Since Julius Caesar and ancient Rome were physical objects, they could, in principle, be rendered with arbitrary accuracy. The task differs only in degree from that of rendering the Centre Court at Wimbledon, including the spectators. Of course, the complexity of the requisite programs would be tremendous. More complex still, or perhaps even impossible in principle, would be the task of gathering the information required to write the programs to render specific human beings. But writing the programs is not the issue here. I am not asking whether we can find out enough about a past environment (or, indeed, about a present or future environment) to write a program that would render that environment specifically. I am asking whether the set of all possible programs for virtual-reality generators does or does not include one that gives a virtual-reality rendering of past-directed time travel and, if so, how accurate that rendering can be. If there were no programs rendering time travel, then the Turing principle would imply that time travel was physically impossible (because it says that everything that is physically possible can be rendered by some program). And on the face of it, there is indeed a problem here. Even though there are programs which accurately render past environments, there appear to be fundamental obstacles to using them to render time travel. These are the same obstacles that appear to prevent time travel itself, namely the so-called ‘paradoxes’ of time travel.
Here is a typical such paradox. I build a time machine and use it to travel back into the past. There I prevent my former self from building the time machine. But if the time machine is not built, I shall not be able to use it to travel into the past, nor therefore to prevent the time machine from being built. So do I make this trip or not? If I do, then I deprive myself of the time machine and therefore do not make the trip. If I do not make the trip, then I allow myself to build the time machine and so do make the trip. This is sometimes called the ‘grandfather paradox’, and stated in terms of using time travel to kill one’s grandfather before he had any children. (And then, if he had no children, he could not have had any grandchildren, so who killed him?) These two forms of the paradox are the ones most commonly cited, and happen to require an element of violent conflict between the time traveller and people in the past, so one finds oneself wondering who will win. Perhaps the time traveller will be defeated, and the paradox avoided. But violence is not an essential part of the problem here. If I had a time machine, I could decide as follows: that if, today, my future self visits me, having set out from tomorrow, then tomorrow I shall not use my time machine; and that if I receive no such visitor today, then tomorrow I shall use the time machine to travel back to today and visit myself. It seems to follow from this decision that if I use the time machine then I shall not use it, and if I do not use it then I shall use it: a contradiction.
A contradiction indicates a faulty assumption, so such paradoxes have traditionally been taken as proofs that time travel is impossible. Another assumption that is sometimes challenged is that of free will — whether time travellers can choose in the usual way how to behave. One then concludes that if time machines did exist, people’s free will would be impaired. They would somehow be unable to form intentions of the type I have described; or else, when they travelled in time, they would somehow systematically forget the resolutions they made before setting out. But it turns out that the faulty assumption behind the paradoxes is neither the existence of a time machine nor the ability of people to choose their actions in the usual way. All that is at fault is the classical theory of time, which I have already shown, for quite independent reasons, to be untenable.
If time travel really were logically impossible, a virtual-reality rendering of it would also be impossible. If it required a suspension of free will, then so would a virtual-reality rendering of it. The paradoxes of time travel can be expressed in virtual-reality terms as follows. The accuracy of a virtual-reality rendering is the faithfulness, as far as is perceptible, of the rendered environment to the intended one. In the case of time travel the intended environment is one that existed historically. But as soon as the rendered environment responds, as it is required to, to the user kicking it, it thereby becomes historically inaccurate because the real environment never did respond to the user: the user never did kick it. For example, the real Julius Caesar never met Dr Johnson. Consequently Dr Johnson, in the very act of testing the faithfulness of the rendering by conversing with Caesar, would destroy that faithfulness by creating a historically inaccurate Caesar. A rendering can behave accurately by being a faithful image of history, or it can respond accurately, but not both. Thus it would appear that, in one way or the other, a virtual-reality rendering of time travel is intrinsically incapable of being accurate — which is another way of saying that time travel could not be rendered in virtual reality.
But is this effect really an impediment to the accurate rendering of time travel? Normally, mimicking an environment’s actual behaviour is not the aim of virtual reality: what counts is that it should respond accurately. As soon as you begin to play tennis on the rendered Wimbledon Centre Court, you make it behave differently from the way the real one is behaving. But that does not make the rendering any less accurate. On the contrary, that is what is required for accuracy. Accuracy, in virtual reality, means the closeness of the rendered behaviour to that which the original environment would exhibit if the user were present in it. Only at the beginning of the rendering does the rendered environment’s state have to be faithful to the original. Thereafter it is not its state but its responses to the user’s actions that have to be faithful. Why is that ‘paradoxical’ for renderings of time travel but not for other renderings — for instance, for renderings of ordinary travel?
It seems paradoxical because in renderings of past-directed time travel the user plays a unique double, or multiple, role. Because of the looping that is involved, where for instance one or more copies of the user may co-exist and interact, the virtual-reality generator is in effect required to render the user while simultaneously responding to the user’s actions. For example, let us imagine that I am the user of a virtual-reality generator running a time-travel-rendering program. Suppose that when I switch on the program, the environment that I see around me is a futuristic laboratory. In the middle there is a revolving door, like those at the entrances of large buildings, except that this one is opaque and is almost entirely enclosed in an opaque cylinder. The only way in or out of the cylinder is a single entrance cut in its side. The door within revolves continuously. It seems at first sight that there is little one can do with this device except to enter it, go round one or more times with the revolving door, and come out again. But above the entrance is a sign: ‘Pathway to the Past’. It is a time machine, a fictional, virtual-reality one. But if a real past-directed time machine existed it would, like this one, not be an exotic sort of vehicle but an exotic sort of place. Rather than drive or fly it to the past, one would take a certain path through it (perhaps using an ordinary space vehicle) and emerge at an earlier time.
FIGURE 12.1 Spacetime path taken by a time traveller.