On the Origin of Time: Stephen Hawking's Final Theory

by Thomas Hertog

The anthropic principle is a counsel of despair, he wrote, my bemusement mounting in sync with his clicking. It is a negation of our hopes of understanding the underlying order of the universe, on the basis of science. Well, this was surprising. Having read A Brief History of Time, I was well aware that the early Hawking had frequently flirted with the anthropic principle as part of the explanation for the universe.

Both inside black holes and at the big bang, the macroworld of gravity truly merges with the microworld of atoms and particles. Under these extreme conditions, Einstein’s relativity theory of gravity and quantum theory had better work together. Except they don’t, and this is widely viewed as one of the biggest unsolved problems in physics. For example, both theories embody a radically different view of causality and determinism. Whereas Einstein’s theory adheres to the old determinism of Newton and Laplace, quantum theory contains a fundamental element of uncertainty and randomness and retains only a reduced notion of determinism, about half of what Laplace thought it was.

Like so many scholars before him, the early Hawking regarded the fundamental laws of physics as immutable, timeless truths. “If we do discover a complete theory…we would truly know the mind of God,” he wrote in A Brief History of Time. More than ten years on, however, during our first meeting—and with Linde’s multiverse breathing down our neck—I sensed he felt a crack in this position. Does physics really provide godlike foundations operating at the big bang origin of time? Do we need such foundations?

Stephen and I came to see the big bang not only as the beginning of time but also as the origin of physical laws. At the heart of our cosmogony lies a new physical theory of the origin, which, we came to realize, at the same time encapsulates the origin of theory.

When Jim or Stephen said “the universe,” they meant the abstract quantum universe, awash in uncertainty, with all its possible histories living in some sort of superposition. But it was precisely their thoroughly quantum outlook that eventually made a genuine Darwinian revolution possible in cosmology.

Had the hot big bang been perfectly uniform everywhere, there would be no galaxies today. The ancient CMB snapshot marks our cosmological horizon: We cannot look back any farther. But we can glean something about processes operating in yet earlier epochs from cosmological theory.

Slowing down appears to be the exception rather than the rule on the scales of deep time and deep space. This is one of those seemingly fortuitous biofriendly properties of the universe, for only in a slowing universe does matter aggregate and cluster to form galaxies. If it hadn’t been for the extended near-pause in expansion in our past, there would, again, be no galaxies and no stars, and thus no life.

We live in a universe with three large dimensions of space. Is there anything special about three? There is. Adding just a single space dimension renders atoms and planetary orbits unstable. Earth would spiral into the sun instead of tracing out a stable orbit around it. Universes with five or more large space dimensions have even bigger problems.

So the riddle of design in cosmology is that the fundamental laws of physics appear to be specifically engineered to facilitate the emergence of life. It is as if there is a hidden plot at work that weaves together our existence with the basic rules on which the universe runs.

Aristotle’s teleological views held up, largely unchallenged, for almost two millennia. But then, in the sixteenth century, somewhere on the outskirts of the Eurasian landmass, the work of a small circle of scholars sparked the modern scientific revolution. Copernicus, Descartes, Bacon, Galileo, and their contemporaries stressed that our senses can betray us. They embraced the Latin dictum Ignoramus, literally, “We do not know.”

Miletus, the richest of the Greek Ionian cities, was founded at a natural harbor near where the river Meander flows into the Aegean Sea. There the legendary Thales, much like modern scientists, was willing to look beneath the surface appearances of the world in order to pursue knowledge at a deeper level.

Darwin found the sweet spot between the “why” and the “how” in biology, integrating causal explanations with inductive reasoning in a single coherent scheme. He showed that despite its fundamentally historical and accidental nature, biology can be a proper productive science that enhances our understanding of the living world.

The maximum speed is reached when motion through time is fully diverted into motion through space. That is the speed of light—a cosmic speed limit. Loosely speaking, moving at the speed of light through space leaves nothing for traveling through time. If a particle of light had a wristwatch, it wouldn’t tick at all.

People used to think that the past and the future were simply glued to each other at the present. But special relativity teaches us that for you, the observer, they touch only at the point marking your particular location in the universe.

In November 1915, in the dark days of World War I, Einstein could finally put forward his theory of general relativity, a new theory of gravity, consistent with his special relativity theory of spacetime, that would become his most sweeping scientific accomplishment. General relativity describes gravity in geometric terms—the geometry, in fact, of spacetime itself.[6] The theory conceives of gravity as a manifestation of the curving and bending of the fabric of spacetime by mass and energy. For example, the theory holds that Earth moves around the sun not because there is a mysterious force acting over that vast distance, somehow pulling upon Earth, but because the mass of the sun slightly warps the shape of space in its vicinity. This warping creates a sort of valley that guides Earth (and the other planets) into nearly elliptical orbits around the sun. We can’t see this valley but we feel it—it’s gravity!

This equation isn’t difficult to read. On the right-hand side we have all the matter and energy in a region of spacetime, denoted by Tµv. The left side describes the geometry, Gµv, of that region. The equal sign in the middle is where the magic happens: It tells, with mathematical precision, how the geometry of spacetime on the left (Gµv) is tied to a given configuration of matter and energy (Tµv) on the right, and this relationship, Einstein’s theory says, is what we experience as gravity. Hence gravity doesn’t enter Einstein’s theory as an independent force. It rather emerges from the interplay between matter and the shape of spacetime. As the American physicist John Archibald Wheeler put it, “Matter tells spacetime how to curve. Spacetime tells matter how to move.”[7]

Einstein’s genius was to identify spacetime itself as the physical field responsible for gravity.

Few physicists believe there is much to see or feel at the event horizon of a large black hole, but the horizon is of huge significance to the causal structure of black holes. Inside the horizon surface, space and time in some sense switch identities. If an intrepid astronaut were to venture inside the horizon of a black hole, the ever-increasing tilting of the light cones means he would necessarily have to keep moving toward the center. That is, the radial dimension of space inside acquires the properties of a time dimension, a direction in which one can’t stop or reverse but must move forward. The spacetime singularity of infinite curvature that awaits in the center isn’t really a place in space but more like a moment in time—the last one.

Now, what happens when two black holes enter each other’s sphere of influence and begin to circle each other? General relativity predicts that this interaction generates gravitational waves, oscillating disturbances of spacetime that propagate across the universe at the speed of light. This is just the Einstein equation at work: Two black holes orbiting each other form a periodically changing configuration of masses to which, the Einstein equation says, spacetime responds with its own periodic disturbances. These ripples are gravitational waves.

Einstein’s and Eddington’s perspectives on the beginning were steeped in the old determinism going back to Newton, to which Einstein’s classical theory of general relativity comports. Within this scheme, any beginning requires initial conditions with the same degree of tuning as the universe that evolves from them. A universe that evolves to become complex late in its evolution requires initial conditions of the same level of complexity early on. A universe that appears specially designed to bring forth life requires initial conditions that encode that same level of biofriendliness all the way back at the start. This makes it seem as if an “act of God” was involved to set our fine-tuned, biophilic universe in motion.

Lemaître speculated that under the extreme conditions in the earliest stages of the universe, even space and time would become fuzzy and uncertain. “The notions of space and time would altogether fail to have any meaning at the beginning,” he wrote in his big bang manifesto. “Instead space and time would only begin to have a sensible meaning when the original ‘quantum’ had been divided into a sufficient number of quanta,” enigmatically adding, “If this suggestion is correct, the beginning of the world happened a little before the beginning of space and time.”

Far from the concordist interpretations that sought to bring the truths of faith in line with scientific discoveries, Lemaître insisted that science and religion each had its own playing field. Of the primeval atom hypothesis, he said in this regard, “Such a theory remains entirely outside any metaphysical or religious question. It leaves the materialist free to deny any transcendental Being….For the believer, it removes any attempt to [achieve] familiarity with God. It is consonant with the wording of Isaiah speaking of the ‘Hidden God,’ hidden even in the beginning of creation.”[51]

At Mercier’s institute Lemaître learned to differentiate between two levels of existence, between the beginning of the physical world in a temporal sense and metaphysical questions of existence: “We may speak of this event [the disintegration of the primeval atom] as of a beginning. I do not say a creation. Physically everything happens as if it was really a beginning, in the sense that if something has happened before, it has no observable influence on the behavior of our universe….Any pre-existence of our universe has a metaphysical character.”

Ever since Galileo and Newton, physics has been based on a dualism of some sort, in that it has relied on a fundamental separation between two distinct sources of information. First, there are the laws of evolution, mathematical equations 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 system at a given moment in time.

When we arrive at the beginning we reach a paradox. What determines the ultimate boundary conditions at the origin of the universe? 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 would appear to be dragged into the laws we seek to understand.

By describing electrons not as traveling particles but as propagating waves of probability, the Schrödinger equation predicts that, much like interfering waves on a lake, fragments of an electron’s wave function coming out of different slits will intermingle, yielding a pattern of high and low probabilities for where on the screen each individual electron will land. Where the wave fragments emerging from both slits arrive in step with each other, they will reinforce; where they arrive out of step, they will cancel.

In the words of Erwin Schrödinger, the quantum universe is “not even thinkable,” for “however we think it, it is wrong; not perhaps quite as meaningless as a triangular circle, but much more so than a winged lion.”

Feynman’s description of the two-slit situation exemplifies that there is no hope to find out from observations on the screen alone through which slit the electron actually came. This should not come as a surprise. By having not one but many histories playing out, quantum mechanics obviously limits what we can say about the past. The quantum past is inherently fuzzy. It isn’t the kind of sharp and definite history we usually think of when we consider the past.

there need not be a fundamental contradiction between classical and quantum mechanics. The reason is that the sum-over-histories scheme applies both to small and to large objects, but that for larger objects, the only trajectories with any significant probability are those lying everywhere along the single path predicted by Newton’s classical laws of motion.

This time-into-space rotation is often described as making time imaginary, because mathematically the rotation corresponds to multiplying time by an imaginary number, namely the square root of minus one. Obviously this operation renders void all notion of normal evolution. It would be no use whatsoever to set your alarm to a.m. to catch your morning train.

“One could take the attitude that quantum gravity and indeed the whole of physics is really defined in imaginary time,” he declared at one point. “It is simply a consequence of our perception that we interpret the universe in real time.”

But Jim and Stephen didn’t want to rotate back to real time. The audacity of their no-boundary proposal was that when it comes to the origin of the universe, the transformation of time into space isn’t merely a clever calculational trick but fundamental. The story of the universe, the theory holds, is that once upon a time there was no time.

Earlier on I mentioned that classical physics and the ordinary quantum mechanics of particles alike subscribe to the orthodox dualistic framework of prediction that separates laws from initial conditions. Not so for no-boundary cosmology, which abandons this dichotomy in favor of a more general framework that treats initial conditions and dynamics on equal footing. According to the no-boundary hypothesis, the universe doesn’t quite have a point A where external conditions would have to be specified.

The agreement between the Planck satellite’s observational data—the dots—and the theoretical predictions—the curve—is stunning. This wavy pattern of variations has become one of the iconic images of modern cosmology. It is widely recognized as the first strong evidence that our deepest origins lie in quantum jitters amplified and stretched in a brief surge of primeval inflation.

the largest piece of the cosmic cake is invisible, antigravitating dark energy, responsible for the surge in expansion in the universe’s recent era. This reading of the CMB corroborates the spectacular discovery by two teams of astronomers who, in 1998, from observations of light emitted by distant exploding stars, found that the expansion of space had been speeding up in the last few billion years.[9]

Just as the quantum mechanics of an electron particle unites different possible trajectories in one entity—the electron wave function—the no-boundary wave function brings together different possible expanding universes under a single umbrella. Precisely herein lies its capacity to yield further theoretical insights into the question “Which curve should be ours?,” so central to the riddle of design.

Time in quantum cosmology loses its meaning as a fundamental organizing principle.[12] Instead, a sensible notion of time emerges only as an intrinsic quality within each individual expanding space. The reason is that a measure of time always involves a change of one physical property relative to another. As a clock within our own universe, for example, we could use the monotonic cooling of the cosmic background radiation with expansion (although this wouldn’t be a practical unit of time to schedule your meetings). But the evolution of the temperature of the CMB in one spacetime is obviously of no use as a clock in a different spacetime.

What matters is not what is most probable in the theory but what is most probable to be observed. Cosmological histories that don’t produce observers don’t quite count when we compare our theories to our observations.