### Causality in the Universe, Duh

How To Build The Universe

Including cause-and-effect in equations produces four-dimensional space-time

Philip Ball

Is causality an inherent and necessary characteristic of the Universe, or just an illusion produced by the way our brains interpret the world?

It's real, say physicists, who believe they have worked out how the Universe is constructed from the tiniest building-blocks of space-time. The finding could also help the development of a theory of quantum gravity, which would marry the two currently estranged physical theories of the Universe: quantum theory and relativity.

Quantum theory describes the Universe at the tiniest possible scale - about 10

Physicists have long been trying to figure out how the fuzzy nature of space-time at this tiny scale can give rise to the large four-dimensional Universe we see around us, as described by Einstein's theory of relativity.

Scientists studying the problem assume that each tiny piece of the foam is a kind of four-dimensional triangle, with three dimensions of space and one corresponding to time. The smooth fabric of space-time can be built up by gluing these triangular tiles together, just as a smoothly curved surface can be made from flat, two-dimensional tiles.

Because the quantum foam fluctuates through all kinds of configurations, constructing the physical Universe means adding up all the possible tiling patterns. You might think that this would inevitably generate a four-dimensional Universe - but it doesn't. Earlier researchers found that they got a space-time with either an infinite number of dimensions or just two. Neither of these looks at all like our Universe.

Renate Loll of Utrecht University in the Netherlands and her co-workers have now found a way to assemble the pieces so that they inevitably produce a four-dimensional Universe. Instead of assuming that all tilings are allowed, they impose two constraints.

First, the theory of relativity must apply within each individual tile (so that nothing can travel through it faster than light) and second, the assembly must preserve causality. This means that a piece of space-time cannot be constructed in such a way that an 'event' - some change in the Universe - precedes its cause.

When they enforced these criteria on their calculations, the researchers ended up with universes with three spatial dimensions and one time dimension - just like our own

Even more startling, they found that typical universes generated this way started off small and got bigger - they expanded, just like the real Universe has done since the big bang. This was completely unexpected - there was nothing in the tiling rules that seemed to demand it. "We're completely stunned," says Loll.

She admits that there's no

Read the news at Nature.com

Including cause-and-effect in equations produces four-dimensional space-time

Philip Ball

Is causality an inherent and necessary characteristic of the Universe, or just an illusion produced by the way our brains interpret the world?

It's real, say physicists, who believe they have worked out how the Universe is constructed from the tiniest building-blocks of space-time. The finding could also help the development of a theory of quantum gravity, which would marry the two currently estranged physical theories of the Universe: quantum theory and relativity.

Quantum theory describes the Universe at the tiniest possible scale - about 10

^{-35}metres (about 10^{20}times smaller than the radius of a proton). It predicts that on this scale the apparently smooth fabric of space and time must degenerate into a kind of 'foam' in which connections between different points are constantly appearing and vanishing.Physicists have long been trying to figure out how the fuzzy nature of space-time at this tiny scale can give rise to the large four-dimensional Universe we see around us, as described by Einstein's theory of relativity.

Scientists studying the problem assume that each tiny piece of the foam is a kind of four-dimensional triangle, with three dimensions of space and one corresponding to time. The smooth fabric of space-time can be built up by gluing these triangular tiles together, just as a smoothly curved surface can be made from flat, two-dimensional tiles.

Because the quantum foam fluctuates through all kinds of configurations, constructing the physical Universe means adding up all the possible tiling patterns. You might think that this would inevitably generate a four-dimensional Universe - but it doesn't. Earlier researchers found that they got a space-time with either an infinite number of dimensions or just two. Neither of these looks at all like our Universe.

**Construction work**Renate Loll of Utrecht University in the Netherlands and her co-workers have now found a way to assemble the pieces so that they inevitably produce a four-dimensional Universe. Instead of assuming that all tilings are allowed, they impose two constraints.

First, the theory of relativity must apply within each individual tile (so that nothing can travel through it faster than light) and second, the assembly must preserve causality. This means that a piece of space-time cannot be constructed in such a way that an 'event' - some change in the Universe - precedes its cause.

When they enforced these criteria on their calculations, the researchers ended up with universes with three spatial dimensions and one time dimension - just like our own

^{1}. It was "like magic", says Loll.Even more startling, they found that typical universes generated this way started off small and got bigger - they expanded, just like the real Universe has done since the big bang. This was completely unexpected - there was nothing in the tiling rules that seemed to demand it. "We're completely stunned," says Loll.

She admits that there's no

*a priori*reason to demand that quantum space-time has to observe causality: the researchers put it into their equations by hand. But that, it seems, is the only way to end up with a realistic Universe.Read the news at Nature.com

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