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Can the electron be cut in half?

New Scientist

AT THE TIME no one even realised it had happened. More than thirty years ago, researchers in Minnesota did the unthinkable and broke the "indivisible" electron into fragments. This, at least, is the contention of British physicist Humphrey Maris, and no one has yet been able to prove him wrong. "Electron fragments behave to all intents and purposes like entirely separate particles," says Maris, who is based at Brown University in Rhode Island. "I call them electrinos."

Pause a moment to consider what Maris is saying. The electron is the lightest subatomic particle and the one with the greatest claim to being absolutely fundamental. In fact, in the 103 years since its discovery, there has been no other evidence whatsoever that the electron is divisible. It is the modern incarnation of Democritus's "uncuttable" atom.

The claim that electrons are divisible is therefore nothing short of a bombshell dropped into the world of physics. "If Humphrey is correct, it means a Nobel Prize," says Gary Ihas of the University of Florida. Nobel prizewinner Philip Anderson of Princeton University thinks Maris must be wrong. "But it's not obvious why," he admits.

Maris does not have definitive proof of his hypothesis. But earlier this year he published a paper that put it on a firm theoretical basis, and marshalled supporting evidence from past experiments. Now he is doing his own experiments, trying to break up the electron.

Whether Maris succeeds or not, he may have found a large crack in one of the foundation stones of modern physics. "Humphrey has succeeded in exposing a fundamental flaw in the framework of quantum theory," says Peter McClintock of the University of Lancaster.

This astonishing heresy is centred around the electron's wave function, the mathematical entity that, according to quantum theory, encapsulates everything about the electron that it is possible for us to know. Among other things, an electron's wave function describes the probability of finding it at any particular location. The wave function of an electron confined to, say, a spherical cavity is the three-dimensional description of how the electron's location is "smeared out" over the space.

In its lowest energy state, the wave function is spherical. The next highest energy level gives the wave function a dumb-bell shape. "It was while thinking about this state I was led to the conclusion that an electron might split in two," says Maris. If the dumb-bell could be stretched and pinched, he reasoned, might it simply divide?

Maris is expert in liquid helium, a substance that gives physicists the perfect opportunity to test this idea because electrons can exist independently and autonomously within it. When electrons from a radioactive source are fired into a vat of helium, repeated interactions with the electrons of the helium atoms slow them down until, finally, they grind to a halt. The intruding electrons do not attach themselves to helium atoms as a third electron, however. The Pauli exclusion principle makes sure of that, because it forbids more than two electrons from sharing the same quantum state. Faced with helium atoms whose electrons have bagged the lowest energy state-the ground state-an interloper with no spare energy has no choice but to lodge in the space between atoms. There it clears a bubble of space around itself-an electron bubble.

Electron bubbles form only in certain types of liquid-those in which the van der Waals force of attraction between atoms is weak enough to allow an electron to push them apart. In fact only two substances fit the bill: liquid helium and liquid hydrogen. At very low temperatures in helium, electron bubbles displace more than 700 helium atoms, creating a cavity around 38 angstroms (3.8 nanometres) across. Inside this cavity quantum mechanics rules, ensuring that the electron can occupy only a limited set of energy states.

Light touch
Maris worked out that an electron in a bubble could be put into the dumb-bell-shaped excited state by illuminating the helium with light that had a wavelength of about 10 micrometres, which is easily supplied by a carbon dioxide laser. In this state, Maris calculated, the electron imparts most of its force to the ends of the dumb-bell; this force is enough, he realised, to make the bubble wall wobble violently. "I found that the force exerted by the electron was enough to elongate the bubble until it formed a thin neck," he says. "If the pressure in the liquid was great enough, there was the possibility of it pinching off the neck so that the bubble might actually split in two."

This sounds harmless enough, but the implications are staggering. If the bubble split, half of the electron's wave function would be trapped in each of the two daughter bubbles (see Diagram). As the wave function is the essence of an electron, the electron would be split into two. The indivisible would have been divided.

Maris planned to test his idea in the laboratory but first decided to search back through the literature to see whether anyone had done the kind of experiments he had in mind. He soon found what he was looking for. In the late 1960s, Jan Northby and Mike Sanders at the University of Minnesota studied the speed of electron bubbles moving in an electric field in liquid helium. They measured the electric current that flowed as the bubbles moved, and then illuminated the helium with light. The researchers expected this to increase the current. They reasoned that light would eject some of the electrons from the bubbles, and that these would whiz through the helium, boosting the current-and that is exactly what they observed.

But as physicists have since realised, this reasoning was flawed. "We now know that knocked-out electrons form new electron bubbles," says Maris. "The current should not have increased." Inexplicably, however, it did. In 1990 and 1992, researchers at Bell Labs in New Jersey ran a similar experiment, with the same result. No explanation has ever been found-until now, perhaps.

Maris suggests that, instead of ejecting the electrons, the light boosted them from the ground state to the dumb-bell-shaped excited state, and the electron bubbles split. "There were more bubbles, and being smaller they were more mobile," says Maris. Although the total charge in the system remained the same, the smaller bubbles felt less drag in the helium, and thus moved faster. "Consequently, the current went up," Maris explains.

Maris believes he has further evidence to support his explanation. Northby and Sanders saw the increased current only below 1.7 kelvin, exactly the temperature at which Maris's theory says the effect should take hold. According to his calculations, electron bubbles should split apart only below a critical temperature of 1.7 K. The crucial factor is viscosity. If it is too great, says Maris, the liquid will behave like treacle, resisting the elongation of the bubble and squeezing it back to a sphere. Below 2.19K liquid helium becomes a superfluid: as you cool it, its viscosity starts to disappear. By 1.7 K, Maris calculated, the liquid would be so slippery that it couldn't stop the bubbles dividing.

Other experimenters have studied the mobility of electrons in a more precise way. They include Gary Ihas and Mike Sanders at the University of Michigan in 1971 and Van Eden and McClintock of the University of Lancaster in 1984. These physicists created a short burst of about a million bubbles which they carefully timed as they moved through liquid helium in an electric field. Since the bubbles were created together, they should have crossed the finishing line together. To the surprise of the experimenters, most of the bubbles arrived in three separate clumps.

Maris's explanation is again simple. Unlike the electrons in the Minnesota experiment, these electrons had been created in an electrical discharge-a miniature bolt of lightning. This produced light, and Maris says that some of this light boosted electrons within the bubbles to the excited state, causing them to split, and split again. Hence the spread of arrival times, with whole, half and quarter charges making up most of the current.

McClintock is not yet convinced by Maris. But he admits that nobody else has come up with a plausible explanation. "The electrino idea offers a possible way out," he concedes.

Maris has long realised the furore his ideas would cause. He spent several years working out the details of electron bubble fission and gathering experimental evidence without ever telling anyone what he was thinking. "It took time to get used to the idea and pluck up the courage to announce it," he admits. Finally, in June this year, he decided to go public. He presented his work at a Minneapolis conference on quantum fluids and solids, and then published it in a paper in the Journal of Low Temperature Physics (vol 120, p 173).

The conference organisers thought Maris's work important enough to give him an extra two-hour session. At the end, more than 100 physicists questioned every aspect of the theory. "My first reaction was extreme scepticism, like everyone else," McClintock says. Maris, though, had an answer for everything. "He'd obviously thought long and hard about the whole thing," McClintock concedes.

Maris was encouraged by the response -or lack of it-from his peers. "I was nervous someone would find a hole," he admits. "But to my relief nobody dismissed the idea out of hand."

Experts in quantum theory are not so accommodating, though. "The idea of an electron splitting into fractionally charged fragments is totally incompatible with quantum field theory," says Anthony Leggett of the University of Illinois at Urbana-Champaign. He admits that there could be something wrong with quantum field theory. "However, given its overwhelming success in explaining the world, this is highly unlikely," he says.

According to quantum theory, it is possible to have strange "superposition states", where the whole electron exists in both bubbles until a measurement forces it to be in one or the other. "But we cannot consider states which have half an electron on each," Leggett insists. It is impossible to solve the equations of quantum mechanics with anything other than a whole-charge electron. The formulations of quantum electrodynamics, the area of physics that deals with the behaviour and properties of electrons, don't allow for half electrons, or any other fraction.

"If the electron splits and you can measure a fractional charge, this flies in the face of standard quantum mechanics as well as high-energy physics," agrees David Pritchard of the Massachusetts Institute of Technology. "The idea that the electron is a point particle without structure is established up to very high energies."

Half measures
Like Leggett and Pritchard, most physicists are convinced that Maris's claim falls at the first fence, though they cannot pinpoint why. Their scepticism is understandable. If Maris is right then quantum theory is wrong-and nobody has the slightest idea what they would use to replace it.

Maris being right would have some positive practical consequences, however. He speculates about building a device which introduces a partition into a cavity to divide the wave function of an electron. This could lead to circuits which exploit the properties of fractionally charged particles, he says. Half-mass, half-charge electrons might give electronics a whole new dimension. Then there's the possibility of a new kind of chemistry. Maybe you could take an electron bubble out of the liquid, attach the electron fragment to an atom and do novel chemistry with fractional electrons. Could this really happen? Maris says he doesn't know.

The electron fragments, having once been part of the same electron, might even be "entangled", sharing a strange telepathic link. Quantum physicists have already managed to achieve this with photons, and used these entangled particles of light to perform astonishing feats such as teleportation and elementary quantum computing. Fractional charge might add a new string to their bow.

The most profound consequences of splitting the electron, though, would be on theoretical physics. Maris's only concrete claim is that an electron's wave function can be split and mimic a fractional electron. He has no idea of the full consequences of this-and neither has anyone else. Maris's hypothesis seems to throw everything we know about quantum theory into confusion. At the very least, he believes, his work challenges physicists to be specific about what they mean by the fuzzy entity that describes quantum systems. "People are going to have to hone their ideas of the wave function," he says. "Most importantly, they are going to have to address the question: what is a wave function? Is it a real thing, or just a mathematical convenience?"

Physicists have always been content to think of the wave function as a mathematical device with observable consequences. But Maris believes the time has come for the idea to be grounded in reality. For the electron bubbles in helium, he says, the size of the bubble is determined by how much of the wave function is trapped inside the bubble. If there is no part of the wave function inside the bubble, the bubble will collapse. "This makes the wave function seem to be a tangible object," he argues.

Maris remains an experimentalist at heart, though. Since the theorists have nothing to say about the myriad questions he has raised, he believes answers won't be found until there is some more evidence to go on-and that means doing more experiments. Maris and others, he believes, are now looking for that evidence. "Already, the results of my experiments are encouraging," he says.

But Maris also insists that he won't be upset if his idea is eventually disproved. Having lobbed in his bombshell, he seems to have decided to sit on the sidelines, enjoying the ensuing chaos. "What I have come up with is an intriguing puzzle," he says. "I want people to think. I would be happy if I was completely wrong but made a lot of people think."


New Scientist issue: 14th October 2000


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