Hands up who really understands what Stephen Hawking is telling us?

The great scientist's attempts to popularise his ideas about the Universe have been bestsellers, but few have read until the end. Steve Connor admits to feeling slightly baffled, but gamely unravels the rival contenders for a Final Theory of Everything

We came a little closer to knowing the mind of Stephen Hawking this week when he was interviewed by John Humphrys for a special edition of the Today programme on Radio 4. It is a mind filled with dark matter, black holes and multidimensional space-time. Perhaps the easiest concept to emerge from the brain of Britain's most celebrated living scientist was the notion that our future survival depends on whether we can colonise distant planets orbiting far-away stars.

Hawking, a mathematical cosmologist at Cambridge University, wrote A Brief History of Time, a book that famously attempted to shed light on the deeper recesses of cosmology. It has been a consistent best-seller since it was first published in 1988, but few people - including myself - have been able to finish it.

To me there are only two things worth remembering about cosmology. The first is that cosmologists are often in error, but never in doubt. The second is that there are lies, damn lies ... and cosmology.

In this, his first book, Hawking talked about the possibility of discovering a final theory of everything - a theory that can unify all the laws of nature. With such a theory, Hawking wrote in a phrase that has come to haunt him, we will surely know the mind of God.

"What I meant when I said we would know the mind of God was that if we discovered the complete set of laws, and understood why the universe existed, we would be in the position of God. We are making progress towards that goal, but we still have some way to go," Hawking told Humphrys.

A Final Theory of Everything is now the prime goal of modern physics. Indeed, for the past quarter century, about as long as I have been writing about science, physicists have said they are close to realising their ultimate ambition. Hawking predicted in 1988 that the final theory would be found by the end of the 20th century. Now he suspects that it may take until end of the present century.

So why is a theory of everything so important? Well, one problem with physics is that it appears to be governed by a set of unrelated laws that deal with the four fundamental forces of the known universe. A final, unified theory would explain these forces as different aspects of a single force.

The known forces of nature operate at different levels. There is gravity, affecting everything from apples to galaxies. There is electromagnetism, which interacts with electrically-charged particles such as electrons. And then there are the strong and weak nuclear forces that operate at the level of the atomic nucleus, involving exotic subatomic particles such as quarks, leptons and muons.

Bringing all these forces under one roof would mark a supreme achievement of science. As Hawking writes in his most recent, and more readable book, A Briefer History of Time: "It would bring to an end a long and glorious chapter in the history of humanity's intellectual struggle to understand the universe. But it would also revolutionise the ordinary person's understanding of the laws that govern the universe."

Modern physics stems from the work of Isaac Newton. His laws of motion and gravity are fundamental, and one important implication is the idea that there is no absolute position in space.

Hawking cites the metaphor of a ping-pong ball bouncing on a table to explain what this means. Imagine it takes a second for the ball to bounce up one metre and back again. For someone standing next to the table, the ball has merely bounced up and down by one metre without moving to the left or to the right.

However, imagine that the table is in the carriage of a fast-moving train travelling at a constant velocity of 40 metres per second. Anyone by the side of the railway track will not just see the ball's up and down movement. They will also see it travel 40 metres in the direction the train is travelling.

The implications are important, according to Hawking. "It means that we cannot determine whether two events that took place at different times occurred in the same position in space," he writes in A Briefer History of Time.

Indeed, Newton was worried about the implications of his own work because it meant that the lack of absolute position, or an absolute point in space, did not fit it with his idea of an absolute God. Fast forward 250 years, to the time of Albert Einstein, and now carry out a similar experiment on a fast-moving train but this time using an electric torch rather than a ping-pong ball. The light shining from the torch also travels through space. Again the two observers would disagree on the distance the light has travelled.

We know that the speed of light is constant. We also know that speed is distance divided by time. If the two observers disagree on the distance the light has travelled, the only way they are going to agree on the known constant speed of light is if the two observers disagree about the time the trip has taken.

This is the basis of Einstein's special theory of relativity, which ended the idea of absolute time. Identical clocks carried by different observers need not agree with one another - it was a revolutionary idea when Einstein first proposed it in 1905.

But it was Einstein's general theory of relativity, published in 1915 that gave birth to a concept that has become so important for modern physics. The idea is that space and time can be merged into a single entity called space-time.

Newton defined gravity in relation to mass and the distance apart from two massive objects. Einstein came up with a new concept of gravity, which he described as a consequence of the fact that space-time is not flat, as previously supposed, but curved or "warped".

The concept is not as difficult to imagine as you may suppose. In everyday life we treat the ground as flat. But in fact we know the Earth is a sphere. This means that if we walk in one direction and keep on walking (and walking) we finally end up back in the same position. It seems odd if we view the ground as flat, but not when we see the Earth for what it is - a sphere.

Einstein saw space-time as having four dimensions, with the three dimensions of space and the one dimension of time. It also has another peculiar property - the curved nature of space-time, which is how Einstein explained gravity, can bend light.

We are used to the idea of light being bent by optical lenses, but the general theory of relativity suggested that the gravitational attraction of the stars and galaxies can also bend light.

This was indeed observed by the astronomer Sir Arthur Eddington in 1919 during a total eclipse of the Sun. It was a powerful vindication for Einstein, who was having trouble explaining his theory to a wider audience.

In fact when asked by a journalist at the time of the announcement whether it was true that only three people in the world understood the general theory of relativity, Eddington was said to have replied: "Who's the third?"

The curved nature of space-time has also suggested another intriguing concept. If it can be warped far enough, it may be possible to create a short-cut from one point in space-time to another. Through this "wormhole" - a thin tube of space-time connecting one reasonably flat region with another - it may be possible to travel through time. It would mean that it may be possible to travel to the nearest star of Proxima Centauri through a wormhole of just a few million miles, even though the star is 20 million million miles away.

General relativity and its four-dimensional concept of space-time may be difficult enough for people to comprehend, but what about the idea of a universe of many more dimensions?

This is one of the implications of another Hawking favourite - string theory. This concept has grown into a likely contender for the theory of everything. In string theory, the basic objects are not point particles but things that have a length but no other dimension.

For the past 20 years or so, physicists have grown to favour string theory, even though one of its predictions is that space-time has more than the four dimensions imagined by Einstein. Without going into the mathematics, the string theorists predict a multidimensional universe with either 10 or 26 dimensions.

When asked by the likes of me to explain what they mean by so many dimensions, cosmologists are drawn to metaphors. Some use the concept of a garden hosepipe lying on the lawn. Other prefer a drinking straw resting on a bar.

Both objects are long, thin tubes. They have one obvious dimension when viewed from a distance - long and thin - but when inspected closely they have two more, hidden dimensions curled in on themselves to form a hollow tube. The extra dimensions of space-time may also be so small and curled that they escape our notice.

Hawking and his colleagues are toying with yet another mind-boggling concept to try to explain what is meant by these hidden dimensions of space. They call it a "brane" world, which takes it name from the membranes of biology.

Since about 1994, the concept of curling up the extra dimensions of space into branes has grown in importance. If particles can be viewed as occupying points in space, and strings are seen as lines, then branes are two dimensional, or even higher-dimensional, entities.

In this concept, a 2-brane entity is like a two-dimensional membrane. Hawking and his colleagues believe that the universe may be like such a brane - and it is expanding like the surface of an inflated balloon.

"The idea is that matter and light would be confined to the brane so we cannot travel through or see through the extra dimensions," said Hawking.

One implication is that there are aspects of the universe that we cannot see - which is indeed the case because 95 per cent of the material of the universe is invisible, which is why it is called dark matter. "There could be shadow galaxies, shadow stars and even shadow people," Hawking said.

Under this concept, it is perfectly possible that there is another Milky Way galaxy with another planet Earth and another Stephen Hawking grappling with the biggest questions imaginable. Awesome.

Headbending concepts

* Anthropic Principle: The idea is that the universe is the way it is otherwise we would not be here to observe it. It is based on the idea that the basic numbers governing the laws of nature - such as the mass of an electron - seem to be perfect for life.

* Branes: Drawn from the analogy of membranes in biology, brane theory is about using the concept of multidimensional structures to explain the universe. The easiest to understand is the 2-brane concept, which is like the surface of an inflated balloon on which the galaxies and stars are moving through space. Brane theory suggests a universe with up to 26 dimensions.

* Space-time: The concept devised by Albert Einstein to explain gravity. It has four dimensions, the three dimensions of space and the one dimension of time. Gravity is the result of a curved or "warped" space-time.

* Relativity: Albert Einstein formulated two theories of relativity, the special and the general. The first described how the laws of nature are the same for all observers, no matter how they are moving, in the absence of graviational phenomena. The second, general theory explained the force of gravity in terms of the curvature of four-dimensional space-time.

* String theory: A favourite concept to explain a single, unified theory of everything. Here particles are described as waves on strings, which have length but no other dimension.

* Wormholes: When space-time is warped enough it could form thin tubes connecting one region of relatively flat space with another. Such wormholes could allow time travel or long-distance space journeys from to parallel universes.

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