THE beams of protons that circulate around the 27km-circumference ring of the Large Hadron Collider (LHC), the world’s biggest particle accelerator, carry as much kinetic energy as an American aircraft-carrier sailing at just under six knots. Andrew Geraci’s equipment, on the other hand, comprises a glass bead 300 billionths of a metre across, held in a lattice of laser light inside an airless chamber. The power it consumes would run a few old-fashioned light bulbs. Like researchers at the LHC, Dr Geraci and his team at the University of Nevada, in Reno, hope to find things unexplained by established theories such as the Standard Model of particle physics and Newton’s law of gravity. Whereas the LHC cost around SFr4.6bn ($5bn) to build, however, Dr Geraci’s set-up cost a mere $300,000 and fits on a table about a metre wide and three long.

A century ago these were the normal dimensions for experiments in fundamental physics. The electron, the proton and the neutron were all found using kit this size. (J.J. Thomson and his electron-discovery device are pictured above.) But digging deeper into theories of reality requires more energy, and thus bigger machines—of which the LHC is the latest. Since finding the Higgs boson in 2012, though, this behemoth has drawn a blank. Dr Geraci and those like him aspire, by contrast, to find evidence for those theories’ veracity by making precise measurements of the tiny forces that the particles they predict are expected to exert on other objects.

In Dr Geraci’s experiment the suspended bead scatters laser light onto a detector. If a force displaces the bead, the pattern of light changes, permitting the bead’s new position to be calculated. In work published last year in Physical Review A, his team showed that the apparatus can detect forces of a few billionths of a trillionth of a newton. (A newton is about the force exerted by Earth’s gravity on an apple.) Their next step will be to move a weight past the bead at a distance of five microns (five thousandths of a millimetre), to measure the gravitational attraction between them. That experiment is now under way.

The search for deviation

Dr Geraci is looking for deviations from Newton’s inverse-square law of gravity (that the gravitational force between two objects is inversely proportional to the square of the distance between them). Any departure from this law would provide support for theories which hope to solve what is known as the hierarchy problem of physics. This is the question of why gravity is so much weaker than the other three fundamental interactions between particles, namely electromagnetism and the weak and strong nuclear forces. The disparity between gravity and these forces explains, for example, why a small magnet can pick up a paper clip against the gravitational force of an entire planet.

One putative explanation, known as ADD after the initials of the surnames of three of its inventors, invokes extra dimensions to account for the difference. Gravity, this theory suggests, “spreads out” through these dimensions, dissipating its strength. The other forces, by contrast, are confined to the familiar three spatial ones, plus time. ADD conceives of the extra dimensions as being shrunken, compared with the familiar ones. But it suggests they should be detectable in the gravitational interactions of objects less than 100 microns apart. Measuring that is tricky, but Dr Geraci’s apparatus is one way of doing so.

Another is that employed by Eric Adelberger of the University of Washington, in Seattle—who copied the idea from Henry Cavendish, a British scientist of the 18th century. Cavendish was the first to measure the gravitational force between objects in a laboratory directly. To do so, he used a piece of apparatus called a torsion balance. And that is what Dr Adelberger uses. A decade ago he showed that Newton’s predictions remained correct for objects 44 microns apart. He is now trying again, at still-closer distances.

If either Dr Geraci or Dr Adelberger do overthrow the inverse-square law, they will open the way to a test of string theory—an attempt to explain physics at the most fundamental level. A recent version of string theory posits the universe to have 11 dimensions, seven of which are beyond human ken. Bringing even one or two of these within the realm of experiment, as ADD would if proved correct, would be a huge advance in understanding.

A second area in which tabletop experiments may beat the big guns is the search for dark matter. This mysterious stuff, not composed of the familiar protons, neutrons and electrons that make up atoms, is thought to pervade space and to constitute about 85% of the matter in the universe. Its gravitational effects can be seen on the ways that galaxies move. But, in a topsy-turvy parody of the hierarchy problem, it shows little or no sign of interacting with atomic matter through any of the other three known forces.

Many physicists, however, suspect that it may do so through forces as yet unknown. Some theories of dark matter predict the existence of force-carrying particles called axions and dark photons—and that these things interact, albeit weakly, with familiar matter. One searcher after such interactions is Hendrick Bethlem of the Free University of Amsterdam, in the Netherlands. He hopes to see signs of them in the spectra of individual molecules.

His dark materials

Dr Bethlem’s molecules of choice are ammonia. To examine them he uses a device called a molecular fountain. This employs pulses of electricity to propel the molecules under investigation to the top of an air-filled chamber, whence they fall slowly back down again, under gravity’s influence. While they are falling, they can be detected individually by a laser, and then interrogated spectroscopically.

This interrogation measures, with great precision, the energy levels of the electrons within a molecule. These depend, in turn, on the masses of those electrons, and also of the protons in the nuclei of the molecule’s constituent atoms (or, to be precise, on the ratio of these two masses). Since all protons and all electrons in the universe are identical, that ratio should not vary unless some outside influence is involved. Axions and dark photons, if they exist, would bring such influence to bear.

If space is, indeed, full of dark matter, Earth’s movement around the sun will bring seasonal changes to any interaction which that matter has with the ammonia molecules in Dr Bethlem’s laboratory. He might therefore expect to see annual variations in the energy levels he is measuring.

In 2008 a group at the Institut Galilée, in Paris, showed, by a different technique involving caesium atoms, that any such variation in the electron/proton mass ratio could not be more than 50 parts in a thousand trillion. Dr Bethlem thinks he can beat that level of precision by a factor of ten—and thereby either find evidence of dark matter or further constrain the definition of what it might be.

In California, meanwhile, Surjeet Rajendran and Peter Graham are using a different approach in their search for dark matter. Dr Rajendran works at the University of California, Berkeley. Dr Graham is at Stanford. Together, they are building a prototype dark-matter “radio”, consisting of a sensitive magnetometer known as a SQUID and a resonant circuit of the sort used to tune ordinary radios. These are inside a canister 170cm high and 17cm across, shielded from external magnetic fields. Dr Rajendran and Dr Graham, too, are looking for axions and hidden photons. The force these particles would carry should induce electromagnetic waves in the apparatus with a frequency of somewhere between a kilohertz and a gigahertz—in other words, radio waves. The pair propose to tune in to these frequencies on their SQUID radio, to see what they can hear.

Dr Rajendran and Dr Graham have two other ideas, as well, for hunting down these elusive particles. One, called CASPEr Wind, will use a cubic centimetre of liquid xenon. If axions are flying through the xenon, they should set its atoms’ nuclei wobbling. That would create a magnetic field large enough to spot with a SQUID. This experiment is now being built at Johannes Gutenberg University, in Mainz, Germany, by a team led by Dmitry Budker. A second experiment, called CASPEr Electric, uses a material called lead titanate. This substance is ferroelectric, meaning it is polarised so that one side of a crystal composed of it is positively charged, while the other is negatively charged. This makes such crystals useful for detecting the small polarising effect certain axions would have on atomic nuclei—again, assuming that they really do exist.

Dr Geraci, meanwhile, is collaborating with Asimina Arvanitaki of the Perimeter Institute in Waterloo, Canada, to build a device called Ariadne. This contains a vial filled with a form of helium, 3He, that has two protons and a single neutron, unlike normal helium, which has two of each. The vial is held around 100 microns from a rotating tungsten cog inside a chamber shielded from magnetic fields.

The protons and neutrons inside a nucleus act as magnets. If a nucleus contains an even number of these particle-magnets, they will all pair up, north poles neutralising south poles. If there is an odd number, though, as in 3He, the unpaired particle will make the nucleus itself magnetic.

Theory predicts that when the teeth of the cog are closest to the helium, axions should give rise to interactions between the two—interactions that will abate when the teeth move away. These interactions will show up as a magnetic field that varies as Ariadne’s cog rotates.

Like Dr Rajendran and Dr Graham, Dr Geraci and Dr Arvanitaki should complete their experiments within a decade. Small though these may be, their ambition rivals that of the largest experiment on the planet. If the LHC’s dry spell continues they may yet beat the collider to discoveries that herald a new era of physics.

Correction (Feb 2nd): An earlier version of this piece misspelt J.J. Thomson's name. This has now been corrected. We apologise for the error.