There is a problem with breaking the speed-of-light barrier. The theory of relativity says that the rocket power needed to accelerate a spaceship gets greater and greater the nearer it gets to the speed of light. We have experimental evidence for this, not with spaceships but with elementary particles in particle accelerators like those at Fermilab or CERN (European Centre for Nuclear Research). We can accelerate particles to 99.99 percent of the speed of light, but however much power we feed in, we can’t get them beyond the speed-of-light barrier. Similarly with spaceships: no matter how much rocket power they have, they can’t accelerate beyond the speed of light.
That might seem to rule out both rapid space travel and travel back in time. However, there is a possible way out. It might be that one could warp space-time so that there was a shortcut between A and B One way of doing this would be to create a wormhole between A and B. As its name suggests, a wormhole is a thin tube of space-time which can connect two nearly flat regions far apart.
There need be no relation between the distance through the wormhole and the separation of its ends in the nearly Hat background. Thus one could imagine that one could create or find a wormhole that world lead from the vicinity of the Solar System to Alpha Centauri. The distance through the wormhole might be only a few million miles even though earth and Alpha Centauri are twenty million million miles apart in ordinary space. This would allow news of the 100-meter race to reach the opening of the Congress. But then an observer moving toward 6e earth should also be able to find another wormhole that would enable him to get from the opening of the Congress on Alpha Centauri back to earth before the start of the race. So wormholes, like any other possible form of travel faster than light, would allow one to travel into the past.
The idea of wormholes between different regions of space-time was not an invention of science fiction writers but came from a very respectable source.
In 1935, Einstein and Nathan Rosen wrote a paper in which they showed that general relativity allowed what they called “bridges,” but which are now known as wormholes. The Einstein-Rosen bridges didn’t last long enough for a spaceship to get through: the ship would run into a singularity as the wormhole pinched off. However, it has been suggested that it might be possible for an advanced civilization to keep a wormhole open. To do this, or to warp space-time in any other way so as to permit time travel, one can show that one needs a region of space-time with negative curvature, like the surface of a saddle. Ordinary matter, which has a positive energy density, gives space-time a positive curvature, like the surface of a sphere. So what one needs, in order to warp space-time in a way that will allow travel into the past, is matter with negative energy density.
Energy is a bit like money: if you have a positive balance, you can distribute it in various ways, but according to the classical laws that were believed at the beginning of the century, you weren’t allowed to be overdrawn. So these classical laws would have ruled out any possibility of time travel. However, as has been described in earlier chapters, the classical laws were superseded by quantum laws based on the uncertainty principle. The quantum laws are more liberal and allow you to be overdrawn on one or two accounts provided the total balance is positive. In other words, quantum theory allows the energy density to be negative in some places, provided that this is made up for by positive energy densities in other places, so that the total energy re-mains positive. An example of how quantum theory can allow negative energy densities is provided by what is called the Casimir effect. As we saw in Chapter 7, even what we think of as “empty” space is filled with pairs of virtual particles and antiparticles that appear together, move apart, and come back together and annihilate each other. Now, suppose one has two parallel metal plates a short distance apart. The plates will act like mirrors for the virtual photons or particles of light. In fact they will form a cavity between them, a bit like an organ pipe that will resonate only at certain notes. This means that virtual photons can occur in the space between the plates only if their wavelengths (the distance between the crest of one wave and the next) fit a whole number of times into the gap between the plates. If the width of a cavity is a whole number of wavelengths plus a fraction of a wavelength, then after some reflections backward and forward between the plates, the crests of one wave will coincide with the troughs of another and the waves will cancel out.