Using faster-than-light velocities we could telegraph into the past. (Einstein, quoted by Sommerfeld, 1908)
If you could travel faster than light, you could kill your grandmother before she gave birth to your mother. Since this is impossible, we have a second argument for the celestial speed limit. The strategy of the argument is a reductio ad absurdum. That is, the assumption that faster-than-light travel is possible is shown to lead to nonsense, and thus must be discarded.
Take as the three events above your grandmother’s adolescence (A), the present moment (B) and a distant exploding star, that is, a supernova (X). Suppose that the explosion is so far away that its light does not reach Earth for many centuries from now. Thus the explosion is earlier or later than your grandmother’s adolescence, or the explosion is earlier or later than the present moment, depending on which set of rulers and clocks is used. Now assume, contrary to the theory of relativity, that a magical rocket is somehow capable of travelling faster than light. This means that it can, for example, travel from Earth out to the exploding star and return again before light from the explosion manages to reach Earth for the first time. In fact, it would enable you to board the rocket and travel for a sightseeing tour of the explosion. Since the explosion is “later” than the present, your trip would seem like an ordinary trip: the arrival at the star would be after the departure from Earth. Since the explosion is also “before” your grandmother’s adolescence, however, you could instruct the pilot to return to visit your 13-year-old grandmother and kill her.
Such a return trip would also seem like an ordinary trip: from one event to another in its future.
In effect, the magical rocket is a time machine. Since relativity theory says that distant events are not ordered in time, the rocket can travel backwards in time by hopscotching across to a distant event and then returning to the past. Faster-than-light speeds would not enable a trip directly into your past; it would be necessary to visit distant places that are outside your time order, and then re-enter your time order.
In the example of the queues above, this would be like jumping between the two queues. By shifting back and forth, you could enter the club earlier than someone directly in front of you, and thus jump ahead in time (or later, if you were unlucky and jumped to a slower queue).
But, as the example shows, time travel leads to contradictions. If you are reading this, your grandmother did give birth to your mother.
But if the magical rocket makes time travel possible, you could kill your adolescent grandmother before your mother’s birth. Thus your mother would be born and not born. There’s clearly something wrong about all this, and it leads to the following argument:
Time travel is contradictory
A. There is faster-than-light travel. (P: leads to absurdity)
B. Some distant events have no definite order in time. (P)
C. If there is faster-than-light travel and distant events have no definite order, then there is time travel. (P)
D. So, there is time travel. (from A,B,C)
E. If there is time travel, then there are contradictions. (P)
F. So, there are contradictions. (D,E)
G. But there are no contradictions. (P)
H. So, there is no faster-than-light travel.
The last line does not follow rigorously. When an argument crashes into contradiction, one or more of the preceding premises must be thrown out. But it is sometimes not immediately clear which premise is the culprit responsible for the contradiction. Additional arguments may be needed to justify pointing the finger of blame at a particular premise.
In this case the second and third premises, B and C, are conse- quences of relativity theory, and the last, G, is our bedrock assump- tion. If we stand by these, then we must reject either faster-than-light travel (premise A), or the idea that travel back in time would produce contradictions (premise E).
Most philosophers do reject time travel because it would lead to contradictions. In a surprising essay, however, the metaphysician David Lewis argued that time travel would not lead to contradictions.
In brief, he says that any visit to the past has already happened, and thus could not change the way the past happened. If it is a fact that your grandmother gave birth to your mother, then it is a fact that any time traveller who happened to be there did not kill her first. A murderous time traveller would find that quite ordinary circum- stances contrived to forestall her death: the gun misfired, and so on. If Lewis is correct, then there is no logical argument – like the above – against time travel. We can throw out premise E instead of the first premise, and still avoid the contradiction. Philosophers often describe something as “possible” if it is not contradictory. Something may be logically possible in this sense, even though physical laws forbid it.
Lewis can therefore conclude that “time travel is possible”.
Physicists are more interested in the question of whether time travel is physically possible. Most would quickly say “no”, but an intriguing line of research was opened up by Kip Thorne and others in the early 1990s. He asked whether, if space can really bend and curve as Einstein says (see Chapter 13), it is so flexible that “tubes” or “tunnels” could connect the present to the past. If so, then anything travelling down through the tube would emerge at an earlier time, and time travel would in fact be physically possible. Although surprising progress was made on the theory of such wormholes through spacetime, most physicists remain sceptical. But the final word is not yet in.