Picture This: Stephen Hawking's Blackboard

Famed physicists' loopy scribbles give clues to the origins of time and space.
Rectangular wooden blackboard from the 1980 Nuffield Workshop in Cambridge, UK, on Superspace and Super Gravity.Courtesy of the Science Museum Group.

This blackboard hung in Stephen Hawking’s office at the University of Cam­bridge. After Hawking’s passing, it was acquired for the nation by the London Science Museum Group, where it’s now displayed in the Exploring Space gallery. Filled with inscrutable doodles, drawings, inside jokes, and half-finished equations, this blackboard is a glimpse into the abstract universe of theoretical physicists. There is a floppy-nosed squid climbing over a brick wall, but also a tin can labeled “EXXON SUPERGRAVITY” and ample references to hypothetical species of particles. Hawking himself is mysteriously drawn in the center near the bottom, with his back toward us.

I first saw this blackboard in 1998 as a beginning PhD student of Hawking’s. At the time, I wondered whether these scribbles could be some of his last hand-scrawls. This isn’t the case, as it turns out. The writings are from participants of a month-long workshop that Hawking and his Cambridge colleagues convened in the summer of 1980, called Superspace and Supergravity. The blackboard is a memento from this workshop. Quite a few of the drawings were made by Hawking’s co-organizer and postdoc at the time, Martin Roček, whose face can be seen, sketched in chalk, near the board’s center. As a matter of fact, a picture of this blackboard decorated the cover of the conference proceedings, published after the workshop’s end. Hawking refers to it in his foreword, before summarizing the meeting as “an instructive way to spend four weeks.”

In that same year, as incumbent of the Lucasian Chair of Mathematics at the University of Cam­bridge, Hawking delivered his inaugural lecture, “Is the End in Sight for Theoretical Physics?” In this lecture, at the zenith of his confidence in the power of physical theory, he predicted that physicists would find the final theory of everything by the end of the twentieth century. Moreover he famously—and controversially—put forward the theory of supergravity as the prime candidate for such a theory. “The best hope for a unifying quantum theory of gravity seems to lie in an extension of general relativity called supergravity,” he said, before adding a key caveat: that “a complete theory includes besides a theory of dynamics, such as supergravity, also a set of boundary conditions.” Elaborating on this point, he added, “Many people would claim that the role of science was confined to the first of these and that theoretical physics will have achieved its goal when we have obtained a set of local dynamic laws. They would regard the question of the boundary conditions of the universe as belong­ing to the realm of metaphysics or religion. But we shall not have a com­plete theory until we can do more than merely say that things are as they are because they were as they were.”

This is an important point. Ever since Galileo and Newton, physics has been based on a dualism of sorts, in that it has relied on a fundamental separation between two distinct sources of information. First, there are laws of evolution, mathematical equations such as those of supergravity, that prescribe how physical systems change in time from one state to another. Second, there are boundary conditions, a concise description of the state of a specific system at a given moment in time. The laws of dynamics take that state and evolve it, either backward or forward in time, to determine what the system was like at an earlier moment or what it will be like at a later moment. It is the combination of the laws of evo­lution and the boundary conditions that yields the framework for predic­tion on which physics prides itself.

"We shall not have a com­plete theory," Hawking said, "until we can do more than merely say that things are as they are because they were as they were."

For example, imagine we want to predict where and when the next solar eclipse will occur. To do so, we can apply Newton’s laws of motion and gravity to describe the future trajectories of Earth and the moon. To put these laws to use, however, one must first specify the position and velocity of Earth and the moon relative to the sun (and to Jupiter) at one particular moment in time. These data are boundary conditions. They describe the state of these two celestial bodies in the solar system at one specific mo­ment in time. No one expects Newton’s laws to explain why these positions are what they are at that moment. Instead, we measure what they are. With this information at hand, we then solve Newton’s equations to determine their positions at future times, in order to predict when and where solar eclipses will occur, or at earlier times, to retrodict documented eclipses.

But this separation between universal, law-like dynamics and ad hoc boundary conditions can become a major embarrassment in cosmology, when we embed our experiments and ex­perimenters—our planet, the stars, and the galaxies—in the much larger evo­lution of the universe as a whole. When we do this, boundary conditions on the original experiment are subsumed into the law-like evolution of the larger system, together with boundary conditions on the latter. Returning to the example of a solar eclipse, a holistic cosmologist could argue that the ve­locities and positions of Earth and the moon at any given moment—the original boundary conditions—follow from their past histories, and that our plane­tary system itself is the outcome of the formation history of the solar sys­tem, which in turn arose from the condensation of remnants of prior stellar systems, whose seeds ultimately grew out of minute density variations in the primeval universe that came from… what?

When we arrive at the beginning we reach a paradox. What determines the ultimate boundary conditions at the origin of time? Clearly these are not up to us to choose and we can’t try out different conditions to see what kind of universes they produce. That is, the beginning of the uni­verse poses a problem of boundary conditions that we do not control. In­stead, very interestingly, the conditions at the big bang appear to be dragged into the laws we seek to understand. Yet dualism in physics holds that boundary conditions aren’t part of the physical laws.

In his Lucasian lecture in 1980, Hawking put his finger on this paradox. More than any other physicist of his generation, he felt that the deeper questions in cosmology required us to rethink the centuries-old framework for prediction in physics. His idea was to take physics beyond its stubborn dualism of eternal laws versus conditions. Such dualism, he felt, was too narrow a way of thinking about the world if we were to truly understand our cosmic origins.

Working with Jim Hartle, Hawking went on to develop an ingenious theory of the ultimate boundary conditions at the universe’s birth. Their model involved turning time into an extra dimension of space back at the beginning, thus quite literally morphing dynamics into state. Next they bent space into a four-dimensional version of a round sphere to close the “past,” thereby excising the notion of a beginning altogether. “Asking what came before the big bang would be like asking what lies south of the South Pole,” Hawking summed up their model, and he went on to refer to their theory as the no-boundary hypothesis, since a sphere has no edge or boundary.

In what may well have been an intended resonance, Hawking first pro­posed his cosmogony at a meeting of the Pontifical Academy of Sciences in the Vatican in Octo­ber 1981. Earlier in the week, Pope John Paul II had told the assembled scientists that “every scientific hypothesis on the beginning of the world … requires knowledge be­yond physics.” As if he were responding to the pope’s allocution, Hawking put forward the bold idea that there might not quite have been a beginning. “There ought to be something very special about the boundary conditions of the universe and what can be more special than the condition that there is no boundary.”

The enigma of the big bang has been one of these rare instances in science where broader philosophical considerations have come to the forefront. Such occasions teach us something not only about nature, but also about the nature of science and what it is that physics ultimately finds out about the world. Over the years, the Vatican and physicists alike have had to revise their positions on this.

A theory of boundary conditions, we came to realize, isn’t just a law of the beginning but also the beginning of laws.

But what fresh philosophy of physics flows from Hartle and Hawking’s cosmogenesis that replaces dualism? For years this has remained mysterious. Worse, the original version of the no-boundary theory didn’t work: it predicted an empty universe devoid of galaxies and life. Starting in the early 2000s, however, Hawking, Hartle, and I set out to rethink their earlier ideas on the big bang from a proper quantum viewpoint. We were led to a fundamentally evolutionary understanding of these earliest stages of the universe, in which the physical laws coevolve with the emerging universe. A theory of boundary conditions, we came to realize, isn’t just a law of the beginning but also the beginning of laws. This was way more radical than what even Hawking initially had in mind.

The younger Hawking sought a final theory of physics that was hovering above the universe—or even the multiverse—like an eternal truth. He assumed there was a fundamental causal explanation for the origin of the cosmos that was to be found deep in the mathematical underpinnings of physics. The later Hawking rejected the idea that the universe is like a machine gov­erned by unconditional laws with some sort of prior existence. The theory we developed toward the end of his life states that physics itself fades away back into the big bang. It is not the laws as such but their capacity to change and evolve that has the final word. One might say our theory provides physics with an epistemic horizon.

While it took many years to develop this new vision, the first inklings in Hawking’s mind go back to the workshops at Cambridge in the early 1980s. Indeed, if he did predict the end of dualism on the blackboard, whatever he wrote with the remaining strength in his hands got eaten by the squid. ♦

To read more about Hawking’s final theory, read Hertog’s new book, On the Origin of Time.

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