In one of the wildest developments in serious science for decades, researchers from California to Moscow have recently been investigating the possibility of time travel. They are not, as yet, building TARDIS lookalikes in their laboratories; but they have realised that according to the equations of Albert Einstein's general theory of relativity (the best theory of time and space we have), there is nothing in the laws of physics to prevent time travel. It may be extremely difficult to put into practice; but it is not impossible.
It sounds like science fiction, but it is taken so seriously by relativists that some of them have proposed that there must be a law of nature to prevent time travel and thereby prevent paradoxes arising, even though nobody has any idea how such a law would operate. The classic paradox, of course, occurs when a person travels back in time and does something to prevent their own birth -- killing their granny as a baby, in the more gruesome example, or simply making sure their parents never get together, as in Back to the Future. It goes against commonsense, say the sceptics, so there must be a law against it. This is more or less the same argument that was used to prove that space travel is impossible.
So what do Einstein's equations tell us, if pushed to the limit? As you might expect, the possibility of time travel involves those most extreme objects, black holes. And since Einstein's theory is a theory of space and time, it should be no surprise that black holes offer, in principle, a way to travel through space, as well as through time. A simple black hole won't do, though. If such a black hole formed out of a lump of non-rotating material, it would simply sit in space, swallowing up anything that came near it. At the heart of such a black hole there is a point known as a singularity, where space and time cease to exist, and matter is crushed to infinite density. Thirty years ago, Roger Penrose (now of Oxford University) proved that anything which falls into such a black hole must be drawn into the singularity by its gravitational pull, and also crushed out of existence.
But, also in the 1960s, the New Zealand mathematician Roy Kerr found that things are different if the black hole is rotating. A singularity still forms, but in the form of a ring, like the mint with a hole. In principle, it would be possible to dive into such a black hole and through the ring, to emerge in another place and another time. This "Kerr solution" was the first mathematical example of a time machine, but at the time nobody took it seriously. At the time, hardly anybody took the idea of black holes seriously, and interest in the Kerr solution only really developed in the 1970s, after astronmers discovered what seem to be real black holes, both in our own Milky Way Galaxy and in the hearts of other galaxies.
This led to a rash of popular publications claiming, to the annoyance of many relativists, that time travel might be possible. In the 1980s, though, Kip Thorne, of CalTech (one of the world's leading experts in the general theory of relativity), and his colleagues set out to prove once and for all that such nonsense wasn't really allowed by Einstein's equations. They studied the situation from all sides, but were forced to the unwelcome conclusion that there really was nothing in the equations to prevent time travel, provided (and it is a big proviso) you have the technology to manipulate black holes. As well as the Kerr solution, there are other kinds of black hole time machine allowed, including setups graphically described as "wormholes", in which a black hole at one place and time is connected to a black hole in another place and time (or the same place at a different time) through a "throat". Thorne has described some of these possibilities in a recent book, Black Holes and Time Warps (Picador), which is packed with information but far from being an easy read. Now, Michio Kaku, a professor of physics in New York, has come up with a more accessible variation on the theme with his book Hyperspace (Oxford UP), which (unlike Thorne's book) at least includes some discussion of the contribution of researchers such as Robert Heinlein to the study of time travel. The Big Bang, string theory, black holes and baby universes all get a mention here; but it is the chapter on how to build a time machine that makes the most fascinating reading.
"Most scientists, who have not seriously studied Einstein's equations," says Kaku, "dismiss time travel as poppycock". And he then goes on to spell out why the few scientists who have seriously studied Einstein's equations are less dismissive. Our favourite page is the one filled by a diagram which shows the strange family tree of an individual who manages to be both his/her own father and his/her own mother, based on the Heinlein story "All you zombies --". And Kaku's description of a time machine is something fans of Dr Who and H.G. Wells would be happy with:
[It] consists of two chambers, each containing two parallel metal plates. The intense electric fields created between each pair of plates (larger than anything possible with today's technology) rips the fabric of space-time, creating a hole in space that links the two chambers.
Taking advantage of Einstein's special theory of relativity, which says that time runs slow for a moving object, one of the chambers is then taken on a long, fast journey and brought back: Time would pass at different rates at the two ends of the wormhole, [and] anyone falling into one end of the wormhole would be instantly hurled into the past or the future [as they emerge from the other end].
And all this, it is worth spelling out, has been published by serious scientists in respectable journals such as Physical Review Letters (you don't believe us? check out volume 61, page 1446). Although, as you may have noticed, the technology required is awesome, involving taking what amounts to a black hole on a trip through space at a sizeable fraction of the speed of light. We never said it was going to be easy! So how do you get around the paradoxes? The scientists have an answer to that, too. It's obvious, when you think about it; all you have to do is add in a judicious contribution from quantum theory to the time travelling allowed by relativity theory. As long as you are an expert in both theories, you can find a way to avoid the paradoxes.
It works like this. According to one interpretation of quantum physics (there are several interpretations, and nobody knows which one, if any, is "right"), every time a quantum object, such as an electron, is faced with a choice, the world divides to allow it to take every possibility on offer. In the simplest example, the electron may be faced with a wall containing two holes, so that it must go through one hole or the other. The Universe splits so that in one version of reality -- one set of relative dimensions -- it goes through the hole on the left, while in the other it goes through the hole on the right. Pushed to its limits, this interpretation says that the Universe is split into infinitely many copies of itself, variations on a basic theme, in which all possible outcomes of all possible "experiments" must happen somewhere in the "multiverse". So there is, for example, a Universe in which the Labour Party has been in power for 15 years, and is now under threat from a resurgent Tory Party led by vibrant young John Major.
How does this resolve the paradoxes? Like this. Suppose someone did go back in time to murder their granny when she was a little girl. On this multiverse picture, they have slid back to a bifurcation point in history. After killing granny, they move forward in time, but up a different branch of the multiverse. In this branch of reality, they were never born; but there is no paradox, because in he universe next door granny is alive and well, so the murderer is born, and goes back in time to commit the foul deed!
Once again, it sounds like science fiction, and once again science fiction writers have indeed been here before. But this idea of parallel universes and alternative histories as a solution to the time travel paradoxes is also now being taken seriously by some (admittedly, not many) researchers, including David Deutsch, in Oxford. Their research deals with both time, and relative dimensions in space. You could make a nice acronym for that -- TARDIS, perhaps?