Riccardo Giacconi
Giacconi won the prize for his pioneering work in X-ray astronomy, in part for the first detection of objects tha are now widely believed to be black holes.
2006 - John C. Mather and George F. Smoot
With the COBE satellite, Mather and Smoot made precise measurements of the black body nature of the cosmic background radiation, confirming an important prediction of the big bang models. The tiny fluctuations observed in the background microwave radiation are the first seeds for the large scale structure in the Universe.