WHEN Heinrich Päs checked his email on 11 April this year, he was in for a surprise. Just months earlier, he had suggested that neutrinos - those ghostly subatomic particles that flit through the Earth as easily as raindrops through a spring sky - might have the ability to travel through time. Now he was getting a deluge of mail from fellow physicists pointing out the spooky similarity between his predictions and some experimental results published earlier that day.

The experiment, called Miniboone, was being run by a team of nearly 80 physicists at the Fermi National Accelerator Laboratory (Fermilab) at Batavia, Illinois - and the results presented a puzzle. They simply didn't match what everyone thought they knew about neutrinos, and in a quest for an explanation physicists were resorting to a variety of exotic ideas, time travel among them. But what really got physicists excited was the possibility that the findings could reveal a gap in the standard model of particle physics and point the way to a "theory of everything" that unites Einstein's general theory of relativity and quantum theory. "The mere idea of this makes you feel kind of funny," says Miniboone team member Janet Conrad of Columbia University in New York.

The Miniboone results are the latest twist in a story that begins in the 1970s in a mine in South Dakota. There physicist Raymond Davis built an experiment using 400,000 litres of cleaning fluid to detect electron neutrinos, one of the three types of neutrino described by the standard model. He expected to spot them coming from the heart of the sun, generated by the same nuclear reactions that create sunlight. Sure enough he found them - but there were far fewer than the theory predicted. Something was making electron-neutrinos disappear on their way from the sun to the Earth. Later experiments, such as Super-Kamiokande in Japan confirmed this.

A related mystery popped up in the Earth's atmosphere. When the high-energy atomic nuclei from space known as cosmic rays slam into nuclei in the atmosphere, they produce electron neutrinos and another type, known as muon neutrinos. These nuclear reactions should, if current theories are correct, create twice as many muon neutrinos as electron neutrinos. Yet the measured ratio is closer to an even split. Something is making muon neutrinos disappear, too.

The theory that emerged to make sense of the disappearance of solar and atmospheric neutrinos is the first ever glimpse of what might lie beyond the standard model. All three types of neutrino - the electron neutrino, the muon neutrino, and a third type associated with the tau particle and called the tau neutrino (see Diagram) - had been assumed to be massless under the standard model. "The puzzling neutrino observations indicated that this was wrong," says Conrad's Columbia colleague Mike Shaevitz. "They had tiny masses, hundreds of thousands of times smaller than the electron, the previous lightest known particle."

The smallness of the masses has an important consequence. Like all quantum entities, neutrinos behave both as localised particles and as spread-out waves. According to quantum theory, small masses are synonymous with waves of very long wavelength. What's more, the theory permits "superpositions", in which several particle waves are superimposed on top of each other.

This was the key to solving the neutrino mystery. Physicists concluded that there is no such thing as an electron neutrino wave on its own. Instead, all three neutrino waves exist together in a ghostly trinity, like a beast that is simultaneously a dog, a cat and a rabbit. In such a superposition - and, crucially, assuming that the masses of the three types of neutrino are slightly different from one another - the waves periodically go in and out of phase, sometimes reinforcing each other, sometimes cancelling each other out. For three neutrinos, this leads to moments when the probability of seeing one particular neutrino type is greater than that of seeing the others. So as these neutrinos travel through space, they continually "oscillate" between the three different types.

One other effect also comes into play. As electron neutrinos flood out of the sun, they occasionally interact with solar electrons. Some 20 years ago, the Soviet physicists Stanislav Mikheyev and Alexei Smirnov, building on work by their American colleague Lincoln Wolfenstein, calculated that interactions with matter cause the electron neutrinos to flip into other types, principally muon neutrinos. Combined with neutrino oscillations, this explained the loss of the solar electron neutrinos and atmospheric muon neutrinos, as well as the results of experiments using man-made neutrino beams. All experiments, that is, except one.

In the mid-1990s, an experiment called LSND (the liquid scintillator neutrino detector) at the Los Alamos National Laboratory in New Mexico examined a beam of muon antineutrinos, looking for evidence that they were changing into electron antineutrinos. The researchers' expectation was that they wouldn't find any, as the beam of antineutrinos was only sent about 35 metres - nothing like long enough for any neutrino oscillations to occur. Yet LSND did, after all, see electron antineutrinos.

Taken at face value, the result blew the oscillation model out of the water. It could only be explained if the muon antineutrino changed into a fourth type of neutrino on its way to the detector and then this fourth type turned into an electron antineutrino. Yet the standard model has room for only three neutrino types, and experiments carried out at the CERN particle physics laboratory near Geneva, Switzerland, have ruled out the existence of a fourth neutrino. The only way theorists could reconcile the findings was to postulate the existence of a "sterile" neutrino that does not interact with matter as strongly as the others, making it super-elusive even by the slippery standards of neutrinos.

The sterile neutrino might not have much impact on matter, but it had a dramatic effect on physicists' thinking. It could, for example, have cosmological implications, accounting for some of the universe's invisible dark matter and affecting the large-scale distribution of galaxies (New Scientist, 15 June 2006, p 46). Remarkable claims require remarkable proof, however, and it had to be admitted that the most likely explanation for the LSND result was that it was wrong - some kind of experimental error.

This is where Miniboone comes in. "We were intrigued by the LSND result," says Conrad. "And we wondered what we could do to check it." So she and her colleagues built a new experiment at Fermilab that tried to look for a beam of muon neutrinos oscillating into electron neutrinos.

Their results, published in April, contained some good news and some bad news. The good news for the standard model was that they saw no sign of the oscillations LSND had detected. "It seems there is no need for a fourth, sterile neutrino," says Shaevitz. "The simple three-flavour neutrino oscillation model is once more compatible with the data."

There is one fly in the ointment, though: as the Miniboone team did not find a completely null signal. On close inspection, their results seemed to indicate that the lowest-energy muon neutrinos were still, apparently, turning into electron neutrinos. Once again, the most likely explanation is that there was some kind of experimental error. "The trouble is, we can't think what it could be," says Conrad.

The mere possibility that the signal is real has fired researchers' imaginations. Some believe they can explain both the Miniboone and the LSND results with not one sterile neutrino but two. A "3+2" model along these lines has been developed by Conrad and her former student Michel Sorel, now at the University of Valencia in Spain, and also independently by Michele Maltoni of the University of Madrid, Spain, and Thomas Schwetz of CERN.

In light of the fact that the standard model's quarks and leptons come in families of three, even two sterile neutrinos may not be enough, Conrad says, though so far this is just a hunch. "The truth is we don't have enough data to constrain the properties of three sterile neutrinos," she admits.

It is here that the notion of a time-travelling neutrino comes in. Last year Päs, who is based at the University of Alabama in Tuscaloosa, together with Sandip Pakvasa of the University of Hawaii in Honolulu and Thomas Weiler of Vanderbilt University in Nashville, Tennessee, looked at neutrinos from the perspective of string theory. This led them to suggest that sterile neutrinos, unlike most of the particles and forces that we see, can take short cuts through one of the normally invisible higher dimensions that string theory provides for, and so appear travel through time (New Scientist, 20 May 2006, p 34).

Their model indicated that if a sterile neutrino time-travelling through extra dimensions has an energy that lies in a particular range, it will flip into a normal neutrino (www.arxiv.org/abs/hep-ph/0611263). "We published a graph predicting just the excess of electron-neutrino events at low energy observed by Miniboone," says Päs.

So does this, or one of the other possibilities opened up by Miniboone, mean that it has caught sight of the theory of everything that will, everyone hopes, one day unite the fundamental forces? According to the favourite theory of neutrino oscillations, the oscillations are caused by subtle differences in neutrinos' masses. There is another way, though.

In our everyday experience, the laws of physics are identical for all observers moving at a constant speed: this so-called "Lorentz invariance" means that no matter what direction or speed a particle is moving, its behaviour is the same. Lorentz invariance has never been broken, as far as we know, yet many candidates for a theory of everything predict that space-time will exert a delicate influence on particles flying past, depending on the direction and speed they are travelling. Perhaps this breakdown of Lorentz invariance could be reflected in neutrino oscillations.

Last year, Alan Kostalecky of Indiana University, Bloomington, and his colleagues came up with a theory that suggests it might. Kostalecky posited that the universe is filled with a force field that imposes a "preferred direction" on space. According to their theory, neutrinos travelling across space can interact with the field to change into other types of neutrino. The farther a neutrino travels, the greater its chance of interacting, so the probability of one type of neutrino changing into another increases with distance, exactly as in the oscillation model. "We get an oscillation-type effect caused by the field and not by neutrino masses," says Rex Tayloe, who developed the idea with Kostalecky.

One of the things that makes this model appealing is its economy: it needs just three parameters to describe all known neutrino experiments - half as many as are required by the other theories. "Shockingly, the idea works very well indeed," says Conrad. "It's quite striking."

The question then arises: how can we distinguish between Conrad's model, with its extra sterile neutrinos, Päs's time-travelling through extra dimensions, and Kostalecky's Lorentz violation? Fortunately, says Tayloe, the three ideas predict distinctive effects for different neutrino energies and wavelengths.

For his team's theory, the key will be an experiment called Nova, due to be up and running in two to three years, which will fire a beam of muon neutrinos between Fermilab and a detector 800 kilometres away in Minnesota. "The standard oscillation picture says that muon neutrinos will change into electron neutrinos," says Tayloe. "We predict that they won't." If no muon neutrinos change, it would support Kostalecky's Lorentz violation.

Neutrino experiments continue to be a rich source of pointers to new physics. "The best thing is it's a field where the theorists - not the experimentalists - are always chasing to catch up," says Conrad. Neutrinos may already be whispering the answers to the universe's secrets. It's now down to us to figure out what they are saying.