CHAPTER FOUR

DATA

Ends the Game For I dipt into the future, far as human eye could see, Saw the Vision of the world, and all the wonder that would

be. From “Locksley Hall, ” by Alfred Lord Tennyson (posted aboard the starship Voyager,)

Whether or not the Star Trek future can include a stable worm-hole, and whether or not the Enterprise crew could travel back in time to nineteenth-century San Francisco, the real stakes in this cosmic poker game derive from one of the questions that led us to discuss curved spacetime in the first place: Is warp drive possible? For, barring the unlikely possibility that our galaxy is riddled with stable wormholes, it is abundantly clear from our earlier discussions that without something like it, most of the galaxy will always remain beyond our reach. It is finally time to address this vexing question. The answer is a resounding “Maybe!”

Once again we are guided by the linguistic perspicacity of the Star Trek writers. I have described how no rocket

propulsion mechanism can ever get around the three roadblocks to interstellar travel set up by special relativity: First, nothing can travel faster than the speed of light in empty space. Second, objects that travel near the speed of light will have clocks that are slowed down. Third, even if a rocket could accelerate a spacecraft to near the speed of light, the fuel requirements would be prohibitive.

The idea is not to use any sort of rocket at all for propulsion, but instead to use spacetime itselfby warping it. General relativity requires us to be a little more precise in our statements about motion. Instead of saying that nothing can travel faster than the speed of light, we must state that nothing can travel locally any faster than the speed of light. This means that nothing can travel faster than the speed of light with respect to local distance markers. However, if spacetime is curved, local distance markers need not be global ones.

Let me use the universe itself as an example. Special relativity tells me that all observers who are at rest with respect to their local surroundings will have clocks that tick at the same rate. Thus, as I move throughout the universe, I can periodically stop and place clocks at regular intervals in space and expect that they will all keep the same time. General relativity does not change this result. Clocks that are locally at rest will all keep the same time. However, general relativity allows spacetime itself to expand. Objects on opposite sides of the observable universe are flying apart at almost the speed of light, yet they remain at rest relative to their local surroundings. In fact, if the universe is expanding uniformly and if it is large enoughboth of which appear to be the casethere exist objects we cannot yet see which are at this very moment moving away from us far faster than the speed of light, even though any civilizations in these far reaches of the universe can be locally at rest with respect to their surroundings.

The curvature of space therefore produces a loophole in special relativistic argumentsa loophole large enough to drive a Federation starship through. If spacetime itself can be manipulated, objects can travel locally at very slow velocities, yet an accompanying expansion or contraction of space could allow huge distances to be traversed in short time intervals. We have already seen how an extreme manipulationnamely, cutting and pasting distant parts of the universe together with a wormholemight create shortcuts through space-time. What is argued here is that even if we do not resort to this surgery, faster-than-light travel might globally be possible, even if it is not locally possible.

A proof in principle of this idea was recently developed by a physicist in Wales, Miguel Alcubierre, who for fun decided to explore whether a consistent solution in general relativity could be derived which would correspond to “warp travel.” He was able to demonstrate that it was possible to tailor a spacetime configuration wherein a spacecraft could travel between two points in an arbitrarily short time. Moreover, throughout the journey the spacecraft could be moving with respect to its local surroundings at speeds much less than the speed of light, so that clocks aboard the spacecraft would remain synchronized with those at its place of origin and at its destination. General relativity appears to allow us to have our cake and eat it too.

The idea is straightforward. If spacetime can locally be warped so that it expands behind a starship and contracts in front of it, then the craft will be propelled along with the space it is in, like a surfboard on a wave. The craft will never travel locally faster than the speed of light, because the light, too, will be carried along with the expanding wave of space.

One way to picture what is happening is to imagine yourself on the starship. If space suddenly expands behind you by a huge amount, you will find that the starbase you just left a few minutes ago is now many light-years away. Similarly, if space contracts in front of you, you will find that the starbase you are heading for, which formerly was a few light-years away, is now close to you, within reach by normal rocket propulsion in a matter of minutes.

It is also possible to arrange the geometry of spacetime in this solution so that the huge gravitational fields necessary to expand and contract space in this way are never large near the ship or any of the star-bases. In the vicinity of the ship and the bases, space can be almost flat, and therefore clocks on the ship and the starbases remain synchronized. Somewhere in between the ship and the bases, the tidal forces due to gravity will be immense, but that's OK as long as we aren't located there.

This scenario must be what the Star Trek writers intended when they invented warp drive, even if it bears little resemblance to the technical descriptions they have provided. It fulfills all the requirements we listed earlier for successful controlled intergalactic space travel: (1) faster-than-light travel, (2) no time dilation, and (3) no resort to rocket propulsion. Of course, we have begged a pretty big question thus far. By making spacetime itself dynamical, general relativity allows the creation of “designer spacetimes,” in which almost any type of motion in space and time is possible. However, the cost is that the theory relates these spacetimes to some underlying distribution of matter and energy. Thus, for the desired spacetime to be “physical,” the underlying distribution of matter and energy must be attainable. I will return to this question shortly.

First, however, the wonder of such “designer spacetimes” is that they allow us to return to Newton's original challenge and to create iner-tial dampers and tractor beams. The idea is identical to warp drive. If spacetime around the ship can be warped, then objects can move apart or together without experiencing any sense of local acceleration, which you will recall was Newton's bane. To avoid the incredible accelerations required to get to impulse sublight speeds, one must resort to the same spacetime shenanigans as one does to travel at warp speeds. The distinction between impulse drive and warp drive is thus diminished. Similarly, to use a tractor beam to pull a heavy object like a planet, one merely has to expand space on the other side of the planet and contract it on the near side. Simple!

Warping space has other advantages as well. Clearly, if spacetime becomes strongly curved in front of the Enterprise, then any light rayor phaser beam, for that matterwill be deflected away from the ship. This is doubtless the principle behind deflector shields. Indeed, we are told that the deflector shields operate by “coherent graviton emission.” Since gravitons are by definition particles that transmit the force of gravity, then “coherent graviton emission” is nothing other than the creation of a coherent gravitational field. A coherent gravitational field is, in modern parlance, precisely what curves space! So once again the Star Trek writers have at least settled upon the right language.

I would imagine that the Romulans' cloaking device might operate in a similar manner. In fact, an Enterprise that has its deflector shield deployed should be very close to a cloaked Enterprise. After all, the reason we see something that doesn't shine of its own accord is that it reflects light, which travels back to us. Cloaking must somehow warp space so that incident light rays bend around a Warbird instead of being reflected from it. The distinction between this and deflecting light rays away from the Enterprise is thus pretty subtle. In this connection, a question that puzzled many trekkers until the Next Generation episode “The Pegasus” aired was, Why didn't the Federation employ cloaking technology? It would certainly seem, in light of the above, that any civilization that could develop deflector shields could develop cloaking devices. And as we learned in “The Pegasus,” the Federation was limited in its development of cloaking devices by treaty rather than by technology. (Indeed, as became evident in “All Good Things ...,” the last episode of the Next Generation, the Federation eventually seems to have allowed cloaking on starships.)

Finally, given this general-relativistic picture of warp drive, warp speeds take on a somewhat more concrete meaning. The warp speed would be correlated to the contraction and expansion factor of the spatial volume in

front of and behind the ship. Warp-speed conventions have never been particularly stable: between the first and second series, Gene Roddenberry apparently decided that warp speeds should be recalibrated so that nothing could exceed warp 10. This meant that warp speed could not be a simple logarithmic scale, with, say, warp 10 being 2 10 = 1024 x light speed. According to the Next Generation Technical Manual, warp 9.6, which is the highest normal rated speed for the Enterprise-D, is 1909 x the speed of light, and warp 10 is infinite. It is interesting to note that in spite of this recalibration, objects (such as the Borg cube) are periodically sighted which go faster than warp 10, so I suppose one shouldn't concern oneself unduly about understanding the details.

Well, so much for the good news....

Having bought into warp drive as a nonimpossibility (at least in principle), we finally have to face up to the consequences for the right-hand side of Einstein's equationsnamely, for the distribution of matter and energy required to produce the requisite curvature of space-time. And guess what? The situation is almost worse than it was for wormholes. Observers traveling at high speed through a wormhole can measure a negative energy. For the kind of matter needed to produce a warp drive, even an observer at rest with respect to the star-shipthat is, someone on boardwill measure a negative energy.

This result is not too surprising. At some level, the exotic solutions of general relativity required to keep wormholes open, allow time travel, and make warp drive possible all imply that on some scales matter must gravitationally repel other matter. There is a theorem in general relativity that this condition is generally equivalent to requiring the energy of matter to be negative for some observers.

What is surprising, perhaps, is the fact, mentioned earlier, that quantum mechanics, when combined with special relativity, implies that at least on microscopic scales the local distribution of energy can be negative. Indeed, as I noted in chapter 3, quantum fluctuations often have this property. The key question, which remains unanswered to date, is whether the laws of physics as we know them will allow matter to have this property on a macroscopic scale. It is certainly true that currently we haven't the slightest idea of how one could create such matter in any physically realistic way.

However, ignore for the moment the potential obstacles to creating such material, and suppose that it will someday be possible to create exotic matter, by using some sophisticated quantum mechanical engineering of matter or of empty space. Even so, the energy requirements to do any of the remarkable playing around with spacetime described here would likely make the power requirement for accelerating to impulse speed seem puny. Consider the mass of the Sun, which is about a million times the mass of the Earth. The gravitational field at the surface of the Sun is sufficient to bend light by less than 1/1000 of a degree. Imagine the extreme gravitational fields that would have to be generated near a starship to deflect an oncoming phaser beam by 90¡! (This is one of the many reasons why the famous “slingshot effect” first used in the classic episode “Tomorrow Is Yesterday” to propel the Enterprise backward in time, again in Star Trek IV: The Voyage Home, and also mentioned in the Next Generation episode “Time Squared”is completely impossible. The gravitational field near the surface of the Sun is minuscule in terms of the kind of gravitational effects required to perturb spacetime in the ways we have discussed here.) One way to estimate how much energy would have to be generated is to imagine producing a black hole the size of the Enterprise since certainly a black hole of this size would produce a gravitational field that could significantly bend any light beam that traveled near it. The mass of such a black hole would be about 10 percent of the mass of the Sun. Expressed in energy units, it would take more than the total energy produced by the Sun during its entire lifetime to generate such a black hole.

So where do we stand at the end of this game? We know enough about the nature of spacetime to describe explicitly how one might, at least in principle, utilize curved space to achieve many of the essentials of interstellar space travel ˆ la Star Trek. We know that without such exotic possibilities we will probably never voyage throughout the galaxy. On the other hand, we have no idea whether the physical conditions needed to achieve any of these things are realizable in practice or even allowed in principle. Finally, even if they were, it is clear that any civilization putting these principles into practice would have to harness energies vastly in excess of anything imaginable today.

I suppose one might take the optimistic view that these truly remarkable wonders are at least not a priori impossible. They merely hinge on one remote possibility: the ability to create and sustain exotic matter and energy. There is reason for hope, but I must admit that I remain skeptical. Like my colleague Stephen Hawking, I

believe that the paradoxes involved in round-trip time travel rule it out for any sensible physical theory. Since virtually the same conditions of energy and matter are required for warp travel and deflector shields, I'm not anticipating them eitherthough I have been wrong before.

Nevertheless, I am still optimistic. What to me is really worth celebrating is the remarkable body of knowledge that has brought us to this fascinating threshold. We live in a remote corner of one of 100 billion galaxies in the observable universe. And like insects on a rubber sheet, we live in a universe whose true form is hidden from direct view. Yet in the course of less than twenty generationsfrom Newton to todaywe have utilized the simple laws of physics to illuminate the depths of space and time. It is likely that we may never be able to board ships headed for the stars, but even imprisoned on this tiny blue planet we have been able to penetrate the night sky to reveal remarkable wonders, and there is no doubt more to come. If physics cannot give us what we need to roam the galaxy, it is giving us what we need to bring the galaxy to us.