His Jewish family fled Nazi Germany to Egypt and Goldhaber earned a master's degree in physics in 1947 from the Hebrew University of Jerusalem.

At Berkeley, Goldhaber was part of a particle physics research team that used photographic emulsion to track the movements of subatomic particles in proton-proton scattering experiments that led to the identification of the antiproton, a discovery that earned Owen Chamberlain and Emilio G. Segrè the Nobel Prize in Physics in 1959.

For his work on the project, Goldhaber won the American Physical Society's Panofsky Prize and was named California Scientist of the Year.

By 1997, data that the group had gathered provided evidence that the rate of the expansion of the Universe was increasing due to what they termed dark energy, contrary to the prevailing theory that expansion would slow down and ultimately reverse itself with a Big Crunch as the ultimate fate of the universe.

His marriage to nuclear chemist Sulamith Goldhaber ended with her death from a brain tumor in 1965 while the couple was traveling in India.