Melting Spacetime

To understand how spacetime might emerge from string theory, in the early cosmos, we need to heat up the equations, and thaw the space and time dimensions.

FQXi Awardees: Joanna Karczmarek

April 30, 2012

Imagine if nothing around you was real. And, no, not in a science-fiction Matrix sense, but in an actual science-fact way.Technically, our perceived reality is a gigantic series of approximations: The tables, chairs, people, and cell phones that we interact with every day are actually made up of tiny particles—as all good schoolchildren learn. From the motion and characteristics of those particles emerge the properties that we see and feel, including color and temperature. Though we don’t see those particles, because they are so much smaller than the phenomena our bodies are built to sense, they govern our day-to-day existence.

Now, what if spacetime is emergent too? That’s the question that Joanna Karczmarek, a string theorist at the University of British Columbia, Vancouver, is attempting to answer. As a string theorist, Karczmarek is familiar with imagining invisible constituents of reality. String theorists posit that at a fundamental level, matter is made up of unthinkably tiny vibrating threads of energy that underlie subatomic particles, such as quarks and electrons. Most string theorists, however, assume that such strings dance across a pre-existing and fundamental stage set by spacetime. Karczmarek is pushing things a step further, by suggesting that spacetime itself is not fundamental, but made of more basic constituents.

High-Risk, High-Payoff

Having carried out early research in atomic, molecular and optical physics, Karczmarek shifted into string theory because she "was more excited by areas where less was known"—and looking for the building blocks from which spacetime arises certainly fits that criteria. The project, funded by a $40,000 FQXi grant, is "high risk but high payoff," Karczmarek says.

Spacetime itself would literally disappear because the theory got too hot.

- Joanna Karczmarek

That may change though. Nathan Sieberg, a string theorist at the Institute for Advanced Study (IAS) in Princeton, New Jersey, has found good reasons for his stringy colleagues to believe that at least space—if not space

*time*—is emergent. "With space we can sort of imagine how it might work," Sieberg says. To explain how, Seiberg uses an everyday example—the emergence of an apparently smooth surface of water in a bowl. "If you examine the water at the level of particles, there is no smooth surface. It looks like there is, but this is an approximation," Seiberg says. Similarly, he has found examples in string theory where some spatial dimensions emerge when you take a step back from the picture (arXiv:hep-th/0601234v1). "At shorter distances it doesn’t look like these dimensions are there because they are quantum fluctuations that are very rapid," Seiberg explains. "In fact, the notion of space ceases to make sense, and eventually if you go to shorter and shorter distances you don’t even need it for the formulation of the theory."

Brane Power

The first inklings that physicists may need to look for something more basic than strings and space came for Karczmarek in 2002 when she read some research about branes. Originally added to the string framework in the 1990s, branes are objects that can sprawl across a number of dimensions, and thus have more versatility than one-dimensional strings. For instance, a D0-brane would look like a particle, a D1-brane would look like a string, while a D25-brane would look like a giant membrane spread in 25 different dimensions.

The mathematics needed for describing strings together with branes is much more complicated than when describing strings on their own. In particular, in the late 1990s, Seiberg and string-supremo Ed Witten, also at IAS, discovered that to mathematically describe higher dimension D-branes as a combination of lower dimensional D-branes you have to use what is known as non-commutative multiplication (arXiv:hep-th/9908142v3). Normal multiplication is commutative, that is, it doesn’t matter which order you multiply a series of numbers, you will always get the same answer. If you want to find the area of a rectangular room, for instance, you could either multiply the length by the breadth, or you could multiply its breadth by its length—both would give you the same result. "But in noncommutative geometry x times y is not the same as y times x," says Karczmarek. "It is a very different space and a lot of really weird things happens."

Since D-branes are intimately connected to spatial geometry in string theory, the discovery that they used non-commutative mathematics led Karczmarek and other string theorists to speculate that space may behave in a non-commutative manner too. In turn, Karczmarek argues, that suggests that there is something more fundamental—an underlying algebraic structure that is non-commutative—from which space inherits these strange properties.

If trying to uncover the structure that underpins space was not hard enough, Karczmarek has also been thinking about whether time too may be emergent. Seiberg agrees that it is likely that if one aspect of spacetime is emergent, then both are, given that time and space get mixed together in ways we don’t fully understand yet in black holes and at the big bang. However, he is quick to point out that, if true, this opens up a whole new realm of challenges. Having an emergent theory of time confuses even our most basic assumptions when constructing models and theories.

HOT TIME

Melting dimensions in string theory models could help explain

how space and time emerge in reality.

Credit: Siarhei Hashnikau

*before*means, if there is no time."

Karczmarek’s work is still in the exciting early exploratory stages where the project could develop in many unpredictable directions. To try and simplify the problem, she is looking at a basic object—a sphere—and trying to calculate how the time dimension is affected as the sphere changes phase. "We think that when you heat it up the sphere might melt," says Karczmarek. But it’s not only the sphere that would be destroyed in her model, she adds: "It’s the spacetime itself that would literally disappear because the theory got too hot."

Melting spacetime may sound like an imaginative step too far! But Karczmarek hopes that her model will lead to a theory that could make predictions about the early universe, when spacetime would have emerged as the hot dense cosmos cooled, leaving observable signs that could be spotted today. The hope is that—eventually—others may be able to take her work and use it to identify signatures for what to look for in the cosmic microwave background radiation—the afterglow of the big bang.

Scarily, the work may also force us to rethink what time actually is: "If one could construct a theory where the entire spacetime including the time were emergent, then you would discover that time is an illusion and have a more fundamental understanding of why it is there," says Karczmarek. "But that’s the holy grail of the field, and I wouldn’t be surprised it if takes fifty years to make any progress on it."