Henry F. Schaefer III was born in Grand Rapids, Michigan. He attended public schools in Syracuse (New York), Menlo Park (California), and Grand Rapids (Michigan), graduating from East Grand Rapids High School in 1962. He received his B.S. degree in chemical physics from the Massachusetts Institute of Technology (1966) and Ph.D. degree in chemical physics from Stanford University (1969). For 18 years (1969-1987) he served as a professor of chemistry at the University of California, Berkeley. During the 1979-1980 academic year he was also Wilfred T. Doherty Professor of Chemistry and inaugural Director of the Institute for Theoretical Chemistry at the University of Texas, Austin. Since 1987 Dr. Schaefer has been Graham Perdue Professor of Chemistry and Director of the Center for Computational Quantum Chemistry at the University of Georgia. In 2004 he became Professor of Chemistry, Emeritus, at the University of California at Berkeley. His other academic appointments include Professeur d’Echange at the University of Paris (1977), Gastprofessur at the Eidgenössische Technische Hochshule (ETH), Zürich (1994, 1995, 1997, 2000, 2002, 2004, 2006, 2008, 2010), and David P. Craig Visiting Professor at the Australian National University (1999). He is the author of more than 1250 scientific publications, the majority appearing in the Journal of Chemical Physics or the Journal of the American Chemical Society. A total of 300 scientists from 35 countries gathered in Gyeongju, Korea for a six-day conference in February, 2004 with the title Theory and Applications of Computational Chemistry: A Celebration of 1000 Papers of Professor Henry F. Schaefer III. In May 2010, the University of California at Berkeley will host a large international conference in Professor Schaefer’s honor, the title of the conference being Molecular Quantum Mechanics: From Methylene to DNA and Beyond.
Let us return to Hawking’s no boundary proposal – the idea that the universe has neither beginning nor end. By treating the universe as a wave function, Hawking hopes to rationalize the universe’s popping into existence 12-15 billion years ago. Critical to Hawking’s research in this regard is the notion of imaginary time. The concept of imaginary time is a powerful mathematical device used on occasion by theoretical chemists and physicists. I remember clearly the day in the autumn of 1965, during my Complex Variables class as a senior at M.I.T., when I learned that the result of contour integration was two pi i times the sum of the residues. For me, it was about as close to a revelation as I had received up to that time in my life. My closest colleague at Berkeley, Professor William H. Miller, in 1969 used imaginary time to understand the dynamics of chemical reactions, and it made him a household word in the world of science. The use of imaginary time is indeed a powerful tool.
Indulge me while I attempt to convey the essence of how imaginary time is exploited in theoretical physics and chemistry. One approaches a well defined problem, with all variables necessarily being real. This means, for example, real positions for all particles, real velocities, and so on. Real problems begin with all quantities real. Then one undertakes a carefully chosen excursion into the complex plane, making one or more variables complex. Subsequently we do some really cool things mathematically. Finally, all the variables revert to real values, and we find that something important has been mathematically derived that would have otherwise been impossible to prove.
Hawking and Hartle’s no boundary proposal begins by adopting a grossly oversimplified model of the universe. Then the authors make time imaginary, and prove in their terribly restricted model that the universe has neither beginning nor end. The flaw in the exercise is that the authors never go back to real time. Thus the notion that the universe has neither beginning nor end is something that exists in mathematical terms only. In real time, to which we as human beings are necessarily attached, rather than in Hawking’s use of imaginary time, there will always be a singularity, that is, a beginning of time.
In an obviously contradictory statement in A Brief History of Time, Hawking actually concedes this point. What we are seeing in this situation is Hawking versus Hawking. I view the following statement as Hawking speaking in his right mind: “When one goes back to the real time in which we live, however, there will still appear to be singularities . . . In real time, the universe has a beginning and an end at singularities that form a boundary to space-time and at which the laws of science break down” (first edition, page 144). Only if we lived in imaginary time (not coming soon to a neighborhood near you!) would we encounter no singularities. In real time the universe was created ex nihilo 12-15 billion years ago.
With some trepidation, I will venture further. A case can be made that the Hartle-Hawking “no boundary proposal” is only of marginal scientific interest. The reasons for this conclusion might include: (a) the theory is a mathematical construct that has no unique empirical support; (b) the theory makes no verifiable scientific predictions that were not achieved earlier with simpler models; (c) the theory generates no significant research agenda. The primary purpose of the theory seems to be an attempt to evade the cosmological argument for the existence of God, via the claim that nature is self-contained and effectively eternal.
I’ll stick with the experimental guy.