That leaves us with the question whether it is physically possible for pathways into the past to exist. This question has been the subject of much research, and is still highly controversial. The usual starting-point is a set of equations which form the (predictive) basis of Einstein’s general theory of relativity, currently our best theory of space and time. These equations, known as Einstein’s equations, have many solutions, each describing a possible four-dimensional configuration of space, time and gravity. Einstein’s equations certainly permit the existence of pathways into the past; many solutions with that property have been discovered. Until recently, the accepted practice has been systematically to ignore such solutions. But this has not been for any reason arising from within the theory, nor from any argument within physics at all. It has been because physicists were under the impression that time travel would ‘lead to paradoxes’, and that such solutions of Einstein’s equations must therefore be ‘unphysical’. This arbitrary second-guessing is reminiscent of what happened in the early years of general relativity, when the solutions describing the Big Bang and an expanding universe were rejected by Einstein himself. He tried to change the equations so that they would describe a static universe instead. Later he referred to this as the biggest mistake of his life, and the expansion was verified experimentally by the American astronomer Edwin Hubble. For many years also, the solutions obtained by the German astronomer Karl Schwarzschild, which were the first to describe black holes, were mistakenly rejected as ‘unphysical’. They described counter-intuitive phenomena, such as a region from which it is in principle impossible to escape, and gravitational forces becoming infinite at the black hole’s centre. The prevailing view nowadays is that black holes do exist, and do have the properties predicted by Einstein’s equations.
Taken literally, Einstein’s equations predict that travel into the past would be possible in the vicinity of massive, spinning objects, such as black holes, if they spun fast enough, and in certain other situations. But many physicists doubt that these predictions are realistic. No sufficiently rapidly spinning black holes are known, and it has been argued (inconclusively) that it may be impossible to spin one up artificially, because any rapidly spinning material that one fired in might be thrown off and be unable to enter the black hole. The sceptics may be right, but in so far as their reluctance to accept the possibility of time travel is rooted in a belief that it leads to paradoxes, it is unjustified.
Even when Einstein’s equations have been more fully understood, they will not provide conclusive answers on the subject of time travel. The general theory of relativity predates quantum theory and is not wholly compatible with it. No one has yet succeeded in formulating a satisfactory quantum version — a quantum theory of gravity. Yet, from the arguments I have given, quantum effects would be dominant in time-travelling situations. Typical candidate versions of a quantum theory of gravity not only allow past-directed connections to exist in the multiverse, they predict that such connections are continually forming and breaking spontaneously. This is happening throughout space and time, but only on a sub-microscopic scale. The typical pathway formed by these effects is about 10–35 metres across, remains open for one Planck time (about 10–43 seconds), and therefore reaches only about one Planck time into the past.
Future-directed time travel, which essentially requires only efficient rockets, is on the moderately distant but confidently foreseeable technological horizon. Past-directed time travel, which requires the manipulation of black holes, or some similarly violent gravitational disruption of the fabric of space and time, will be practicable only in the remote future, if at all. At present we know of nothing in the laws of physics that rules out past-directed time travel; on the contrary, they make it plausible that time travel is possible. Future discoveries in fundamental physics may change this. It may be discovered that quantum fluctuations in space and time become overwhelmingly strong near time machines, and effectively seal off their entrances (Stephen Hawking, for one, has argued that some calculations of his make this likely, but his argument is inconclusive). Or some hitherto unknown phenomenon may rule out past-directed time travel — or provide a new and easier method of achieving it. One cannot predict the future growth of knowledge. But if the future development of fundamental physics continues to allow time travel in principle, then its practical attainment will surely become a mere technological problem that will eventually be solved.
Because no time machine provides pathways to times earlier than the moment at which it came into existence, and because of the way in which quantum theory says that universes are interconnected, there are some limits to what we can expect to learn by using time machines. Once we have built one, but not before, we may expect visitors, or at least messages, from the future to emerge from it. What will they tell us? One thing they will certainly not tell us is news of our own future. The deterministic nightmare of the prophecy of an inescapable future doom, brought about in spite of — or perhaps as the very consequence of — our attempts to avoid it, is the stuff of myth and science fiction only. Visitors from the future cannot know our future any more than we can, for they did not come from there. But they can tell us about the future of their universe, whose past was identical to ours. They can bring taped news and current affairs programmes, and newspapers with dates starting from tomorrow and onwards. If their society made some mistaken decision, which led to disaster, they can warn us of it. We may or may not follow their advice. If we follow it, we may avoid the disaster, or — there can be no guarantees — we may find that the result is even worse than what happened to them.
On average, though, we should presumably benefit greatly from studying their future history. Although it is not our future history, and although knowing of a possible impending disaster is not the same thing as knowing what to do about it, we should presumably learn much from such a detailed record of what, from our point of view, might happen.
Our visitors might bring details of great scientific and artistic achievements. If these were made in the near future of the other universe, it is likely that counterparts of the people who made them would exist in our universe, and might already be working towards those achievements. All at once, they would be presented with completed versions of their work. Would they be grateful? There is another apparent time-travel paradox here. Since it does not appear to create inconsistencies, but merely curiosities, it has been discussed more in fiction than in scientific arguments against time travel (though some philosophers, such as Michael Dummett, have taken it seriously). I call it the knowledge paradox of time travel; here is how the story typically goes. A future historian with an interest in Shakespeare uses a time machine to visit the great playwright at a time when he is writing Hamlet. They have a conversation, in the course of which the time traveller shows Shakespeare the text of Hamlet’s ‘To be or not to be’ soliloquy, which he has brought with him from the future. Shakespeare likes it and incorporates it into the play. In another version, Shakespeare dies and the time traveller assumes his identity, achieving success by pretending to write plays which he is secretly copying from the Complete Works of Shakespeare, which he brought with him from the future. In yet another version, the time traveller is puzzled by not being able to locate Shakespeare at all. Through some chain of accidents, he finds himself impersonating Shakespeare and, again, plagiarizing his plays. He likes the life, and years later he realizes that he has become the Shakespeare: there never had been another one.