IT IS one of the biggest questions confronting physics: why is our universe the way it is? If some of the fundamental laws were even slightly different, our universe would be a strange and lethal place. Instead, it seems exquisitely tuned to make life possible.
So far, string theory, the leading contender for a “theory of everything”, has failed to explain why this should be so. The best it can offer is that our universe is not particularly special because the big bang could have produced any one of a staggering number of vastly different universes, all just as likely as each other. “The anthropic approach is to say that all are real and we just happen to be living in one of them,” says string theorist Michael Duff of Imperial College London.
Now, a group of mathematicians has explored the geometry underlying string theory’s many predicted universes, and say the theory could lead us to a single universe after all. Things may have started out much stranger at the big bang, they speculate, but some physical mechanism might have nudged our universe towards its present form. If correct, the idea could finally help string theory explain why our universe is the way it is.
Advertisement
According to string theory, all particles and forces arise from the vibration of tiny “string-like” objects. For the theory to work, they have to vibrate in 10 dimensions, not the four familiar dimensions of space-time. Physicists explain that we don’t experience these extra dimensions because they are “folded” down so small as to be invisible.
Mathematically, you can fold these dimensions in lots of different ways, and therein lies the rub: solving the string equations for each type of folding results in a different universe, with its own specific type of vacuum and fundamental constants and laws. According to string theory, ours is just one of 10500 possible universes, most of which would probably be hostile to life. For example, if the force binding quarks in atomic nuclei – the strong nuclear force – were just a tad stronger, two protons would stick together to form a “di-proton”. This would lead to a universe without hydrogen – which has only one proton – and consequently no water.
Of course, not all string theorists are bothered by the “theoretical landscape of universes”. “I don’t think it is incumbent upon string theory to solve the problem of the landscape,” says Andrew Strominger of Harvard University. “If we can’t make the landscape go away, it doesn’t mean that string theory is wrong. It just means it is not a complete solution to all our problems.”
However, string theory’s prediction of many universes infuriates its critics, who have slammed it as incorrect and over-hyped. What use is a theory that cannot pick out the “real” universe from the theoretical landscape? Some have derisively called it the “theory of anything”. Even Strominger admits that discovering string theory can single out our universe after all would be spectacular. “We’d all be jumping up and down for joy,” he says.
Mathematicians Philip Candelas, Xenia de la Ossa, Yang-Hui He and Balázs Szendröi at the University of Oxford set out to do just that. “Increasingly, we were dissatisfied with this landscape picture,” says Candelas, “and the fact that people say rather too easily that string theory has no predictive power.”
They started by studying the geometry involved in the folding of string theory’s 10 dimensions down to four. One way in which mathematicians fold, or “compactify”, these extra dimensions is to use a geometrical construction known as a Calabi-Yau manifold. And because each way of folding the dimensions produces a different universe, each of the myriad known manifolds can serve as proxy for these universes.
The group placed all of the known Calabi-Yau manifolds on a diagram, plotting their topological complexity – for instance, how twisted and contorted the manifold is – against their “Euler number”, which mathematicians use to dictate how the extra dimensions can be compacted ().
The plot turned out to have the shape of a cone (see Diagram). Intriguingly, the team found that several of the manifolds in the sparsely populated tip of the cone seemed to generate universes like our own. “It is not as if we set out to find them [in that specific location],” says Candelas. “These manifolds were found from completely different considerations and the people who found them didn’t have these diagrams.” They call the tip of the cone a “special corner” of string theory’s theoretical landscape.
When the team looked more closely at some of the manifolds at the tip, they found that they could be geometrically transformed into other manifolds. In other words, one manifold with a certain number of “holes” and twists in its shape and structure could be mathematically transformed into another’s shape and structure. Previously, researchers had assumed that you could not make such transitions.
“This gives us an interesting speculation,” says He. “No matter where you start in this landscape of possible manifolds, there is a way to trickle down through to the very tip, through this series of geometric transitions.” This means that the universe might have started out completely differently – anywhere on the diagram – and been transformed, through a series of transitions, from one Calabi-Yau manifold to another, ending up at the tip. This would give rise to the universe as we know it, allowing string theory to at last confound its critics and single out our universe as a favoured configuration. “The debate then becomes not why do we have the world that we have but, rather, why do we live on the [tip],” says Candelas.
“The universe might have started out completely differently and been transformed, giving rise to the universe as we know it”
Cosmologist and string theorist Joseph Polchinski of the University of California at Santa Barbara calls the mathematicians’ work “neat”. “Maybe it gives us a clue,” he says. Strominger calls the maths “beautiful”.
However, Duff thinks that reshaping the question to “why we live at the tip” is actually one of the work’s limitations. “The obvious weakness is that they have swapped one mystery for another: what causes the transitions and what dynamical mechanism drives the universe into our particular corner?” Nonetheless, he says that Candelas and his colleagues make “some mathematically sound and interesting observations”. He adds that “some of this was known, but they have articulated it more clearly and in greater depth than had been done before”.
Candelas agrees that they still need to show what might drive a universe to make the transition from one form to another. “Perhaps the universe is minimising something, but we don’t know what it is,” he says.
One possibility for an aspect of the universe that could be minimised comes from a higher-dimensional topological feature of Calabi-Yau manifolds called “handles”, which are also related to their Euler numbers. All manifolds have them. Polchinski points out that the manifolds in the tip of the cone identified by the Oxford group have the smallest number of handles. “[These universes] are topologically simpler,” he says. “If the early universe somehow favoured transitions that removed handles, rather than adding handles, then you would have a mechanism that would drive you towards the bottom [of the cone].” This idea is similar to a mountain stream with high potential energy that moves downhill due to gravity until it reaches the sea, where its potential energy reaches a minimum.
While the mathematicians concede that their idea is a long shot, discovering more transitions between the various manifolds should soon tell them if they are onto something, especially if physicists could also identify plausible physical mechanisms that could drive these transitions. “If you can show that they all trickle down, then you should be looking at a unique [universe]. There should really be only one that looks like the real world,” says He. “This is our grand hope.”
“If you can show that all possible universes ‘trickle down’, there should really be only one that looks like the real world”
