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

by Thomas Hertog

Both inside black holes and at the big bang, the macroworld of gravity truly merges with the microworld of atoms and particles.

When we trace the universe back to its earliest moments, we encounter a deeper level of evolution, at which the physical laws themselves change and evolve in a sort of meta-evolution. The rules of physics transmute in the primeval universe, in a process of random variation and selection akin to Darwinian evolution,

In cosmology we discover the past. Cosmologists are time travelers, and telescopes their time machines. When we look into deep space we look back into deep time,

The CMB sky map confirms that the relic big bang heat is nearly uniformly distributed throughout space, although not quite perfectly. The speckles in the image represent minuscule temperature variations indeed, tiny flickers of no more than a hundred-thousandth of a degree. These slight variations, however small, are crucially important, because they trace the seeds around which galaxies would eventually form. 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.

The Pythagoreans assigned a mystical significance to numbers and attempted to construct the entire cosmos out of numbers. Their idea that the world could be described in mathematical terms was taken up and championed by Plato, who made it one of the pillars of his theory of truth.

It is this mathematical formulation of nature’s laws that embodies what physicists today mean when they use the word “theory.” Physical theories derive their utility and predictive power from the fact that they describe the real world in terms of abstract mathematical equations that one can manipulate in order to predict what will happen without actually observing or performing the experiment. And it works! From the discovery of Neptune to the sensing of gravitational waves to the prediction of new elementary particles and antiparticles, time and again the mathematical groundings of the laws of physics have pointed to new and surprising natural phenomena that were later observed.

The core idea of Darwinism is that nature doesn’t look ahead—it doesn’t anticipate what may be needed for survival. Instead, any trends, such as the changing shapes of beaks or the progressive growth of the length of a giraffe’s neck, follow from environmental selection pressures that act over long periods of time to amplify useful traits. “There is grandeur in this view of life,” Darwin would write more than twenty years later, “with its several powers, having been originally breathed into a few forms or into one; and that, whilst this planet has gone cycling on according to the fixed law of gravity, from so simple a beginning endless forms most beautiful and most wonderful have been, and are being, evolved.”

Thought experiments were always a favorite of Stephen’s.

Einstein understood that if light is always observed to travel at the same speed, then observers moving relative to each other must have different notions of distance and time. After all, speed is a measure of distance traveled divided by the duration of the journey. According to Einstein, instead of a cosmic Big Ben we all carry our own clock, and though all our clocks are equally accurate, when we move relative to one another, they will tick at slightly different rates, measuring different amounts of time between the same two events. The same is true for distance; one observer’s yardstick can differ slightly from another’s. There just aren’t universally valid measures for duration and distance. This was the crux of Einstein’s 1905 theory of special relativity. The term “relativity” here refers precisely to this revolutionary idea that notions of space, time, and simultaneity aren’t objective facts but always tied to the view of a given observer. One may wonder where the differences in distance measured by one observer relative to another go. Are they simply gone? Not quite. They are transformed into an amount of time. You see, motion through space gets mixed with motion through time in Einstein’s relativistic universe. When I look at my sister’s parked sports car I find that all its motion is through time. But if she speeds away, a tiny bit of its motion through time is channeled into motion through space. My sister’s clock will run a tad more slowly than mine. And while...

In 1908, the German mathematician Hermann Minkowski, who had been one of Einstein’s teachers at the Zurich Polytechnic, completed Einstein’s reconceptualization of space and time and famously declared that “henceforth space as such and time as such shall recede to the shadows and only a kind of union of the two shall retain significance.”[4] Minkowski melded the three dimensions of space and the one time direction into a single four-dimensional entity: spacetime.

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. As ripples of geometry, gravitational waves carry massive amounts of energy. This drains the energy from the system of orbiting black holes, causing them to spiral inward and eventually merge to form a single, bigger black hole. Such mergers are by far the most violent events in the universe.

This is a profoundly confusing state of affairs. If time itself began with the big bang, then all questions about what happened before would seem meaningless. Even speculation about what caused the big bang would be out of place, for causes precede effects, which requires some notion of time. This apparent breakdown of basic causality at the origin of time was the core of the matter in the debate that pitted Eddington and Einstein against Lemaître.

In his memoir, Stephen wrote that he became interested in cosmology because he wanted to fathom the depths of understanding.

Singularities are edges to spacetime, really, where the general theory of relativity offers no guidance as to what happens. Indeed the very word “happen” loses meaning at a spacetime singularity. Penrose had shown that, according to relativity theory, time must end inside black holes.

Walking on Earth’s surface in places like the Grand Canyon, one can find rocks that are several billion years old. The simplest forms of bacterial life on Earth are about 3.5 billion years old, and our planet itself isn’t very much older, approximately 4.6 billion years. The big bang singularity theorem is saying that if we were to go back to a time just three times earlier—13.8 billion years ago—there would be no time, no space, no anything. Viewed this way, we are rather close to the beginning of everything.

Quantum mechanics, the second pillar of modern physics, has popped up several times by now. The theory has its roots in a number of mystifying experiments with atoms and light in the early years of the twentieth century that could not be explained by any stretch of the classical mechanics of Newton. Its formulation throughout the turbulent years of the early twentieth century stands as one of the finest examples of international collaboration in the history of mankind.

Schrödinger’s quantum waves describe the world at some kind of preexistence level. Before one measures a particle’s position there is no sense in even asking where it is. It does not have a definite position, only potential positions described by a probability wave that encodes the likelihood that the particle, if it were examined, would be found here or there. It is as if we compel particles to assume a position by looking at them, that there is a tangible physical reality only to the extent that we interact with the world by observing and experimenting. “No question, no answer!” is how Wheeler once put it.

As Feynman put it, “The electron does anything it likes. It just goes in any direction at any speed, forward or backward in time, however it likes, and then you add up the amplitudes [of their paths] and it gives you the wave function.”

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.

I mentioned earlier that Hawking radiation originates in quantum jitters of matter fields in the vicinity of black holes. These jitters give rise to pairs of particles that pop into existence, persist for a short while, and disappear again, like a pair of dolphins rising briefly above the surface of the ocean before diving down again. Physicists call these virtual particles because, unlike real particles, they don’t live long enough to be detected by a particle detector. Near the horizon of a black hole, however, virtual particles can become real. This is because one member of a virtual pair can fall into the black hole, leaving the other particle free to escape into the distant universe where it shows up as faint radiation given out by the black hole.

Time in quantum cosmology loses its meaning as a fundamental organizing principle.

And the complicated fractal-like cosmography of the multiverse spooks us. In an eternally inflating multiverse, you will eventually find an island universe that has a galaxy that looks like an exact copy of the Milky Way, with a solar system that’s just like ours and an identical house in an identical street where your doppelgänger is reading these words. Moreover, there’d be not just one such copy but infinitely many.

The Higgs field is the crucial piece of the Standard Model that gives other elementary particles their masses. Electrons and quarks, and even the exchange particles, have no intrinsic mass in the Standard Model theory but acquire their masses from the resistance they experience as they move through the all-pervading Higgs field. It is as if particles are constantly wading through the mud when they move about, and the resulting drag is what we call mass. The amount of mass that particles end up with depends on how strongly they feel the Higgs field. Quarks interact very strongly with the Higgs field and are heavy, whereas the lighter electrons do so much more weakly, and photons, which don’t interact with it at all, remain massless.

Much like the discovery of dark energy in cosmology, the experimental discovery of the Brout-Englert-Higgs boson shows once again that empty space is not empty but filled with invisible fields, one of which is responsible for part of the mass of the matter that makes up almost everything we encounter in daily life. It also demonstrates that nature really does make use of scalar fields as one of the key ingredients it has at its disposal to shape the physical world. As such, the discovery of the Brout-Englert-Higgs boson lends credence to the existence of a similar field that could have driven inflation in the very early universe.

In string theory there can be different shapes of spacetime that nevertheless describe physically equivalent situations. Such shapes are said to be dual and the mathematical operations linking different geometries are known as dualities.

String theory rests on firm and profound mathematical principles, he explained, but the theory isn’t a physical law in the usual sense. Instead we should think of it as a metalaw that governs a multiverse of countless island universes, each with its own local laws of physics.

The sheer vastness of the possibilities in biological evolution means that any kind of causal deterministic explanation of why we have this particular tree of life is doomed to fail.

To Einstein, the probabilistic nature of quantum mechanics signaled that the theory was incomplete, that there had to be a deeper-lying framework that permitted an objectively real description of physical reality, regardless of any acts of observation. “The [quantum] theory produces a good deal but hardly brings us closer to the secret of the Old One,” he wrote to Born. “I am at all events convinced that He does not play dice.”[11] Niels Bohr, on the other hand, who had a background in philosophy as well as mathematics, had a profound intuition that quantum mechanics was consistent. Bohr took seriously the central tenet of quantum mechanics that observership—the very questions we ask of nature—affects how nature manifests itself. “No phenomenon is a real phenomenon until it is an observed phenomenon,” he held.

Take a high-energy particle released by a radioactive atom like uranium in Earth’s crust. At first this particle exists as a wave function, spreading in every possible direction, not quite real until it interacts with, say, a piece of quartz. When that happens, one of its many possible trajectories condenses. The interaction with the quartz transforms what might have happened into what did happen when the uranium atom decayed. Within any given branch of history, this process shows up as a frozen accident in the form of an array of atoms affected by the high-energy particle, the tracks of which are sometimes used to date minerals. The universe we see around us—this branch of reality—is the collective result of innumerable such environmental acts of observation. Having registered and built upon countless chance outcomes, over a period of billions of years, each contributing a few bits of information to our branch of history, this is how the world around us has acquired its specificity.

Mathematically speaking, Everett’s scheme is supremely elegant: The Schrödinger equation rules. Universally. Everett’s framework demonstrates that Bohr’s classical packaging is excess baggage that can be dispensed with. The interactive process whereby subsystems get entangled, causing the universal wave function to divide into separate, decoherent branches that are mutually invisible, offers an extremely satisfying microscopic description of quantum measurements. Human consciousness, human experimenters, and human observations are neither completely irrelevant in Everett’s scheme nor regarded as separate external entities, obeying different rules. They are simply treated as part of the broader quantum mechanical environment, not fundamentally different from air molecules and photons. Everett put forward an inside-out way of thinking about the quantum world. He showed that we can be riding the universal quantum wave, not just watching from the shoreline.

In a quantum universe—our universe—a tangible physical reality emerges from a wide horizon of possibilities by means of a continual process of questioning and observing.

But observership also reaches into the past. When the Hawkingian oracle said that “the history of the universe depends on the question you ask,” I figured this is exactly what it meant. Stephen was saying that the entire collection of facts that characterize the universe around us, from the biosphere on Earth to the observed low-temperature effective laws of physics, constitutes in effect a grand question we ask of the cosmos. The triptych evokes the idea that this grand question retroactively draws into existence those few branches of cosmological history that have the properties that are being observed. That is, observership in quantum cosmology isn’t a mere afterthought or an anthropic post-selection principle acting in a giant preexisting multiverse, but an agency operating at a deeper level, an indispensable part of the continual process through which physical reality—and physical theory, we argue—come about. A quantum universe and observers emerge in sync, in a sense. The depth of the top-down philosophy that Stephen anticipated back in 2002—even though it took us many more years of thought experiments, dead alleys, and the occasional eureka moments before the mist cleared—is that cosmological theory and observership are bound together.

As I just alluded to, this entangling imbues quantum cosmology with a subtle backward-in-time element. One doesn’t follow the universe from the bottom up—forward in time—because one no longer presumes the universe has an objective observer-independent history, with a definite starting point and evolution. Quite the contrary, built into the triptych is the counterintuitive idea that in some fundamental sense that I have yet to elaborate on, history at the very deepest level emerges backward in time. It is as if a constant flux of quantum acts of observation retroactively carves out the outcome of the big bang, from the number of dimensions that grow large to the types of forces and particles that arise. This renders the past contingent on the present, a further reduction of causality well beyond what even Bohr conceived.

Figure 45. A variant of Young’s double-slit experiment with light particles in which the photographic plate on the right is converted into a venetian blind and a pair of detectors are stationed behind it, each pointing at one of the slits. The experimenter operating the detectors can delay his decision right up to the moment each individual photon reaches the blind, whether to leave the blind closed and perform the usual double-slit experiment, producing interference fringes, or open it and verify which slit the photon came through. One might have thought this delayed choice would confuse the photon. Not at all: Nature is smart, the photons always get it right, demonstrating that the act of observation in quantum theory subtly reaches into the past.

How come? Because the unobserved past in quantum mechanics exists as a spectrum of possibilities only—a wave function. Much like electrons or radioactive decay particles, fuzzy photon wave functions morph into a definite reality only when the future to which they give rise has been fully settled, i.e., observed. The delayed-choice experiment illustrates vividly and strikingly that the process of observation in quantum mechanics introduces a subtle form of teleology into physics, a backward-in-time component. The sort of experiments and observations we do today—the very questions we ask of nature—retroactively transform what might have happened into what did happen and, in doing so, take part in delineating what can be said about the past.

Observership draws the past more firmly into existence, but it doesn’t transmit information back in time. In Wheeler’s cosmic-scale version of the delayed-choice experiment, turning our telescopes on or off in the twenty-first century doesn’t affect the motion of photons billions of years ago. Quantum cosmology doesn’t deny that the past has happened; rather it refines what it means “to happen” and, especially, what can—and what cannot—be said about the past.

Wheeler was fond of illustrating his vision with a variant of the twenty questions game. In this game, a group of colleagues are seated in a living room after dinner. One is sent out. In his absence, the rest decide to play the game with a twist: They agree not to settle on a definite word but to act as if they had agreed upon a word. When the questioner returns and poses his “yes/no” questions, each respondent answers as he pleases, with the one condition that his response should be compatible with all previous ones. So at each stage of the game, everyone in the room has in mind a word that is consistent with all the answers that have been given before. Naturally, successive questions rapidly narrow down the options until both the questioner and the respondents are taken by the hand, as it were, and guided toward a single word. What that final word is, however, depends on the questions the questioner asks and even on the order of the questions. In this variant of the game, Wheeler said, “No word is a word, until that word is promoted to reality by the choice of questions asked and answers given.”[18] In a similar way, a quantum universe constantly puts itself together, piece by piece, out of a haze of possibilities, somewhat like a forest emerging out of the fog on a damp gray morning. Its history is not how we usually think of history, as a sequence of one thing happening after another. Rather it is a marvelous synthesis that includes us and in which what unfolds now ret...

“No question, no answer!” Wheeler said of quantum particles. “No question, no history!” Hawking said of the quantum universe.

It is as if quantum cosmology conceives of observership as the operational headquarters in the unfathomable realm of all that might be.

We create the universe as much as the universe creates us.

Mathematical relationships that transform seemingly distinct theories into each other are known to physicists as dualities. Two theories that are dual are equivalent in some fashion; they describe one and the same physical situation expressed in a different mathematical language. A simple example is the wave/particle duality in quantum mechanics,

Holographic dualities have revealed that relativity and quantum theory aren’t antagonists but merely alternative vantage points on the same physical reality. Physical systems can be gravitational and quantum at the same time, holography says, albeit in different dimensions.

Strikingly, quantum entanglement appears to be the central engine that generates gravity and curved spacetime in holographic physics.

Asking what lies beyond our own universe, would be like asking which slit the electron goes through in the two-slit experiment, Stephen put it.

Science is what scientists do. We advance by exchanging ideas, through argument and reason, based on available evidence and abstraction.

In our search for the ultimate underpinnings of reality we had, in some kind of curious loop of interconnections, been led back to our own observations. “We are a way for the universe to know itself,” Carl Sagan famously said. But it seems to me that in a quantum universe—our universe—we are getting to know ourselves.

Notions of time and law-like patterns are seen to emerge in a way that is contingent on the questions we ask and grounded in the complexity of the universe around us.

Throughout my journey with Stephen, I came to know him as someone who longed for all of us to embrace more of a cosmic perspective on our existence and think in terms of deep time.

Stephen firmly believed that the courage of our questions and the depth of our answers would allow us to navigate planet Earth safely and wisely into the future. The story of his life in which he found, after his terrifying diagnosis with ALS, the will to love, to have children, to experience the world in all of its dimensions, and to grasp the universe, inspired millions and will remain a powerful metaphor for what humanity can achieve. His parting message, beamed into space during a memorial service on June 15, 2018, in Westminster Abbey, encapsulates it all: “When we see the earth from space we see ourselves as a whole; we see the unity and not the divisions. It is such a simple image, with a compelling message: one planet, one human race. Our only boundaries are the way we see ourselves. We must become global citizens. Let us work together to make that future a place we want to visit.” From Stephen Hawking we can learn to love the world so much that we aspire to reimagine it, and never to give up. To be truly human. Though he was nearly immobile, Stephen was the freest man I have known.