Chapter 2: On Time Travel and its Assumptions
Philip: Some philosophers claim to have proof that traveling back in time is logically impossible.^{1}
Matthew: Let’s hear it.
Philip: It’s actually fairly simple. Consider the normal course of events with time obviously moving forward. Then pick some point in time and call it time a, and at time a there’s no time traveler present because it’s the first time everything’s happening, right? So let’s say it’s the future and some guy travels back in time to time a. Now there is a time traveler present. But it’s logically impossible for a time traveler to be both present and not present at time a. That’s like a statement and its negation both being true, which can’t happen.^{2} Therefore, time travel is logically impossible.^{3}
Matthew: Hmm.
Philip: Yeah, I was kind of disappointed when I read it, because Back to the Future and Primer are very enjoyable movies, and nearly believable as well.^{4}
Matthew: We should check the assumptions, though. Allow me to restate the proof with the aide of a diagram.
Philip: Okay.
Matthew: This line represents time, going from left to right, and we have some time a.
The crux of the argument is that certain events happen at a the first time through and it is logically impossible for events to happen any differently a second time through. But the hidden assumption here is that there’s only one line through existence, only one reality. Without this assumption, the proof against time travel is invalid.^{5}
Philip: How do you mean?
Matthew: Let’s say time a is the precise moment that our hypothetical time traveler arrives in his past. If we didn’t assume the singleness of reality, then it would be possible for a new reality to form precisely at time a. Thus, in reality 1 at time a there was no time traveler, and at time a of reality 2 he is present. These are two separate statements and it’s logically possible for them both to be true.^{6}
Philip: So what would this reality 2 be like?
Matthew: With Ockham’s Razor in hand, I would suppose that at the time of the split reality 2 is like reality 1 in every way except for the presence of our time traveler.^{7} Thus, things in reality 2 would continue as they did in reality 1 unless directly or indirectly affected by the time traveler.
Philip: Okay, so if we assume the possibility of multiple realities, we could have time travel. If we assume there’s just one reality, then no time travel. How do we know which assumption is correct?
Matthew: That’s a good question.
Philip: I know that if you asked people about it, they would support the common notion that there’s only a single reality – and we’re in it. But that is just based on senses and perceptions, and it obviously doesn’t constitute a proof.^{8} People also might say, “If time travel becomes possible in the future, why haven’t we ever met a visitor from the future?” But looking at our diagram, it may be the case that we are cruising along in reality 1 where no time traveler has ever landed, so to speak, and it makes sense then that we haven’t met anyone from the future.
Matthew: It is possible that we’re in reality 1, but it’s highly unlikely.
Philip: Why’s that?
Matthew: I’m not saying the multireality assumption is highly unlikely, just the chance that right now we are reality 1 dwellers. Because it’s reasonable to suppose that if time travel ever happens in the future it will happen many times, resulting in not 2, but hundreds or thousands of realities. With that many branches in the timeline, it would be presumptuous to think that we are in reality 1 – but it is possible.
Philip: So for individuals living in reality 1, it would be impossible to tell the difference between their reality and a unireality.
Matthew: Correct. But if you lived in a reality 2 or higher, you would likely know that time travel existed and this would prove the multireality assumption.^{9} Since there would be many of these realities and only one reality 1, an appeal to probability would support the idea that, since we haven’t met or heard of a time traveler, it is the most likely case that there is only one reality.
Philip: But what if I had another explanation for why we haven’t met a time traveler?
Matthew: Let’s hear it.
Philip: We are living in reality before the branching has begun. Perhaps in the future, time traveling capabilities are confined to the era of time traveling capabilities. Say a machine is invented that can take you back to the time of its creation, but no farther.^{10} Then our diagram would look like this.
We could be living in the unireality portion of a multireality timeline. Which basically brings us back to the question of determining which assumption is correct.
Matthew: Since we’ve established that our worldly experiences cannot answer this question, we must look at the assumptions themselves and where they lead. Mathematicians have a lot of experience in this area, and there are basically two camps of thought on the subject. Gottlob Frege was a voice from one perspective, and he felt that axioms or assumptions were things that are true but cannot be proven because they proceed from a source, like an intuition, that is not logical. If Frege were around today, he would probably say that we live in a unireality, and even though we can’t prove it, we simply know it to be true and can accept it as a valid assumption.
On the other hand, David Hilbert represented a view wherein axioms are true so long as they do not contradict one another and do not contradict anything that follows from them, and the assumptions contained within those axioms can be considered valid.^{11} The debate between Frege and Hilbert revolved around the concept of nonEuclidean geometry, and while most people felt Euclidean geometry was the true geometry, it was eventually proven by Eugenio Beltrami that Euclidean and nonEuclidean geometries were equally consistent.^{12} People simply felt better about Euclidean geometry because it represented what they saw on a daytoday basis. However, if people could better comprehend the earth that we live on, then spherical geometry would make more sense to them. Furthermore, if people could better comprehend space and the universe itself, they may well find it to be hyperbolic.
But getting back to our point, it may be the case that there is some essence of time that we cannot yet comprehend, and when we gain that comprehension it could lead us to accept the multireality assumption. Just as Euclidean geometry accurately describes things on a small scale, a single reality fits with our narrow perceptions of time. And as nonEuclidean geometry more accurately describes things on a larger scale, perhaps multiple realities fit the broader sense of time.
Philip: If I correctly understood your discussion of nonEuclidean geometry, people used to feel that Euclidean geometry was the real one because it was most familiar to them, but it turns out that Euclidean geometry is no more consistent than nonEuclidean geometries. Similarly, people today are much more comfortable thinking about a single reality, but an assumption is not proven simply because the general public is comfortable with it. On the contrary, if history is any guide, the general public is quite often dead wrong.
Matthew: Precisely, which is why I am moved to side with Hilbert – if the multireality assumption does not bring about a contradiction, then we cannot disregard it.
Philip: Very interesting. But just a moment ago you mentioned a new level of comprehension that we may achieve in the future. Tell me more about that.
Matthew: Well, I’ve been considering an argument from analogy. Think back with me to our ancestors from several thousand years ago. Back then, they could move with complete freedom in twodimensions – left, right, forward, backward, or some combination of those directions. At that time, they were essentially stuck to the earth’s surface. Yes, they could flirt with the thirddimension by jumping up and down, but that was the extent of it. Now consider our species presently. With the development of flight, we have overcome the forces of gravity and have mastered three dimensions, and, like our ancestors before us, we flirt with the next dimension by altering our state of consciousness, increasing our velocity, and so forth. Perhaps sometime in the future we will overcome the forward motion of time and, just as we conquered the third dimension, our descendants will conquer the fourth.
1 The definition of “time travel” that we will utilize comes from David Lewis. Time travel has occurred when a time traveler departs from a point in time and arrives at a point in time, but the duration of the journey does not coincide with the difference between the arrival time and departure time. If the journey was greater, then the traveler has gone back in time; if the journey was less, then the traveler has gone forward in time. It is also worth noting that this discussion only involves physically traveling back in time. The modes of time travel that are not included in this discussion are the viewing of past events and the forward travel of time. Since the speed of light is finite it is possible to look into the past, into other solar systems, for example. What we see at a particular moment has already happened days, months, or years earlier. Furthermore, it is possible to travel into the futures of other people under the theory of relativity (see Appendix C).
2 We are abiding by Aristotle’s law of noncontradiction, whereby a proposition cannot be both true and not true at the same time and in the same respect. The presence of a contradiction within a system of thought is an indicator of its falsity. Two historical examples of this are provided by Galileo Galilei and Bertrand Russell. In the 17 ^{th} Century, Galileo conducted a thought experiment that revealed a contradiction in the notion that heavier objects fall faster than lighter ones. He considered a large stone falling with a smaller stone tied behind it. Since the stones are tied together they form a single object with more mass than either of its components that should, according to Aristotle, be falling faster than the large stone by itself. On the other hand, the small stone is lighter so it should be acting as a drag on the larger stone and thus, the two together should be falling more slowly than the large stone by itself. Ironically, the Aristotelian teachings of falling bodies violated Aristotle’s own law of noncontradiction. In more recent times, Bertrand Russell uncovered a paradox in set theory when he considered the set of all sets that do not contain themselves. This set must contain itself precisely when it does not contain itself, and must not contain itself if it does contain itself. The discovery of these two contradictions led to the development of new laws of motion and a reinterpretation of the structure of set theory, respectively.
3 Other contradictions that may arise from traveling into the past are the Grandfather and Free Lunch contradictions. The Grandfather contradiction concerns a time traveler who kills one of his ancestors before they have conceived the ancestor of the next generation; hence, the existence to the time traveler has eliminated the existence of the time traveler. The Free Lunch contradiction would result from a creative work being brought back in time to its original creator. The artist could then copy directly from the transported piece, and a creative work would exist without any creativity ever occurring. These contradictions were not used because they would occur after the initial contradiction generated by the mere presence of the time traveler.
4 The 2004 film Primer, written and directed by Shane Carruth, was the primary inspiration for this chapter.
5 The field of mathematics is oft concerned with the explicitness of argumentative assumptions. Since the time of Euclid, over two thousand years ago, mathematicians have employed deductive reasoning in the form of the axiomatic method. A deductive argument is built upon premises, and the dictates of mathematical rigor make it necessary to examine not only the argument, but the premises at their foundation. To allow for this critical examination, mathematicians in general, and Euclid in particular, attempted to set down in writing the definitions, common notions, and postulates that were being used in their work. All theorems and mathematical findings could then follow in a logically valid manner. However, it was later determined that many implicit assumptions were being made. In an attempt to maintain the integrity of the axiomatic method Euclid had inspired, David Hilbert published Grundlagen der Geometrie which contained 21 assumptions concerning incidence, ordering, congruence, and continuity, filling the gaps left by Euclid. It should be noted that these assumptions, though written down, remain assumptions and are not necessarily representative of absolute truth. For more, see Appendix D. Bertrand Russell, along with Gottlob Frege, attempted to do for arithmetic what Hilbert had done for geometry, that is, lay an impenetrably firm logical foundation for the subject. Russell’s The Principle of Mathematics went as far as logically defining “0” and “number” though the later work of Gödel demonstrated that these attempts were essentially futile.
6 Note that each reality remains a onedimensional (linear) entity. For an alternate hypothesis where time is truly twodimensional (planar), see the essay of Murray MacBeath entitled Time’s Square.
7 Ockham’s Razor is the logical notion non est ponenda pluritas sine necessitate, that “pluralities ought not be supposed without necessity.” This comes from the 14 ^{th} Century logician William of Ockham who posited that, said another way, no one should make more assumptions than needed. In the case of multiple realities of time, it is unnecessary to add assumptions regarding other differences between reality 1 and reality 2, such as different laws of nature or different world situations. These extraneous assumptions would be cut away with the razor, leaving the presence of the time traveler as the only discrepancy.
8 Both philosophy and mathematics are highly skeptical of sensual data. In his Allegory of the Cave, Plato famously cautions against the acceptance of that which is perceived merely with the senses. Additionally, the epistemological branch of philosophy is concerned with the theory of knowledge and the validity of human perception. In mathematics, the axiomatic method consciously avoids appealing to the senses, as arguments follow from postulates and prior results, not observational data, and proofs are expected to hold without the aid of diagrams. This distrust of perception flows from the countless instances of deceptions and illusions that have affected mankind throughout history, from the supposed flatness of the Earth to the apparently infinite speed of light.
9 Buddhism submits the following as a fundamental law of life  aes dhammo sanantano – or in the words of Stephen Rowe, “the higher knows the lower but the lower does not know the higher.” This situation of a transparent floor and an opaque ceiling arises in the stages of Buddhist enlightenment as well as many other facets of life. In our particular case, the knowledge of the “lower” is carried into “higher” realities by the time traveler, who has already experienced the previous reality.
10 This is precisely the case in Primer.
12 For more on nonEuclidean geometries, see Appendix D.
