''Things on a small scale behave nothing like things on a large scale," the Nobel laureate Richard Feynman once observed. It seems a fairly self-evident remark, one might think. Bacteria don't sport tusks and trample trees, after all, and elephants don't replicate in their billions every day.
Yet Feynman's point has deep philosophical importance - as physicists know only too well. As they have discovered during the past century, our vision of the universe is divided into two, quite incompatible views: one of the profoundly tiny, and the other of the astronomically large. The former, the very weird realm of the atom - where electrons jump orbit without travelling through intervening space and where photons behave both as waves and particles - can be described by quantum mechanics. And when it comes to explaining how massive objects, such as galaxies, twist and distort the fabric of space and time, Einstein's theory of general relativity does very nicely, thank you.
Put these theorems together, however, and you create an unmixable intellectual brew. The laws governing tiny entities such as quarks are useless at predicting what the universe's largest objects will do, and vice versa. Biologists may have Darwin's law of natural selection to explain the behaviours of tuskers and bugs, but physicists have no unified code to help them understand both big and small events: why stars are bound tightly together inside galaxies and at the same time why the particulate components of atoms don't fly apart.
That is a fundamental problem, as the Columbia University physicist Brian Greene points out. "It is hard to believe that the deepest understanding of the universe consists of an uneasy union between two powerful theoretical frameworks that are mutually incompatible," he says. "We have one universe and therefore should have one theory."
Einstein, who had already united space, time and gravity in his theories, certainly believed this and spent the latter half of his life seeking - unsuccessfully - "a theory of everything" that would combine quantum physics and relativity. At the time, most physicists thought the great man had lost his marbles. But now, 50 years after Einstein's death, scientists have for the first time begun to talk seriously about the prospect of a successful outcome to this grand pursuit. As Greene says: "Einstein's lonely quest has become the driving force for a whole generation of physicists."
The name of this driving force is superstring theory.
According to this remarkable idea, all the various components of the atomic realm (quarks, electrons and the rest) are not really dot-like entities stacked inside each other like Russian dolls (quarks inside neutrons inside atoms, for example), as current atom theory suggests. Instead, each basic particle is made up of a tiny thread of energy a hundred billion billion times smaller than a nucleus.
Each of these identical filaments is shaped like a tiny string, and can vibrate. It is the manner of a string's vibration that determines a particle's physical identity, however, not its size. Thus one that resonates in a particular manner will have the mass and charge of an electron, and indeed will be called an electron. In this way, strings produce the 30 or so fundamental particles - quarks, neutrinos, electrons and others - that make up the Standard Model, the theory that currently explains the nature of matter.
"You can think of the universe as a symphony or song - for both are made up of 'notes' produced by strings vibrating in particular ways," says the Cambridge mathematician Michael Green, one of the first scientists to work on superstring theory.
In addition, strings resonate in ways that also allow them to act as the carriers of the universe's four main forces. They are the gravitational, electromagnetic, strong nuclear and weak nuclear forces that hold the atom together and which control radioactivity. (These carriers are known, respectively, as the graviton, the photon, the gluon and the W or Z particle.) Thus all matter, and all of the forces that hold matter together, can be explained in terms of a single concept: superstrings that vibrate in different ways. More importantly, the theory combines all the ideas of quantum mechanics, and - by including gravity - those that are currently described only by Einstein's great theories. String theory therefore makes the universe explicable from either perspective: large or small.
Put this way, the theory sounds a doddle. (Well, OK, a bit of a doddle.) Things get tougher, however. Superstring theorists also insist we must abandon the simple, safe idea that we live in a universe of three dimensions of space and one of time, and instead accept one in which there are a total of nine (or possibly ten) dimensions of space and one of time. The thought that a great part of the universe is so convoluted that we cannot perceive it is unsettling, if not downright disturbing: as the British physicist Paul Davies recently noted in Nature, it is now "almost impossible for the non-scientist to discriminate between the legitimately weird and the outright crackpot".
Certainly, those extra dimensions raise worrying thoughts. Why can't we see them? And are there great entities out there who look down on our puny 3D world as if it were some flat, two-dimensional cartoon? Superstring theorists remain unperturbed. According to their ideas, those extra dimensions are so tightly crumpled and small that they cannot be detected. Indeed, they may be so minute (about 100 million, billion, billion, billionth of a metre) that their existence may never be measured or proved.
Here we come to the major drawback of superstring theory: proving it. Yes, the idea provides us with the only mathematically consistent method yet devised for combining quantum mechanics with relativity. It is, basically, the only show in town. But finding a single piece of proof to back it will be very, very difficult, as scientists admitted this month at an international conference on the subject in Paris.
The problem is that there is no atom smasher yet built or planned that will have the energy needed to bludgeon superstrings apart, and thus prove their existence. "We have not yet worked out superstring theory in sufficient detail," says Michael Green. "We have only got approximations of it. We need to keep working at the theory to get it absolutely right in every detail. Then we should be able to make testable predictions - the hallmark of a good theory."
Some scientists cannot wait, and at the Paris conference, several research teams proposed ideas for detecting superstrings. One suggestion, put forward by Californian physicists, is to use a new generation of instruments that have been designed to detect gravity waves produced by supernova blasts and the collapses of massive black holes. However, it is also possible that cosmic strings - giant superstrings created not long after the Big Bang - may have jerked about like whiplashes in space in those cosmologically distant days and generated gravity waves that can now be picked up on earth. It is a long shot, however.
And certainly not every mathematician is convinced about the claims made for string theory. The Oxford cosmologist Sir Roger Penrose, generally rated Britain's greatest mathematician, is particularly cautious. "String theory is now being overhyped," he states. Penrose is especially suspicious of the theory's reliance on those extra dimensions to explain the nature of matter. "Most of these dimensions look unstable, which is not really good for the theory," he says. On the other hand, he adds, new theoretical work now being undertaken in the United States may allow theorists to get rid of these pesky dimensions, and that could make the whole thing workable in the end.
Not that superstring supporters worry. Indeed, they remain singularly confident. "The beauty of the theory is that it is not some accommodation or amalgamation of quantum mechanics and relativity," states Michael Green. "It is a unique, original body of work from which relativity and quantum mechanics emerge as logical corollaries."
This point is taken up by Brian Greene. String theory is an accumulation of a great many smaller ideas stitched together as an ever more impressive theoretical edifice, he states. "But what idea sits at the top of that edifice, we still don't really know. When we do have that idea, I believe that it will be like a beacon shining down."
And of all its acts of illumination, by far the most important will be the light it sheds on the origin of the universe - created, as we now know, 13.7 billion years ago in the Big Bang. Ever since, the cosmos has been expanding and matter has been hurtling apart. But what exactly happened at the Big Bang and why did it occur? What existed before it, scientists want to know? Astronomers have been able to provide very few answers, stymied as they are by the irreconcilable nature of quantum mechanics and general relativity. On the one hand, they need to use quantum mechanics to understand the early universe's tiny dimensions. On the other, they need relativity to make calculations about the vast mass of the early cosmos. And as we have seen, the two approaches are incompatible - but not, it is hoped, for much longer.
For the first time, the idea that the small-scale view of the universe may look much the same as the large-scale is being taken seriously, and we may understand just what happened at the creation of the cosmos. Einstein would have been a happy man.
Robin McKie is science editor of the Observer