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Texture of spacetimeA light wave travels through a spacetime that is grainy on the tiniest scales in this artist's illustration. A new study suggests that if spacetime is indeed grainy, the lumps can't be bigger than about 10^-35 meters.T. Piran/Hebrew University

Smaller dots, Georges, please. In their efforts to unify quantum theory and gravity, theoretical physicists have likened spacetime to a Georges Seurat painting, composed of tiny dots or lumps that meld to form a seemingly smooth picture. But if spacetime really does have a grainy structure on the smallest scales, the cosmic painter may need to get finer brushes, a new study reveals.

The study, published online October 28 in Nature, suggests that the dots that may compose spacetime must be smaller than one-hundred-thousandth of a trillionth of the size of a proton. This new limit on the graininess of spacetime is one-thousandth the size that previous, less sensitive experiments had indicated.

Sylvain Guiriec of NASA’s Marshall Space Flight Center and the University of Alabama in Huntsville and his colleagues used a powerful but indirect method to examine the structure of spacetime. The team measured the relative difference in the speed of two particles of light, or photons, of widely different energies. Both photons were emitted by a cosmic explosion known as a short-lived gamma-ray burst.

Many theories that seek to explain the action of gravity on subatomic scales are premised on the notion that space is lumpy or foamy on the tiniest of scales. Such theories also suggest that the speed of light is not constant but varies with a photon’s energy — in contradiction to Einstein’s theory of special relativity. The more energetic the photon is, the slower its speed. In simplified terms, that’s because higher energy photons have shorter wavelengths, which makes them more likely to bump into tiny lumps in spacetime and to be slowed by those structures.

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Telltale timesScientists tested the speed of photons emanating from a cosmic explosion called a gamma-ray burst (illustrated here) and determined that the photons all traveled at essentially the same speed regardless of their energies. The finding upholds Einstein's special relativity theory and rules out some theories of quantum gravity.NRAO

The slowdown would be tiny, but the lower velocity of high-energy photons could in principle be detectable over a journey of several billion light-years.

This strategy led Guiriec and his collaborators to examine photons generated by a gamma-ray burst that erupted in a galaxy 7.3 billion light-years from Earth. Recorded by the Fermi Gamma-ray Space Telescope on May 10, 2009, the burst produced an assortment of gamma-ray photons, including one with an energy of 31 billion electron-volts — about 13 billion times the energy of visible light — and another photon about one-tenth as energetic.

Although the two photons had significantly different energies and journeyed for more than 7 billion light-years, they arrived at the Fermi telescope less than nine-tenths of a second apart. That tiny time difference means that these photons traveled at almost exactly the same speed, just one part in 100 million billion apart, notes study coauthor Peter Michelson of Stanford University. That difference is small enough to suggest that the speed of light is constant regardless of the energy of the photon. The finding therefore rules out any theory of quantum gravity that predicts a large energy-dependent change in velocity, he adds.

The results also indicate that if the speed of light slows in direct proportion, or linearly, to the energy of a photon, then the size of a typical lump in spacetime must be less than 10^-35 meters, notes Guiriec.

The fundamental theories of nature, whether for gravity, electromagnetism or elementary particles, dictate that the laws of physics are identical for all observers, independent of any observer’s speed or direction of motion. That notion, known as Lorentz invariance, is also a foundation of Einstein's theory of special relativity. By ruling out many quantum gravity theories that violate Lorentz invariance, the Fermi result upholds special relativity.

John Ellis of CERN in Geneva agrees that the Fermi results offer the strongest astronomical evidence for the constancy of the speed of light. But he cautions that the effects of spacetime graininess on the speed of photons can’t be easily distinguished from time delays or advances due to other effects such as light scattering in the intergalactic medium. 

Theorist Giovanni Amelino-Camelia of the University of Rome La Sapienza says that if the speed of light does vary linearly with energy and spacetime has lumps just below 10^-35 meters, the Fermi telescope may soon be able to detect that fine graininess.

“These considerations allow us to have a slim hope that Fermi might soon stumble upon a new revolution in physics,” he says. Alternatively, observations over the next few years could rule out a linear relationship between the speed of light and photon energy. In that case, new equipment will be needed to search for a proposed weaker relation between the speed and energy, Amelino-Carnella notes.

Only a few years ago, he says, the possibility that experiments could probe the graininess of spacetime was deemed unlikely. The new result from the Fermi telescope “provides encouragement for the idea that the quantum gravity problem can be treated just like any other scientific problem—only a particularly difficult one.”

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