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Exploring Stephen Hawking’s Flexiverse
20 April 2006
Exclusive from New Scientist Print Edition. Subscribe and get 4 free issues.
Amanda Gefter
http://www.newscientistspace.com/article/mg19025481.300;jsessionid=HLJLBDJLJMOE
HERE'S how to build a universe. Step one: start at the beginning of time. Step two: apply the laws of physics. Step three: sit back and watch the universe evolve. Step four: cross your fingers and hope that it comes out looking something like the one we live in.
That's the basic prescription for cosmology, the one physicists use to decipher the history of the universe. But according to Stephen Hawking of the University of Cambridge and Thomas Hertog of the European Organization for Nuclear Research (CERN), the steps are all backward. According to these physicists, there is no history of the universe. There is no immutable past, no 13.7 billion years of evolution for cosmologists to retrace. Instead, there are many possible histories, and the universe has lived them all. And if that's not strange enough, you and I get to play a role in determining the universe's history. Like a reverse choose-your-own-adventure story, we, the observers, can choose the past.
This bizarre state of affairs has its roots in Hawking's work in the 1970s. Early in his career, Hawking, along with physicist Roger Penrose, proved a theorem showing that our expanding universe must have emerged from a singularity - a place where gravity becomes so strong that space and time are curved beyond recognition. In this situation, general relativity - our best description of how space, time and matter interact - no longer applied.
So what rules did apply? Hawking and Hertog suggest that the universe was so small at this time that quantum effects must have been important. We don't yet have a quantum theory of gravity, so we can't be sure exactly what the rules were, but the principle still stands, they say. "The real lesson of these so-called singularity theorems is that the origin of the universe is a quantum event," Hertog claims. And that, of course, opens the whole universe up to some very strange phenomena.
The famous double-slit experiment highlights the bizarre reality of how a universe born in quantum mode might behave. In the experiment, a screen with two open slits faces a sheet of photographic film. When light is shone through the slits the film registers where it lands. If the light goes through both slits the film shows an "interference pattern" of light and dark bands. Such a pattern is typically produced by interfering waves - one from each slit. What's spooky is that even when a lone photon is fired at the slits it still creates a pattern of light and dark bands - as if it were two waves.
In 1983, Hawking and James Hartle of the University of California at Santa Barbara, took up this picture and applied it to the evolution of the whole universe. They did that using the "sum over histories" interpretation of quantum theory, first set out by the late Richard Feynman. Feynman suggested that the way to interpret quantum phenomena such as the double-slit experiment was to assume that when a particle travels from point A to point B, it doesn't simply take one path - it takes every possible path simultaneously; the photon travels through both slits at the same time and interferes with itself, for example.
In this scheme, when a photon travels from a lamp to your eye it moves in a straight line, but it also dances about in twists and swirls, travels to Jupiter and back, and ricochets off the Great Wall of China. The obvious question, then, is why do we see only ever see one path, straight and simple? Feynman's answer was, because all the other paths cancel each other out. In the sum-over-histories interpretation, each path can be mapped out as a wave. Each wave has a different phase (effectively a starting time), and all the waves added together create an "interference pattern", building upon one another where their phases align and cancelling each other out where their phases are mismatched. The sum of all the waves is one single wave, which describes the path we observe.
Applied to the universe, this idea has an obvious implication. Just as a particle travelling from point A to point B takes every possible path in between, so too must the history of the universe. In one history, the Earth never formed. In another, Al Gore is president. And in yet another, Elvis is still - well, you get the idea. "The universe doesn't have a single history, but every possible history, each with its own probability," Hertog says.
But there is a twist: the history that we see depends on the experimental setup. In the double-slit experiment, it has been shown time and again that if we use a photon detector to find which of the two slits the photon went through, it no longer creates an interference pattern, just a single spot on the film. In other words, the way you look at the photon changes the nature of its journey. The same thing happens in Hawking and Hertog's universe: our observations of the cosmos today are determining the outcome - in this case, the entire history of the universe. A measurement made in the present is deciding what happened 13.7 billion years ago; by looking out at the universe, we assign ourselves a particular, concrete history.
“It's all to do with perspective, Hawking says: if we could stand outside the world, we would see the present affecting the past”
If true, this is no mere curiosity; Hawking and Hertog have tossed the notion of a unique, observer-independent cosmology out the window and thrown the sacred laws of cause and effect into question. But they're not exactly being violated, Hawking says - it's all to do with perspective. If we could stand outside the world, we would be able to see the present affecting the past, as when an observer affects a photon's path through the universe. From inside the universe, though - from the only place we can possibly be - no observer sees causality violated. What we observe in the present, the "final" state, is one entire, causally consistent history or another: from within any given history, cause and effect proceed in the usual manner.
"Observations of final states determine different histories of the universe," says Hawking. "A worm's-eye view from inside the universe would have the normal causality. Backwards causality is an angel's-eye view from outside the universe."
So the idea is that to unravel the past, we must sum together all possible histories of the universe. What does that mean?
Hawking and Hertog equate the cosmic histories with how the geometry of the universe evolves in each possible case of going from point A (the beginning of time) to point B (now). To start with, this seems straightforward enough. We can specify the state of the universe at point B by making certain observations of the world around us - the universe has three large spatial dimensions, its geometry is close to flat, it is expanding, and so on.
What about point A, though? Mapping out the paths of a photon from a lamp to our eye is not too hard because we know the beginning point - the lamp - and the final point: our eye. We know nothing about the universe at the beginning of time, however. After all, that's what cosmology is supposed to tell us.
This is where the sum-over-histories interpretation comes into its own. The mathematics behind this approach to quantum theory contains an oddity: the answers only come out right when the calculation is done in imaginary time. That doesn't mean make-believe time, but rather a time dimension that is expressed using complex numbers. This is not an entirely esoteric idea: electrical engineers routinely use complex numbers, which are split into "real" and "imaginary" parts, to design electrical circuits. In the hands of cosmological engineers, imaginary numbers turn out to have profound consequences.
Hawking and Hartle's original work on the quantum properties of the cosmos suggested that imaginary time, which seemed like a mathematical curiosity in the sum-over-histories approach, held the answer to understanding the origin of the universe.
Add up the histories of the universe in imaginary time, and time is transformed into space. The result is that, when the universe was small enough to be governed by quantum mechanics, it had four spatial dimensions and no dimension of time: where time would usually come to an end at a singularity, a new dimension of space appears, and, poof! The singularity vanishes.
“Like the surface of a sphere, our universe has no definable starting point”
In terms of the universe's history, that means there is no point A. Like the surface of a sphere, the universe is finite but has no definable starting point, or "boundary". Hence the idea's name: the no-boundary proposal.
This has led Hawking to define a new kind of cosmology. The traditional approach, which Hawking calls "bottom-up" cosmology, tries to specify the initial state of the universe and work from there. This is doomed to fail, Hawking says, because we know nothing about the starting conditions. Instead, he suggests, we should use the no-boundary proposal to do "top-down" cosmology, where the only input into our models of the universe comes from what we observe now - together with the idea that our universe has no boundary in the past.
Improbable tuning
The result of this process, he says, solves a long-standing problem of cosmology: fine-tuning. Most cosmologists think, for example, that the universe went through an early burst of rapid expansion, or "inflation". There is some evidence to support the claim, but there's also a problem. Standard inflationary models require a very improbable initial state, one that must have "finely tuned" values that cause inflation to start, then stop in a certain way after a certain time: a complicated prescription whose only justification is to produce a flat universe without any strange topology, and so on - a universe like ours.
Such a prescriptive method makes hard and unsatisfying work of producing the universe we see today. While a cosmologist can put these values into the equations "by hand", it is not exactly a satisfactory way to develop our model of how the universe works. In the no-boundary theory, however, there simply is no defined initial state. "In the usual approach it is difficult to explain how inflation began," says Hawking. "But it occurs naturally in top-down with the no-boundary condition. It doesn't need fine tuning."
To do top-down cosmology, Hawking and Hertog first take a whole raft of possible histories, all of which would result in a universe with features familiar to us. "We then calculate the probability for other features of the universe, given the constraints," Hertog says. Specify a universe that is three-dimensional and flat, for instance, and you can have histories that involve inflation and histories that don't. "Top-down cosmology does not predict that all possible universes have to begin with a period of inflation, but that inflation occurs naturally within a certain subclass of universes," Hertog says. The process creates a probability for each scenario, and so Hertog can see which kind of history is most likely. "What we find is that the inflating histories generally have the largest probability."
In many ways, top-down cosmology is an unsettling idea. Usually, science demands that our observations come out as output - we certainly don't expect them to be the input. That, after all, denies us the chance to see if the theory matches up with observations. What's more, the sum over histories is formed by calculating the various probabilities for a universe like ours to arise out of literally nothing: that means we can never know anything for certain about how our universe got to be as it is.
We shouldn't be surprised, Hertog says: quantum theory has long shown us that it is impossible for us to know everything about the world around us. In "classical" physics, we can predict both the exact momentum and position of a particle at any time, but quantum mechanics doesn't allow it. No one suggests that quantum mechanics is wrong because of this, Hertog points out - and experiments have shown that it is not. What quantum theory has given us now, Hertog says, is some indication about the nature of inflation, where before we had none. "Before, we had no prediction at all - and indeed no notion of likeliness - on this issue."
For many, it remains a difficult argument to swallow. Science since Copernicus has aimed to model a universe in which we are mere by-products, but top-down cosmology turns that on its head, rendering the history of the universe a by-product of our observations. All in all, it is very like the "anthropic landscape" argument that is causing controversy among string theorists (see "Putting the you into universe").
Princeton University physicist Paul Steinhardt is certainly unimpressed by Hawking and Hertog's scheme. "It's kind of giving up on the problem," he says. "We've all been hoping to calculate things from first principles. Stephen doesn't think that's possible, but I'm not convinced of that. They might be right, but it's much too early to take this approach; it looks to me like throwing in the towel."
Stanford University's Andrei Linde is similarly unconvinced. There are a number of technical assumptions that make him sceptical. "I don't buy it," he says.
The past is out there
The merits of Hawking and Hertog's new approach to cosmology might be decided by experiment. The theory predicts specific kinds of fluctuations in two cosmological phenomena: the cosmic microwave background radiation produced just after the big bang, and the spectrum of primordial gravitational waves. These fluctuations arise from applying the uncertainty principle of quantum mechanics to Hawking and Hertog's scheme: in this scenario, the universe's shape is never precisely determined, but is influenced by other histories with similar geometries.
If Hawking and Hertog are right, quantum uncertainty will manifest as slight differences from what standard inflationary theory predicts for the CMB. The top-down predictions only differ from the standard cosmological model at a level of precision that has not yet been reached in observations, however. The top-down signature in the gravitational wave spectrum should be easier to differentiate, but since we haven't yet detected any gravitational waves, we'll have to wait for that proof too.
For Hawking and Hertog, there's simply no doubt that top-down cosmology is the only answer. It's simple: if you can't know the initial state of the universe, you can't work forwards from the beginning: the top-down approach is the only one that works.
Hartle agrees. Hawking and Hertog's scheme may seem strange, but it is the only way forward because we are part of the experiment we are trying to observe. "It's a different viewpoint, but it's sort of inevitable," he says. "Colsmologists certainly should be paying attention to this work."
The trouble, of course, is that if they are right, we're involved in the making of that history. In that case, we have a new set of instructions for building a universe. Step one: look around you. Step two: find the set of all possible histories that end up as a universe like the one you see. Step three: add them together and create a history for yourself.
From issue 2548 of New Scientist magazine, 20 April 2006, page 28
Putting the you into universe
Hawking and Hertog's cosmology adds an interesting twist to the ongoing debate in physics about the existence of multiple universes. At issue is the fact that string theory, physicists' most popular candidate for a "theory of everything", describes not just one universe but a near infinity of them. Some physicists are willing to accept that these theoretical universes actually exist, both because string theory doesn't seem to favour any particular universe over all the others in the bunch, and because their existence could help explain the apparently fine-tuned features of our universe.
Take, for example, the value of the cosmological constant, the force that appears to be causing the expansion of the universe to speed up. It is a very small force, and no one has yet explained why it should be so. The trouble is, its size happens to be a number that sits in a very narrow range of values that would allow life to exist. This coincidence has compelled some physicists to make the so-called anthropic argument: maybe there are multiple "pocket" universes that branch off from one another, and within each the constants take a different value. In that scenario, there is bound to be one universe with a cosmological constant like ours and we should not be surprised to find ourselves in the one universe hospitable to life.
Many physicists argue that this is just giving up on the problem of explaining why our universe is the way it is - it is not, they say, science. Hawking and Hertog's new idea adds fuel to this fire. The picture of a never-ending string of pocket universes is only meaningful from the perspective of an observer outside any one universe, Hawking says - and that, by definition, is impossible. Parallel pocket universes can have no effect on a real observer inside a single pocket, so, according to Hawking, they are theoretical baggage that should be eliminated from cosmology.
But Hawking has a replacement in mind - and it is just as mind-boggling. His view is that the string theory landscape is populated by the set of all possible histories. Rather than a branching set of individual universes, every possible version of a single universe exists simultaneously in a state of quantum superposition. When you choose to make a measurement, you select from this landscape a subset of histories that share the specific features measured. The history of the universe - for you the observer - is derived from that subset of histories. In other words, you choose your past.
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