Wave function of the Universe. Offprint from: Physical Review D, Vol. 28, No. 12, 15 December 1983

HAWKING'S NO-BOUNDARY PROPOSAL: HOW THE UNIVERSE COULD HAVE ARISEN FROM NOTHING. First edition, very rare offprint, and Hawking's own file copy, of this famous paper describing the 'no-boundary proposal' for the origin of the universe. "Stephen sought to understand the whole universe in scientific terms. As he said famously, 'My goal is simple. It is a complete understanding of the universe' . From 1982 onwards, Stephen concentrated his efforts on the deeper puzzle of the boundary conditions required to bring about inflation and the probability of them coming about . The singularity theorems proved by Stephen, Penrose and others showed conclusively that the classical Einstein equation implied that the universe began in a hot Big Bang. But the singularity theorems also showed that the beginning could not be described by a classical space-time geometry obeying the Einstein equation with three space directions and one time direction at each point. Rather, they showed something more sweeping: the classical Einstein equation breaks down at the Big Bang and, along with that, the notion that it could be described by a classical space-time . [it was therefore necessary to try] to describe the quantum birth of the universe. Stephen first put forward a proposal along these lines at a conference in the Vatican in 1981, where he suggested that the universe began with a regular Euclidean geometry having four space dimensions which made a quantum transition to a Lorentzian geometry with three space dimensions and one time dimension that we have today. To put this idea on a solid footing required a quantum state-a wave function of the universe" (Carr et al.). "'Murray Gell-Mann used to ask me,' Hartle said, referring to the late Nobel Prize-winning physicist, 'if you know the wave function of the universe, why aren't you rich?'" (Wachover). "Because one is using Euclidean space-times, in which the time direction is on the same footing as directions in space, it is possible for space-time to be finite in extent and yet to have no singularities that formed a boundary or edge. Space-time would be like the surface of the earth, only with two more dimensions . the quantum theory of gravity has opened up a new possibility, in which there would be no boundary to space-time and so there would be no need to specify the behavior at the boundary. There would be no singularities at which the laws of science broke down, and no edge of space-time at which one would have to appeal to God or some new law to set the boundary conditions for space-time. One could say: 'The boundary condition of the universe is that it has no boundary.' The universe would be completely self-contained and not affected by anything outside itself. It would neither be created nor destroyed, it would just BE" (Hawking). "The scientific importance of the no-boundary proposal is not just as a successful theory of the origin of the basic structure of the universe-it has also had a significant effect on how we think about the universe and our place in it" (Carr et al.). We are not aware of any other copy of this offprint having appeared on the market. Provenance: the estate of Professor Stephen Hawking (1942-2018). "In 1981, many of the world's leading cosmologists gathered at the Pontifical Academy of Sciences, a vestige of the coupled lineages of science and theology located in an elegant villa in the gardens of the Vatican. Stephen Hawking chose the august setting to present what he would later regard as his most important idea: a proposal about how the universe could have arisen from nothing" (Wachover). At that time the standard theory of the origin of the universe was the 'Big Bang' model. This had apparently been confirmed by the discovery of the cosmic microwave background by Arno Penzias and Robert Wilson in 1965. But the Big Bang theory had some problems. Not only was there the question of what happened before the Big Bang, but the theory predicted a universe that was not near.…