It's interesting that many of the more exotic ideas for achieving interstellar travel derive their inspiration from science fiction. Perhaps the most obvious example of this is the warp drive, with which we have become familiar through Gene Roddenberry's epic Star Trek series.

Miguel Alcubierre, a Mexican theoretical physicist, was intrigued by this idea, and in the early 1990s he set about attempting to find a way of describing how it might work within the formal framework of Einstein's theory of general relativity. As a consequence, he published a rather mathematical paper in 1994 in the learned journal Classical and Quantum Gravity, and since then his name has become synonymous with the idea of warp drive. As we mentioned in Chapter 1, Einstein's general relativity is essentially a new way of looking at how gravity works, which involves the notion that space and time are curved, or warped, by the presence of mass. Since Einstein also said that mass and energy are simply different forms of the same thing (see Chapter 6), space-time is also warped by the presence of energy. In Chapter 1 we saw how Newton's theory of gravity was overthrown by Einstein's new vision, in which the planets moved along their orbits around the Sun, like racing cars on a banked circuit, governed by the curvature of space-time produced by the Sun.

The key issue is how a warp drive-powered starship can travel at arbitrarily large speeds, effectively in excess of light speed, without violating the light speed limit. This sounds like an impossible trick, but there are ways to do this. The explanation resides in the more precise statement that, in general relativity, nothing can travel locally faster than the speed of light. In his deliberations about warp drive, Alcubierre found the illustration of the motion of objects in an expanding universe helpful in explaining his idea. So let's have a look at it to see if it helps.

One of the great triumphs of Einstein's theory of general relativity is that it predicts the expansion of the universe. This is one of the most profound achievements of theoretical physics in the 20th century, but it is also associated with an affair that Einstein himself considered to be one of his biggest blunders. Soon after the publication of his general theory in 1916, Einstein set about applying it to the universe as a whole, and showed that the universe would naturally be in a state of expansion. However, on the basis of the limited astronomical data then available, he was convinced that in fact the universe was actually static, so he introduced a new term into his equations of general relativity, essential a fudge factor, which he called the cosmological constant. With this new term in the equations he could model a static universe, in accord with what he then believed to be the case. However, in 1929, an astronomer named Edwin Hubble (after whom the famous space telescope is now named) published detailed observational evidence that, on the large scale, the universe is most definitely in a state of expansion. If only Einstein had believed his own analysis, he could have made one of the most profound predictions of theoretical physics, but it was not to be, and

Einstein had to return to his original equations, abandoning his cosmological constant (in fact, Einstein's cosmological constant has had a checkered history, and recent developments in theoretical physics have provoked scientists to consider its reintroduction into Einstein's theory).

What does it mean to say that the universe is expanding? A common misunderstanding is that the universe is effectively an infinite expanse of space-time, and at some moment in time, and at a particular point in space, the Big Bang happened. Thereafter, all the matter (galaxies) in the universe would appear to be moving away from each other and from a common point in space-time (the location of the Big Bang), gradually filling the huge expanse of space-time. However, the currently accepted view of the universe's expansion is subtly different from this. Rather than thinking of the universe as an explosion in a huge, fixed expanse of space-time, we have to envisage the universe—and by this I mean the fabric of space-time itself—as expanding. A good model of this, which is often quoted, is that of blowing up a balloon, although we have to lose a couple of dimensions. The four dimensions of space-time are now represented by the two dimensions of the rubber membrane of the balloon's surface. It is quite instructive to perform this simple experiment yourself, which emulates the expansion of the Universe. As we inflate the balloon, the rubber membrane (space-time) expands, and it is easy to see that each galaxy moves away from every other galaxy, representing Hubble's profound observational result that the balloon (the universe) is expanding.

Getting back to our attempt to understand Alcubierre's warp drive, it's important that you grasp the subtleties of the last paragraph, so if you haven't, I suggest you go back and give it another go. Because here's the point: as the balloon expands, "galaxies'' on opposite sides of the balloon can move away from each other at speed, and yet at the same time they are stationary with respect to the rubber membrane (space-time). If we now contemplate the real, expanding universe in which we live, and think about the implications of this statement, we can have a situation where two galaxies are so far apart that the expansion of space-time itself causes their speed relative to each other to be in excess of the speed of light, while at the same time neither galaxy is locally exceeding light speed.

It is this kind of thinking that underlies Alcubierre's idea of how a warp drive-powered starship might work. He envisaged a drive system that warps the space-time surrounding the starship, in such a way that space-time is expanded behind the starship, and contracted ahead of it, as illustrated in Figure 11.2. The expansion of space-time behind the starship effectively pushes the departure point many light-years back, while the contraction in front of the vehicle acts to bring the destination similarly closer. The starship

itself is left in a locally flat region of space-time between the two warped regions. In this way, motion faster than light is possible, as seen by an observer outside the region disturbed by the warp drive, while at the same time light speed is not exceeded locally by the starship—a really neat idea!

Is warp drive technology a feasible means of interstellar travel? To warp space-time behind and ahead of the vehicle, we know that the drive system must be able to manage and manipulate huge amounts of mass and energy. (Star Trek fans now have some idea what the famous dylithium crystals do in energizing Enterprise's warp drive.) Alcubierre wrote down the equations defining the necessary warp field for a starship, and then went on to investigate the kind of mass-energy source that would be needed to generate such a field. And here's the really bad news: the required space-time curvature needs the presence of a negative energy density. What this means is that the Alcubierre warp drive can be fueled only by a form of material that the scientists call exotic matter. Effectively, this comprises material that possesses characteristics such as negative mass, and there is debate among the experts about whether such matter even exists. Classical physics says it does not, whereas quantum theory says maybe it does. Either way, so far it is something that has escaped detection by scientists. Obviously, this is a bit of a blow to the feasibility of the Alcubierre warp drive, but his paper is probably not the last word on this topic. Fundamentally, we know that warp drive will be a difficult nut to crack, simply because of the huge amounts of mass-energy that is required to manipulate the curvature of space-time. However, I am sure alternate views will be presented in the future by theoretical physicists, and perhaps one of them will find a viable technical foundation for such a form of interstellar travel.

In many ways, wormholes are an even more curious idea than warp drive, but one that is a little easier to explain. Again, it is a technique that has its foundations in Einstein's theory of gravity for achieving super-light-speed travel without actually exceeding the light speed limit. Like warp drive, the wormhole concept has been grasped enthusiastically by science-fiction writers to overcome that awkward problem of how their space-faring heroes can travel with ease across the Galaxy. One such example, among many, can be found in Carl Sagan's novel Contact, in which the heroine Ellie travels 25 light years to the star Vega in the blink of an eye through a network of wormholes engineered by a long-lost civilization.

Space-time is not just a means of measuring where and when an event takes place, but it is also a dynamic entity that can be warped and curved by the presence of mass and energy. It has been known for many years that the equations of Einstein's theory allow solutions that permit space-time to be multiply connected. In other words, it allows for the existence of what are essentially short cuts through space and time, so that two distant regions of the universe can be connected by a much shorter higher-dimensional route. The term wormhole, first coined by physicist John Wheeler in 1957, has been universally adopted to label this curious feature of relativity theory, having its origins in the analogy used to explain the phenomenon. The usual analogy is to imagine a worm moving on the surface of an apple, starting out at a point A and moving to a point B that is on the other side of the apple (Fig. 11.3a). It has two choices: either it can go the long way round on the two-dimensional surface of the apple (route 1), or it can take a shorter journey (route 2) via a wormhole through the three-dimensional interior of the apple.

We can relate this analogy to a starship journeying between two points in space-time that are light years apart (Fig. 11.3b). It too can take the long route through space-time (represented by the two-dimensional curved surface) or use a conveniently located wormhole (represented by the three-dimensional passageway through hyperspace) to take a short cut. The wormhole allows the starship to effectively cover the distance at super-light speed, but without actually exceeding Einstein's speed limit. The analogy of the apple is helpful, but again we have lost a couple of dimensions in the discussion of the process.

So, is this form of interstellar travel a viable proposition for the future? Well, things are not quite as simple as the above analogy implies. One of the earliest wormhole solutions to the equations of general relativity was found by Einstein himself, in collaboration with a colleague Nathan Rosen, in 1935. This was christened an Einstein-Rosen bridge, but it took a good few years more for the theoretical physicists to realize that this type of wormhole was

Route 1

Route 1

Our Universe

Our Universe

Figure 11.3: (a) Moving from point A to point B, the worm has a choice of taking the longer route on the apple's surface, or the shortcut through the middle. (b) This analogy is often used to illustrate the idea of a using a shortcut through a cosmic wormhole between two points A and B in the universe that may be light years apart.

Figure 11.3: (a) Moving from point A to point B, the worm has a choice of taking the longer route on the apple's surface, or the shortcut through the middle. (b) This analogy is often used to illustrate the idea of a using a shortcut through a cosmic wormhole between two points A and B in the universe that may be light years apart.

unstable. It would close as soon as it was formed, making the transfer of people or starships through the cosmic passageway impossible. Since then, a great deal of work has been done investigating the stability of wormhole solutions of Einstein's theory, and again the bottom line is not good news for prospective interstellar travelers. The theory suggests that to keep a traversable wormhole open requires the use of exotic matter—the same stuff that we cannot find to power the warp drive! So although wormholes remain an intriguing prospect for the future, we seem to have hit the buffers again, with the engineering of such a scheme requiring huge amounts of negative mass and energy.

However, all is not lost. It should be borne in mind that the current wormhole solutions of Einstein's equations are based on his original classical theory, which focuses on the physics of the very large: planets, stars and galaxies, and the like. However, physicists are currently struggling to find a theory of everything that will describe the universe, not only on the large scale, but also on the very small scale where quantum mechanics presently reigns. Nobody really knows what such a theory will say about the future prospect of engineering a cosmic wormhole network as a kind of interstellar metro system!

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