Physicists in the US have used a tabletop experiment to rule out the existence of strong, gravitational-like forces at short length scales. Such forces, which could hint at additional space–time dimensions or weird new particles, would cause Newton’s inverse square law of gravity to break down. By directly measuring the gravitational force on a micromechanical cantilever, however, Andrew Geraci and co-workers at Stanford University have found no evidence for such effects down to a distance of about 10 μm.

These are the most stringent constraints on non-Newtonian forces to date at this length scale Andrew Geraci

The result represents a small reduction in the amount of “wiggle-room” available in theories that attempt to incorporate gravity with the other three forces of nature, in particular string theory. “These are the most stringent constraints on non-Newtonian forces to date at this length scale,” says Geraci, who is currently based at the National Institute of Standards and Technology in Boulder.

Mysterious force

Gravity is the most mysterious of nature’s four known forces. Because it is so weak, researchers have only been able to test Newton’s inverse square law — which states that the gravitational force between two masses is inversely proportional to the square of their separation — down to distances of about 0.1 mm in the last few years. Compare this with electromagnetism, which is some 40 orders of magnitude stronger than gravity and has been tested at subatomic scales.

On the theoretical side, gravity poses even more of a challenge. Unlike electromagnetism and the strong and weak nuclear forces, which are described by quantum field theories, gravity is described by Einstein’s general relativity — a geometric theory which reduces to Newtonian gravity in everyday situations but which breaks down at the quantum scale. The lack of experimental constraints on gravity at distances less than a millimetre has given theorists broad scope to hypothesize how gravity relates to the other three forces. Testing gravity at short length scales therefore helps put these ideas on more solid ground.

Attonewton measurement

Geraci and co-workers have used an interferometer to measure how much a 0.25 mm-long silicon cantilever loaded with a 1.5 μg test mass is displaced by a source mass located 25 μm beneath it (arXiv:0802.2350; submitted to Phys Rev D). Keeping the apparatus at cryogenic temperatures to reduce thermal noise, this allowed the team to measure the attonewton (10–18 N) forces between two masses directly. This contrasts with the precision torsion-balance experiments that have tested Newtonian gravity at sub-millimetre scales by measuring torque, namely those performed by Eric Adelberger’s group at the University of Washington (see: Exclusion zone).

As is usual when testing for departures from the inverse square law, the team then looked for evidence of a corrected “Yukawa-type” potential: VN(1+α e–r/λ), where VN is the Newtonian gravitational potential, α describes the relative strength of the new force and λ is its range. Although the Stanford apparatus does not allow the Newtonian gravitational interaction between the test masses (i.e. corresponding to α ~1) to be measured, the experiment probes large forces in the regime where α = 104 – 108 at length scales of about 10 μm. It is here that some rather outlandish theories suggest powerful new forces will show up.

Extra dimensions

A decade ago, theorists suggested that all matter and the quantum fields of the strong, weak and electromagnetic interactions (i.e. our entire material universe) are confined to a 3D “brane” that floats around in a higher dimensional space where gravitons (the supposed mediators of gravity) roam wild. The apparent weakness of gravity would therefore be an illusion to inhabitants of the brane: gravity is merely diluted as it spreads out into additional dimensions that we cannot perceive.

In accordance with Gauss’s law, each extra dimension would increase the exponent in Newton’s law: if a single extra dimension turned up at a certain length scale, then the inverse square law would become an inverse cube law at that scale, for example. Provided the extra dimensions are large enough, they could also harbour new “gauge” particles that mediate forces many orders of magnitude stronger than gravity. Unlike gravity, the range of such forces (which are of the order of a fraction of a millimetre owing to the finite masses of the particles) might be independent of the number and size of the extra dimensions, and the forces can be repulsive rather than attractive.

We have taken out a sizeable chunk of the parameter space for moduli Andrew Geraci

Similar forces can arise in string theory, which is the inspiration behind such “braneworld” scenarios and the leading contender for a quantum theory of gravity. String theory demands six extra dimensions, and the exchange of certain “light moduli” particles that determine the way these dimensions are compactified at small scales could mediate forces at least 10,000 times as strong as Newtonian gravity. These forces may be present even if the dimensions are not large but curled up at the Planck length (about 10–33 cm), as most string theorists think is the case.

Moduli constraints

According to Geraci, it is these light moduli that the Stanford experiment has constrained most dramatically. “We have taken out a sizeable chunk of the parameter space for moduli,” he says. “Of course we can not rule out string theory, but we are able to place meaningful bounds on the mass [which determines the range, λ] and coupling strength of moduli [which determines α] that are quite generic.” This adds to constraints set in 2003 by researchers at the University of Colorado using a planar oscillator separated by a gap of 108 μm, which operates at length scales that are intermediate between the Stanford and Washington set-ups (see: Exclusion zone).

The results represent a four-fold improvement on previous experiments performed by the same team in 2003, but the researchers are currently working on a new “rotary” experiment that has a larger interaction area for the test and source masses. With this, the team expects to constrain parameter space in alpha by a further one to two orders of magnitude within a year or so, which would allow the “strange-modulus region” to be surveyed almost entirely (see: Exclusion zone).

“This is a pioneering experiment,” says Stanford theorist Savas Dimopoulos, who was one of the first to propose braneworld scenarios in 1998.