Stephen Hawking was the greatest theoretical gravitational physicist since Einstein. Using the assumptions of Einstein's classical theory of gravity, general relativity, plus reasonable conditions on the energy density and pressure of matter, Hawking showed that the observed expansion of the universe would imply that the universe had a beginning, a big bang singularity at the beginning of time. Under similar assumptions, he showed that the surface of a black hole, called the event horizon, would have an area that cannot decrease with time but could only stay the same (if nothing fell into the black hole) or get bigger (if energy did fall into the hole).
Later, Hawking turned his attention to quantum theory, which can lead to violations of the usual reasonable conditions on the energy density and pressure of matter. He then found that actually black holes can create and emit particles, now called Hawking radiation, and shrink, presumably eventually disappearing entirely into a final burst of radiation.
This prediction of Hawking radiation is perhaps Hawking's most well known discovery, and it has almost entirely been accepted by other physicists who have studied the situation of a black hole with negligible incoming energy. However, this 1974 discovery led Hawking in 1976 to make the more radical proposal that when a black hole forms and then evaporates away, information is lost from our universe. (In more technical terms, a pure quantum state would become a mixed quantum state, with greater von Neumann entropy.)
Starting with a paper of mine in 1980 that questioned Hawking's argument for information loss and with a very small number of other papers on this in the early years, a growing crescendo of papers have appeared on black hole information. Eventually, particularly as a result of string theory arguments, the majority of papers have questioned information loss and supported the older view that information is not lost. In 2004, Hawking reversed his opinion and conceded a famous bet he had made in 1997 with John Preskill. In 2007, Hawking conceded an even earlier bet he had made with me in 1980, paying me a dollar that was actually a fake dollar with a picture of Marilyn Monroe, whom he considered to be "a model of the universe." However, there are several renowned physicists who think Hawking was originally correct and should not have conceded his bets.
Hawking also applied quantum theory to the universe and, with James Hartle of the University of California at Santa Barbara in 1983, proposed the no-boundary wave function of the universe. This was conceptually a major innovation, proposing laws of physics not only for how the universe evolves but what it was like at some initial time. The Hartle-Hawking no-boundary quantum state pictures the universe as not having a singular beginning and in some sense no beginning at any precise time at all, thereby giving a different picture than the singular beginning proved by his singularity theorems under the approximation of classical general relativity. However, one should note that it is almost certainly premature to give a precise quantum state for the universe, and indeed there are some technical problems with the Hartle-Hawking proposal. Nevertheless, it is a major conceptual advance to bring the quantum state within the laws of physics.
These are just a few of the highlights of the remarkable achievements Hawking has achieved in physics. Besides his academic work, he has done a great service in popularizing his and other advances in physics and cosmology with books such as the bestseller, A Brief History of Time. His courage in the face of enormous physical adversity has also been an inspiration to millions of people.
On a personal note, Stephen Hawking was an outstanding mentor for me, from being a co-supervisor (along with my main supervisor Kip Thorne) of my Ph.D. during his 1974-75 visit to Caltech and during my postdoctoral position under his supervision at the University of Cambridge 1976-79. He has indeed been crucial in my career, both in getting me my academic positions and in giving me plenty of ideas that I have continued to work on throughout my career. He and his family were also very close personal friends (going back to my living in his home and helping him out while being a postdoc in Cambridge). I shall miss him greatly.
--
Don Page is a theoretical physicist at the University of Alberta, Edmonton. He and his wife Cathy Page have also paid tribute to the late Stephen Hawking on CBC's Calgary Explorer, Edmonton AM, and "Quirks and Quarks."