The virtual-reality generator now has recordings of many different versions of what happened in that laboratory between noon and five minutes past. Which one depicts the real history? We ought not be too concerned if there is no answer to this question, for it asks what is real in a situation where we have artificially suppressed interactivity, making Dr Johnson’s test inapplicable. One could argue that only the last version, the one depicting the most copies of me, is the real one, because the previous versions all in effect show history from the point of view of people who, by the artificial rule of non-interaction, were prevented from fully seeing what was happening. Alternatively, one could argue that the first version of events, the one with a single copy of me, is the only real one because it is the only one I experienced interactively. The whole point of non-interactivity is that we are temporarily preventing ourselves from changing the past, and since subsequent versions all differ from the first one, they do not depict the past. All they depict is someone viewing the past by courtesy of a universal image generator.
One could also argue that all the versions are equally real. After all, when it is all over I remember having experienced not just one history of the laboratory during that five-minute period, but several such histories. I experienced them successively, but from the laboratory’s point of view they all happened during the same five-minute period. The full record of my experience requires many snapshots of the laboratory for each clock-defined instant, instead of the usual single snapshot per instant. In other words, this was a rendering of parallel universes. It turns out that this last interpretation is the closest to the truth, as we can see by trying the same experiment again, this time with interaction switched on.
The first thing I want to say about the interactive mode, in which I am free to affect the environment, is that one of the things I can choose to make happen is the exact sequence of events I have just described for the non-interactive mode. That is, I can go back and encounter one or more copies of myself, yet nevertheless (if I am a good enough actor) behave exactly as though I could not see some of them. Nevertheless, I must watch them carefully. If I want to recreate the sequence of events that occurred when I did this experiment with interaction switched off, I must remember what the copies of me do so that I can do it myself on subsequent visits to this time.
At the beginning of the session, when I first see the time machine, I immediately see it disgorging one or more copies of me. Why? Because with interaction switched on, when I come to use the time machine at five minutes past noon I shall have the right to affect the past to which I return, and that past is what is happening now, at noon. Thus my future self or selves are arriving to exercise their right to affect the laboratory at noon, and to affect me, and in particular to be seen by me.
The copies of me go about their business. Consider the computational task that the virtual-reality generator has to execute, in rendering these copies. There is now a new element that makes this overwhelmingly more difficult than it was in the non-interactive mode. How is the virtual-reality generator to find out what the copies of me are going to do? It does not yet have any recordings of that information, for in physical time the session has only just begun. Yet it must immediately present me with renderings of my future self.
So long as I am resolved to pretend that I cannot see these renderings, and then to mimic whatever I see them do, they are not going to be subjected to too stringent a test of accuracy. The virtual-reality generator need only make them do something — anything that I might do; or more precisely any behaviour that I am capable of mimicking. Given the technology that we are assuming the virtual-reality generator to be based on, that would presumably not be exceeding its capabilities. It has an accurate mathematical model of my body, and a degree of direct access to my brain. It can use these to calculate some behaviour which I could mimic, and then have its initial renderings of me carry out that behaviour.
So I begin the experience by seeing some copies of me emerge from the revolving door and do something. I pretend not to notice them, and after five minutes I go round the revolving door myself and mimic what I earlier saw the first copy doing. Five minutes later I go round again and mimic the second copy, and so on. Meanwhile, I notice that one of the copies always repeats what I had been doing during the first five minutes. At the end of the time-travelling sequence, the virtual-reality generator will again have several records of what happened during the five minutes after noon, but this time all those records will be identical. In other words, only one history happened, namely that I met my future self but pretended not to notice. Later I became that future self, travelled back in time to meet my past self, and was apparently not noticed. That is all very tidy and non-paradoxical — and unrealistic. It was achieved by the virtual-reality generator and me engaging in an intricate, mutually referential game: I was mimicking it while it was mimicking me. But with normal interactions switched on, I can choose not to play that game.
If I really had access to virtual-reality time travel, I should certainly want to test the authenticity of the rendering. In the case we are discussing, the testing would begin as soon as I saw the copies of me. Far from ignoring them, I would immediately engage them in conversation. I am far better equipped to test their authenticity than Dr Johnson would be to test Julius Caesar’s. To pass even this initial test, the rendered versions of me would effectively have to be artificial intelligent beings — moreover, beings so similar to me, at least in their responses to external stimuli, that they can convince me they are accurate renderings of how I might be five minutes from now. The virtual-reality generator must be running programs similar in content and complexity to my mind. Once again, the difficulty of writing such programs is not the issue here: we are investigating the principle of virtual-reality time travel, not its practicality. It does not matter where our hypothetical virtual-reality generator gets its programs, for we are asking whether the set of all possible programs does or does not include one that accurately renders time travel. But our virtual-reality generator does in principle have the means of discovering all the possible ways I might behave in various situations. This information is located in the physical state of my brain, and sufficiently precise measurements could in principle read it out. One (probably unacceptable) method of doing this would be for the virtual-reality generator to cause my brain to interact, in virtual reality, with a test environment, record its behaviour and then restore its original state, perhaps by running it backwards. The reason why this is probably unacceptable is that I would presumably experience that test environment, and though I should not recall it afterwards, I want the virtual-reality generator to give me the experiences I specify and no others.
In any case, what matters for present purposes is that, since my brain is a physical object, the Turing principle says that it is within the repertoire of a universal virtual-reality generator. So it is possible in principle for the copy of me to pass the test of whether he accurately resembles me. But that is not the only test I want to perform. Mainly, I want to test whether the time travel itself is being rendered authentically. To that end I want to find out not just whether this person is authentically me, but whether he is authentically from the future. In part I can test this by questioning him. He should say that he remembers being in my position five minutes ago, and that he then travelled around the revolving door and met me. I should also find that he is testing my authenticity. Why would he do that? Because the most stringent and straightforward way in which I could test his resemblance to the future me would be to wait until I have passed through the time machine, and then look for two things: first, whether the copy of me whom I find there behaves as I remember myself behaving; and second, whether I behave as I remember the copy behaving.