Extra Dimensions

tra dimensions strengthen gravity much more quickly than usual at short distances, it still only catches up with the other forces near 10-19 meter and remains very feeble compared with them at larger distances.

A much more serious concern relates to gravitons, the hypothetical particles that transmit gravity in a quantum theory. In the theory with extra dimensions, gravitons interact much more strongly with matter (which is equivalent to gravity being stronger at short distances), so many more of them should be produced in high-energy particle collisions. In addition, they propagate in all the dimensions, thus taking energy away from the wall, or membrane, that is the universe where we live.

When a star collapses and then explodes as a supernova, the high temperatures can readily boil off gravitons into extra dimensions [see upper illustration on page 68 ]. From observations of the famous Supernova 1987A, however, we know that a supernova explosion emits most of its energy as neutrinos, leaving little room for any energy leakage by gravitons. Our understanding of supernovae therefore limits how strongly gravitons can couple to matter. This constraint could easily have killed the idea of large extra dimensions, but detailed calculations show that the theory survives. The most severe limit is for only two extra dimensions, in which case gravitons cool supernovae too much if the fundamental Planck scale is reduced below about 50 TeV. For three or more extra dimensions, this scale can be as low as a few TeV without causing supernovae to fizzle.

Theorists have examined many other possible constraints based on unacceptable changes in systems ranging from the successful big bang picture of the early universe to collisions of ultrahigh-energy cosmic rays. The theory passes all these experimental checks, which turn out to be less stringent than the supernova constraint. Perhaps surprisingly, the constraints become less severe as more dimensions are added to the theory. We saw this right from the start: the case of one extra dimension was excluded immediately because gravity would be altered at solar system distances. This indicates why more dimensions are safer; the dramatic strengthening of gravity begins at shorter distances and therefore has a smaller impact on the larger-distance processes.

Answers by 2010

The theory solves the hierarchy problem by making gravity a strong force near TeV energies, precisely the energy scale to be probed using upcoming particle accelerators. Experiments at the Large Hadron Collider (LHC), due to begin around 2005, should therefore uncover the nature of quantum gravity! For instance, if string theory is the correct description of quantum gravity, particles are like tiny loops of string, which can vibrate like a violin string. The known fundamental particles correspond to a string that is not vibrating, much like an unbowed violin string. Each different "musical note" that a string can carry by vibrating would appear as a different exotic new particle. In conventional string theories, the strings have been thought of as only 10-35 meter big, and the new particles would have masses on the order of the traditional Planck energy—the "music" of such strings would be too high-pitched for us to "hear" at particle colliders. But with large extra dimensions, the strings are much longer, near 10-19 meter, and the new particles would appear at TeV energies—low enough to hear at the LHC.

Similarly, the energies needed to create micro black holes in particle collisions would fall within experimental range [ see lower illustration on next page]. Such holes, about 10-19 meter in size, would be too small to cause problems—they would emit energy called Hawking radiation and evaporate in less than 10-27 second. By observing such phenomena, physicists could directly probe the mysteries of quantum black hole physics.

Even at energies too low to produce vibrating strings or black holes, particle collisions will produce large numbers of gravitons, a process that is negligible in conventional theories. The experiments could not directly detect the emitted gravitons, but the energy they carry off would show up as energy missing from the collision debris. The theory predicts specific properties of the missing energy—how it should vary with collision energy and so on—so evidence of graviton production can be distinguished from other processes that can carry off energy in unseen particles. Current data from the highest-energy accelerators already mildly constrain the large-dimensions scenario. Experiments at the LHC should either see evidence of gravitons or begin to exclude the theory by their absence.

A completely different type of experiment could also substantiate the theory, perhaps much sooner than the particle colliders. Recall that for two extra dimensions to solve the hierarchy problem, they must be as large as a millimeter. Measurements of gravity would then detect a change from Newton's inverse square law to an inverse fourth power law at distances near a millimeter. Extensions of the basic theoretical framework lead to a whole host of other possible deviations from Newtonian gravity, the most interesting of which is repulsive forces more than a million times stronger than gravity occurring between masses separated by less than a millimeter. Tabletop experiments using exquisitely built detectors are now under way, testing Newton's law from the centimeter range down to tens of microns [see illustration on page 69].

To probe the gravitational force at submillimeter distances, one must use objects not much larger than a millimeter, which therefore have very small masses. One must carefully screen out numerous effects such as residual electrostatic forces that could mask or fake the tiny gravitational attraction. Such experiments are difficult and subtle, but it is exciting that they might uncover dramatic new physics. Even apart from the search for extra dimensions, it is important to extend our direct knowledge of gravity to these short distances. Three researchers are currently conducting such experiments: John C. Price of the University of Colorado, Aharon Kapitulnik of Stanford University and Eric G. Adel-

Mif&S

GRAVITY

PARALLEL UNIVERSES may exist invisibly alongside ours, on their own membranes less than a millimeter away from ours. Such parallel universes could also be different sheets of our own universe folded back on itself. So-called dark matter could be explained by ordinary stars and galaxies on nearby sheets: their gravity (red) can reach us by taking a shortcut through the extra dimensions, but we cannot see them because light (yellow) must travel billions of light-years to the folds and back.

Mif&S

GRAVITY

PARALLEL UNIVERSES may exist invisibly alongside ours, on their own membranes less than a millimeter away from ours. Such parallel universes could also be different sheets of our own universe folded back on itself. So-called dark matter could be explained by ordinary stars and galaxies on nearby sheets: their gravity (red) can reach us by taking a shortcut through the extra dimensions, but we cannot see them because light (yellow) must travel billions of light-years to the folds and back.

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