Black Holes and Time Machines

Ever since the beginning, gravity has been making our universe less and less uniform and building up ever-larger contrasts of density and temperature. In the end, gravity overwhelms all the other forces in stars, and in anything larger, even though the effects of rotation and nuclear energy delay its final victory.

There are some entities in which gravity has already triumphed over all other forces. These are black holes - objects that have collapsed so far that no light or any other signal can escape them, but that nonetheless leave imprints, distortions of space and time, frozen in the space they've left.

An Astronaut who ventured too close to a black hole would pass into a region from which there is no return and from where no light signals can be transmitted to the external world; it is as though space itself were being sucked inward faster than light moves through it. An external observer would never witness the falling astronaut's final fate: any clock would appear to run slower and slower as it fell inward, into the hole, so the astronaut would appear impaled at a horizon, frozen in time.

The Russian theorists Yakov Zeldovich and Igor Novikov, who studied how time was distorted near collapsed objects, coined the term 'frozen star' for such objects. Zeldovich, one of the last polymaths of physics, holds a prominent place in modern cosmology. He was a dynamic and charismatic personality; from the 1960s onward, his research school in Moscow spearheaded many key discoveries (even though cosmology and relativity had previously been ideologically tainted in the USSR). The term 'black hole' itself was not coined until 1968, when John Wheeler described how an infalling object 'becomes dimmer millisecond by millisecond…light and particles incident from outside …go down the black hole only to add to its mass and increase its gravitational attraction."

Black holes, the most remarkable consequences of Einstein's theory, are not just theoretical constructs. There are huge numbers of them in our Galaxy and in every other galaxy, each being the remnant of a star and weighing several times as much as the Sun. There are much larger ones, too, in the centres of galaxies. Near our own galactic centre, stars are orbiting ten times faster than their normal speeds within a galaxy. They are feeling, close up, the gravity of a dark object, presumably a black hole, as heavy as 2.6 million suns. Yet our Galaxy is poorly endowed compared to some others, in whose centres lurk holes more massive than a billion suns, betraying their presence by the high speed motions of surrounding stars and gas, induced by their gravitational pull.

Black holes are among the most exotic entities in the cosmos. But they are actually among the best understood. They are constructed from the fabric of space itself and are as simple in structure as elementary particles. A newly formed black hole quickly settles down to a standardised stationary state characterised stationary state characterised by just two numbers: those that measure its mass and its spin. (In principle, electric charge is a third such number, but stars can never acquire enough electric charge for this factor to be relevant to real collapse). The distorted space and time around black holes is described exactly by a solution of Einstein's general relativity equations that was first discovered in 1963 by Roy Kerr, a mathematician who later forsook research to become an internationally recognised bridge player. In general, macroscopic objects seem more and more complicated as we view them closer up, and we can't expect to explain their every detail; but black holes are an exception to this rule.

Viewed from outside, no traces remain that distinguish how a particular hole formed, nor what kind of object it swallowed. The great Indian astrophysicist Subrahmanyan Chandrasekhar was deeply impressed by this realisation, aesthetically as well as scientifically: " In my entire scientific life," he wrote, "the most shattering experience has been the realisation that an exact solution of Einstein's equations of general relativity, discovered by the New Zealand mathematician Roy Kerr, provides the absolutely exact representation of untold numbers of massive black holes that populate the Universe." Roger Penrose, the theorist who perhaps did most of to stimulate the renaissance in relativity theory that occurred in the 1960s, has remarked. "It is ironic that the astrophysical object which is strangest and least familiar, the black hole, should be the one for which our theoretical picture is most complete". The discovery of black holes thus opened the way to testing the most remarkable consequences of Einstein's theory.

Black Holes interest astronomers because the flow patterns and magnetic fields around them generate some of the most spectacular pyrotechnics in the universe. But they challenge basic physics as well. Around any black holes is a horizon, a surface shrouding from view an interior from which not even light can escape. A hole's size is proportional to its mass: if the sun became a black hole, its radius would be 3 kilometres, but some of the supermassive holes in galactic centres are as big as our whole solar system. If you fell inside one of these monster holes, you would be treated to several hours of leisurely observation before you approach the centre, where increasingly violent tidal forces would shred you apart. Right at the centre, you, or your remains, would encounter the singularity where the physics transcends what we yet understand. The new physics that we'll need is the same that governs the initial instants of the Big Bang.

Fast-Forward and Backward in Time?

Good science fiction should respect the fundamental constraints of physical law. In that sprit, it is worth mentioning that an observer could, in principle, observe the far future in what, subjectively, seemed quiet a short time. According to Einstein, the speed of a clock depends on where you are and how you're moving. If your subjective clock ran very slowly compared to the cosmic clock, you could travel "fast forward" into the future. This would happen if you were moving at a velocity close to the speed of light. Furthermore, strong gravity would distort time; clocks on a neutron star would run 20 or 30 percent slower. Near a black hole, the distortions would be even greater. If you were to fall into one, your future would be finite; you would be ripped apart - spaghettified - by ever more violent gravitational forces. However, a more prudent astronaut who managed to get into the closest possible orbit around a rapidly spinning hole without falling into it would also have interesting experiences, space-time is so distorted there that his clock would run arbitrarily slow and he could, therefore, in a subjectively short period, view an immensely long future timespan in the external universe.

This elasticity in the rate of passage of time may seem counter to our intuition. But such intuition is acquired from our everyday environment (and perhaps, even more, that of our remote ancestors), which has offered us no experience of such effects. Few of us have travelled faster than a millionth of the speed of light (the speed of a jet airliner); we live on a planet where the pull of gravity is 1000 billion times weaker than on a neutron star. But time dilation entails no inconsistency or paradox.

More problematic, of course, would be time travel back into the past. More than fifty years ago, the great logician Kurt Godel discovered that the theory of general relativity did not in itself preclude a time machine. He discovered a valid solution of Einstein's equations that described a bizarre universe where some of the worldlines were close loops - in other words, you could come back into your own past. But Godel's solution was not realistic: it described a universe that was rotating and not expanding.

Other theoretical examples of systems that seem to obey the laws of physics but which allow closed loops in time have been proposed. For example, Princeton theorist Richard Gott showed that a time machine could be constructed from two so called cosmic strings - long microscopically thin tubes of hyperdense material, heavy enough to distort space. Gott and his colleague Li-Xin Li also devised a cosmological model even stranger than Godel's in which an entire universe, with a finite life cycle, traces out a loop in time so that its end is also its beginning.

One much-discussed design for a time machine involves a "wormhole": two black holes linked together by a tunnel or "spacewarp". The tunnel could exist only if it were made of a substance that has very large negative pressure (or tension). Theorists speculate that exotic stuff of this kind did exist in the early universe, but even if such material still existed, the mass needed in order to make a wormhole wide enough to be comfortably traversed by a human would be 10,000 times that of the Sun!

Godel's discovery and its aftermath opened up a debate. Is there a future law of physics, more restrictive than Einstein's equations that rule out such effects? One might call it a "chronology protection law". Or could a time machine in principle exist? Such an artefact plainly still lies in the hypothetical reaches of science fiction, but we can still ask whether the barriers to constructing a time machine are merely technological, or whether there is a fundamental physical law that prohibit them. (To clarify the distinction, most physicists would say that a large spaceship travelling at 99.99 percent of the speed of light is in the first category, but one that travels faster than light is in the second.)

The events on the time loop must close up self-consistently, as in a movie whose last scene recapitulates its first. Paradoxes arise if you come back into the past and undo something that was a precondition of your existence: for instance, murdering your grandmother in her cradle would raise issues of logical consistency, not just of ethics. Time travel makes sense only if some law of nature precludes inconsistency of this kind. The implication that there must be "time police" to constrain our free will might seem paradoxical. But I am convinced by the robust retort of Igor Novikov, a leading physicist who has explored these ideas, that physical laws already constrain our choices: we cannot, for instance, exercise our free will by walking on the ceiling. The prohibition on violating the consistency of a time loop is, in a sense, analogous.

Even if a time machine could be built, it would not enable us to travel back prior to the date of its construction. So the fact that we have not been invaded by tourists from the future may tell us only that no time machine has yet been made, not that it is impossible.

- Sir Martin Rees, Astronomer Royal