Einstein hated dice. Or at least he hated what dice represented: a world in which chance trumped fate. Einstein believed in a cosmic time that ticked into the future along a preordained route, each moment the inevitable product of the one preceding. Einstein’s universe had no room for luck.
Or so Einstein’s deterministic view of reality is often represented. Actually, his time didn’t even tick. It preexisted. His time was just a dimension in a vast continuum, with no point having a better claim to representing “now” than any other. “Physicists,” Einstein once wrote, meaning physicists like him, “believe the separation between past, present, and future is only an illusion.”
Einstein’s belief that time is illusory did not stem from a mere devotion to Newtonian determinism. After all, he had disregarded Newton before, rewriting the laws of motion that underpinned deterministic philosophy in the first place. In so doing, Einstein introduced a new notion of time, more radical than even he at first realized. In fact, the view of time that Einstein adopted was first articulated by his onetime math teacher in a famous lecture delivered one century ago. That lecture, by the German mathematician Hermann Minkowski, established a new arena for the presentation of physics, a new vision of the nature of reality redefining the mathematics of existence. The lecture was titled “Space and Time,” and it introduced to the world the marriage of the two, now known as spacetime.
It was a good marriage, but lately physicists’ passion for spacetime has begun to diminish. And some are starting to whisper about possible grounds for divorce.
Minkowski’s lecture featured one of the most quoted passages in the history of science, frequently appearing in basic expositions of Einstein’s theory of special relativity. “Henceforth space by itself, and time by itself, are doomed to fade away into mere shadows, and only a kind of union of the two will preserve an independent reality,” Minkowski declared in Cologne on September 21, 1908, at the Assembly of German Natural Scientists and Physicians.
A decade earlier, he had been a professor at the Zurich Polytechnic university, where the young Einstein often skipped his math classes. Minkowski was sure Einstein would never amount to anything. But shortly after 1905, when Einstein authored a lifetime’s worth of revolutionary results in a single year, Minkowski took notice, turning his mathematical prowess to better formulate Einstein’s physics. Before long, Minkowski saw deep consequences of Einstein’s ideas, especially how they implied that time and space could not be torn asunder. Einstein’s famous insistence that the velocity of light is a cosmic speed limit made sense, Minkowski saw, only if space and time were intertwined.
“Nobody has ever noticed a place except at a time,” he avowed, “or a time except at a place.”
Minkowski perceived new meaning in Einstein’s proof that distant events cannot be unambiguously simultaneous (different observers, moving rapidly with respect to each other, may not always perceive the same time-order of events). Thus Minkowski’s math described a world consisting not of a dynamic set of events occurring in some specific sequence, but rather a four-dimensional realm consisting of everything, with all “events” occupying points distributed throughout an eternal spacetime continuum. “Distances” between such points no longer reflected mere linear separation in space, but the combined separation of space plus time. The speed of light is constant, and inviolable, because it is a conversion factor, converting between time units and length units.
In the century since Minkowski spoke, spacetime has become the stage for all of physical science’s portrayals of nature, the conceptual framework for formulating scientific descriptions of reality. Building on Minkowski’s foundation, Einstein generalized his theory of relativity to describe the interplay of spacetime with matter, thereby rewriting the law of gravity. All the rest of physics, it seemed, fit in the framework that Minkowski and Einstein constructed. Through the lens of spacetime, scientists glimpsed deep and surprising truths about the origin and history of the cosmos.
Yet for all its successes, spacetime has somehow fallen short of solving all the mysteries the universe poses, and recently its primacy has been challenged. Making Einstein’s relativity mesh with quantum mechanics has proven so tough that scientists are now willing to seek answers from beyond spacetime (as it is ordinarily conceived). Many physicists now believe that at its roots, nature is built from elements more basic, that space and time emerge from something messier, and then merge into the mirage that human inquiry is able to access. Physicists of the 21st century therefore face the task of finding the true reality obscured by the spacetime mirage.
Doing so, some scientists think, will require looking more closely at how space and time fit together. In particular, some investigators suggest, it might be time to rethink time.
Since Saint Augustine confessed that he knew what time was until somebody asked him to explain it, philosophers and physicists alike have never ceased grappling with its elusiveness. Newton tried to define “absolute time” as “duration” — flowing “equably without regard to anything external.” But Einstein demolished that idea, pointing out that time travels at different rates for rapid travelers. Most scientists, though, don’t waste time worrying about time’s ultimate essence — for them, time is simply what clocks measure. But therein lies a problem: how to choose the clock.
Andreas Albrecht, a cosmologist at the University of California, Davis, has thought deeply about choosing clocks, leading him to some troubling realizations.
Clock as homewrecker
In a lab, time is simple. You can watch experiments and record what happens as time passes simply by referring to the clock on the wall (or the computerized timers on the lab bench). But suppose you are studying the universe as a whole, attempting to formulate the laws of quantum gravity that rule the cosmos. There is no wall enclosing the universe on which to hang a clock, no external timekeeper to gauge the whenness of being.
Yet quantum physics requires time to tell the universe what to do — time is necessary for things to happen. Or, as the famous restroom graffito puts it, time is nature’s way of keeping everything from happening at once.
In quantum math, time is represented in a formula called a wave function, which describes a multiplicity of possible realities. For an electron, the wave function does not specify, say, a precise position, but tells the odds of finding that electron in various possible locations. Those odds are not forever constant, but change as time goes by; the part of the math that specifies those changes is, in some abstract sense, a clock. On a cosmic scale, the situation is similar — the quantum math describes multiple possible states of the universe, as well as how the universe changes as “time” proceeds — as the cosmic clockwork turns the future into the past. You can compute what happens to the universe as one piece of the math alters in value, like the ever-changing angle that a second hand makes as it sweeps around a clockface.
But when deriving that math to begin with, there’s no way to know in advance which part corresponds to the master cosmic clock. You have to choose something to represent time from within your equations, Albrecht notes. “Your first job is to identify what you mean by time,” he says.
But here’s where it gets tricky. When you choose one piece of the math to describe time, the rest of the math becomes the formula for the laws of nature, describing how the universe behaves. Suppose, though, that you choose a different part of the equations to play the role of clock. Now you have a different formula for the laws of nature — what happens in the universe doesn’t stay the same, Albrecht figured out.
“I showed that you could make different choices of what you mean by time and get any laws of physics you want,” he says. Freedom to choose “time” therefore implies that the laws of physics aren’t indelibly inscribed with Sharpies on indestructible stone tablets, but are more like multiple drafts of legislative bills with details still at the whim of editors wielding word processors. Some of those laws might not even include any provision for space, leaving time partnerless.
Albrecht calls this time-choice conundrum the clock ambiguity, described with his UC Davis collaborator Alberto Iglesias in a paper published this year in Physical Review D. “We tried to show that there was something wrong with this picture, that the freedom to choose any clock would somehow contradict itself,” Albrecht says. But it didn’t.
In that paper and a subsequent one available online (arxiv.org/abs/0805.4452), Albrecht and Iglesias further explore the implications of this time-freedom for the laws of nature. If you can choose any time you like and get different laws, it makes no sense to say that the universe is ruled by a single Constitution of Physics. The cosmos becomes more like the United Nations, a hodgepodge of jurisdictions with diverse codes of conduct. “The clock ambiguity suggests that we must view physical laws as emergent from a random ensemble of all possible laws,” Albrecht and Iglesias write.
In other words, there is no one set of laws, but a whole library of different cosmic law books. Yet somehow physics finds order from chaos; there must be some principle behind the regularities that govern the interaction of entities. Albrecht suggests that the universe offers such a principle: the idea that individual entities exist at all.
Space time reunion
“The remarkable thing about our experience as observers in the universe is we are fairly isolated from the universe, so we have our own isolated existence,” Albrecht says. “The universe doesn’t instantly destroy us.” Stars, planets and people aren’t blended in a cosmic mixmaster, but remain somewhat separate — exhibiting what Albrecht calls “quasiseparability.”
“Quasiseparability means the universe can be separated into different things, different objects, that have their own identity,” he says. “That’s how we stay safe in a universe full of potentially antagonistic physical objects.”
And that’s how it’s possible to experience meaningful laws of physics even in a universe without a master clock. Freedom to choose different clocks means choosing from among a multitude of possible laws, some wildly different from those in human textbooks. But quasiseparability places limits on which sets of laws humans could possibly experience. Only those laws consistent with quasiseparability would permit systems containing objects like physicists.
This separability requirement brings something like space back into the cosmic picture. In a sense, time and space get back together not because that’s the way the world is, but because that’s the only way that humans can comprehend it.
So even though many laws of nature are possible, some should, in an inhabited universe, be statistically much more likely than others. With quasiseparability as a guiding principle, Albrecht and Iglesias show that even a random choice of clock is very likely to produce laws that look like the ones that physics already knows, describing fields of matter and energy that act locally to generate the behavior of the whole cosmos.
This development is strikingly analogous to the original quantum revolution, which established the idea that science’s laws were not absolute but statistical — producing the cosmic dice-playing that Einstein deplored. Now, it seems, even the laws themselves may not be absolute, but merely — given quasiseparability — the most likely set of rules drawn from a statistical distribution of all possible rules. “Maybe we should have seen it coming,” Albrecht says.
What he and other pioneers on the spacetime frontiers have seen coming is an intellectual crisis. The approaches of the past seem insufficiently powerful to meet the challenges remaining from Einstein’s century — such as finding a harmonious mathematical marriage for relativity with quantum mechanics the way Minkowski unified space and time. And more recently physicists have been forced to confront the embarrassment of not knowing what makes up the vast bulk of matter and energy in the universe. They remain in the dark about the nature of the dark energy that drives the universe to expand at an accelerating rate.
Efforts to explain the dark energy’s existence and intensity have been ambitious but fruitless. To Albrecht, the dark energy mystery suggests that it’s time for physics to drop old prejudices about how nature’s laws ought to be and search instead for how they really are. And that might mean razing Minkowski’s arena and rebuilding it from a new design.
“It seems to me like it’s a time in the development of physics,” says Albrecht, “where it’s time to look at how we think about space and time very differently.”
