The Paradoxes and Oddities of Time Travel

This page presents summaries of some of the puzzling things which might happen if time travel were possible as reflected in the science fiction literature, arguments for the impossibility of time travel, and criticism of these arguments.

Time travel is a source of intrigue for various reasons. To some it offers the hope of returning to visit childhood friends or neighborhoods as they were. To others it seems to allow the exciting possibility of witnessing historic events or studying extinct life forms. At the same time, it has caused worry in some people: what if a time traveler were to go back in time and ensure that I am not born? To philosophers, time travel is an interesting test case for theories of free will, causation, personal identity, and the nature of time.

The Nature of and Logical Possibility of Time Travel

What is time travel? On the surface it may seem that time travel is movement through time, so that when a person goes from one time to the next, the person has time traveled. This kind of movement is an activity humans are specially suited to, even more than upright walking. In fact, itís something we cannot prevent. So, in this sense all humans are time travelers; we are all moving through time together.

Actually, this is an extremely misleading way of describing the passage of time. Consider the expression Ďmovement through time.í What does this mean? Movement through space is simply the change of spatial location with respect to time. Modeled analogously, movement through time should be defined as the change of temporal location with respect to time. Yet, this definition is, on the face of it, meaningless. If something (say, an event) has a temporal location, this location does not change with respect to time. It is a location in time. Some philosophers have tried to make sense of some notion of passage through time by postulating two different time dimensions, so that oneís temporal location in one time dimension can change with respect to the second time dimension. These accounts are left with the daunting task of explaining how the two time dimensions can be explanatory when only one time dimension is apparent to us.

So, once again, what is time travel? Time travelers are not normal people. They carry strange ray guns from the future or dinosaur eggs from the past. Tim, wearing his camouflage and empty sack, steps into the time machine, activates the appropriate electronics, disappears along with his time machine, reappearing 5 minutes lateró3 big eggs in his sack, 3 big claw marks on his face. Tim, according to his account, spent 2 minutes in the time machine before and after his week-long adventure in the Triassic. Tim traveled for 2 minutes and ended up 60 million years ago. In other words, the two events, Timís activating the time machine and Timís entrance into the world of sauropods, were separated by two different amounts of time, 2 minutes and 60 million years. How is this possible? How can two events be separated by two unequal amounts of time?

One answer is given by David Lewis in his 1976 article, The Paradoxes of Time Travel. He claims there are two different kinds of time at work here. The first is personal time, the time as it seems to Tim and as measured by Timís wristwatch. The second is external time, the time as it seems to the rest of the objects in the world like the moon, the rocks, and the dinosaurs. If one had a stopwatch activated when Tim appeared in the Triassic age and was left on the ground, only stopped when Tim activated his time machine, it would measure some 60 million years. If one had a stopwatch activated when Tim activated the switch and stopped when Tim appeared in the Triassic age, it would measure 2 minutes. For normal people all the clocks in our vicinity measure the same passage of time between events. Time travelers are distinguished because there is a mismatch between their personal time and external time. If one starts at time t and travels for some amount of personal time, p and ends up at an external time e, then one can tell whether one has time traveled. If t+s>e then one has traveled towards the past. If t+s<e then one has traveled towards the future. If t+s=e then one hasnít time traveled at all.

How one makes the notion of personal time precise is an interesting issue. According to a common- sense understanding of time traveling we are not time traveling when time seems to be passing quickly, nor are we time traveling when our watches run slow. Progress towards a better standard of personal time might be made by measuring personal time by how much passage a highly accurate atomic clock would measure if it were with the time traveler. Such a standard, I believe is a good one, although it does suppose that an atomic clock (or whatever other accurate timepiece) will accurately measure time during the time traveling procedure. Since we donít have a general account of all the physical circumstances which allow time travel, we donít know for certain whether any given clock will operate sufficiently well. Another way of making precise the notion of personal time, via the length of time-like curves, will be discussed shortly.

Time Travel to the Future is Possible

Time traveling to the future occurs when less of oneís personal time elapses than external time. Here are two physically possible ways of slowing down oneís personal time:

Cryogenic Time Travel

Freezing a person in order to halt aging temporarily will allow a kind of time travel. Conceptually quite simple, cryogenic preservation offers the possibility of maintaining someone at close to the same physical state for a relatively large amount of time, perhaps limited only by the lifetime of all the refrigeration equipment used and the inevitable effects of freezer burn. The procedure is easy to picture if not to bring about: freeze a passenger so that the personís physical makeup is not harmed too much. Upon thawing, the personís physiology could return to normal functioning. The psychological features would be preserved as well (unless some implausible version of mind-body dualism is true). The thawed passenger will have perceived a passage of time on the order of hours or days, perhaps. Upon completion of the procedure, the person may be staring at January 2624 on the calendar. A less ductile than average reader may balk at cryogenic storage as genuine time travel if one does not count freezing as a pause in personal time. While it is true that the travelerís perceived passage of time is similar to the passage of time observed by any normal human during deep non-dreaming sleep, unlike the sleeper, the travelerís hair does not grow, nor do her arteries harden.

Special Relativistic Time Travel

Even more resistant to charges of artificiality is the possibility of time traveling via rocket ship. It is a consequence of Einsteinís 1905 special theory of relativity that two space travelers may disagree about the passage of time between two events, even if the travelers have perfectly accurate timepieces at hand. The time registered on a perfectly functioning clock is determined by the length of the clockís world line in Minkowski space-time. If Stacie and Tim start perfect stopwatches at the same location and instant and then travel along different pathways to meet later on in their lives, it is possible that their clocks will differ in reading. The amount of the difference will depend on the exact path taken. For example, if Stacieís clock has a straight world line and Timís bends around a lot (which is what will happen if Tim accelerates a lot), Timís clock will show less passage of time. Tim and everything traveling along with him undergo a smaller passage of time than Stacie. Any accurate measure of time based on the local physical features of Tim and his carry-on baggage will register this slow-down relative to Stacie. Thus, to travel towards the future one needs just to travel with a small world line relative to the world line of the environment where one wishes to land. One conceptually simple way for an earthling to do this is to travel very nearly at the speed of light away from Earth and then turn around and come straight back. By increasing the length and speed of the voyage, one can arrive back at Earth further in its future. As to the details of the rocket engine and tidal force amelioration equipment, thatís another story.

Some Paradoxes of Time Traveling to the Past

Time travel to the past has been thought to pose special problems for free will because of the special constraints to which time travelers are subject. Traditionally, the problem has been represented as the grandfather paradox, although the same theme has been presented in various interesting forms. The interest of the stories comes in great part from the implications of the unusual constraints which time travel necessarily involves. First, I mention two closely related paradoxes of time travel, then I criticize an explicit argument based on the paradoxes which tries to establish the impossibility of time travel.

Grandfather Paradox

Time travel seems to allow the possibility for someone to change the past, yet the past is immutable. The scenario in which one returns to the past to kill grandfather is recounted in many forms. It is not clear why Grampa is usually the victim of attempted paradoxes although some suspect that those tedious stories about the good old days lends appropriate irony to an otherwise senseless blood bath. The standard story goes something like this: a time traveler, Tim, eager to prevent some horrible deed his grandfather Wilbur did in the past, gets into a time machine on a mission to murder Wilbur. Tim arrives safely in the past and attempts to carry out the deed. Here, if the story is consistent, Tim will not succeed in the task. But it seems that Tim could succeed in killing Wilbur. He is a free agent after all, and there is no guardian angel making sure that Tim doesnít alter the past. Yet, if he does kill Wilbur, Tim wonít be born and wonít be able to travel back in time to commit the murder.

Bilking Paradox

A gun, set to be fired automatically into a box through a shutter, is aimed directly at a panel on the back of the box. The panel is created so that if it is hit by a gunshot, it sends a secret radio signal into a wormhole which transmits the signal into the past. The box also has a receiver which is connected to an antennae focused on where the radio signal would be emitted from wormhole. The box is set so that it closes the shutter if and only if it receives the secret signal from the future. On the one hand, every individual part of the device can in principle be made to operate as reliably as one wants. Yet the operation of the device must always fail because the deviceís function is to make itself fail.

An Argument for the Impossibility of Time Travel

Here is a simple formulation of an argument against the possibility of time travel:
Premise 1. If time travel is possible then Tim can go back and time and kill his grandfather before the conception of his father (because Tim is a well-armed, cold-blooded, time-traveling killer).
Premise 2. Tim can never kill his grandfather before the conception of his father (because if he did, Tim would never be born).
Conclusion. Time travel is impossible.

This argument, I believe, is in the final analysis specious, for the reasons mentioned in David Lewis' 1976 The Paradoxes of Time Travel. The valid modus tollens logical form employed in the argument belies an equivocation in the word Ďcan.í Premise 1 claims that Tim has an ability to kill his grandfather in the distant past in the sense that it is compatible with local facts about Tim such as his (macroscopic) physical makeup and psychological predisposition that he kill his grandfather. Premise 2 claims that Tim has no ability to time travel in the sense that it is incompatible with global facts about Tim such as his being a direct descendent of his grandfather. Because the word Ďcaní is employed in two quite different senses, the argument is not a good argument against time travel. The argument is analogous to the following obviously fallacious argument:
Premise 1. If I registered, then I can vote (because I have satisfied whatever legal requirements exist).
Premise 2. I canít vote (because I donít have enough time to make it to the polls before they close).
Conclusion. I am not registered to vote.

The expression Ďcan voteí here has been used with respect to two significantly different background contexts. Because of the shift of venue in the movement from premise 1 to premise 2, the intended conclusion does not follow. What the argument against time travel shows us is not that time travel is impossible, but that certain constraints exist governing what kinds of time travel stories are logically consistent. Time travel stories involving Tim going back in time to kill his grandfather make sense when one focuses only on the events very close to one another. For instance, if you consider Tim with his gun in hand with Wilbur approaching, it seems very plausible that Tim can kill Wilbur. Only when you add in additional facts, like the fact that Wilbur will later father George who in turn will father Tim, that the plausibility melts away.

Time Travel is (Worry-)Free: No New Physics Required!

The constraints on what time travelers can and cannot do, let it be noted, are logical constraints. It follows as a matter of logic that no two incompatible propositions about the state of the world at some location and time can be true. For instance, it cannot be true that Tim did kill his grandfather at the time in question and that he didnít at the time in question. So any story which gives two or more incompatible descriptions of some event is either a) making a grave logical error, or b) not describing events of the same time (but perhaps of some other relevantly similar time in a different time branch, if that can be meaningfully done). This critical feature of the nature of global constraints on time travel is not a constraint forced upon the world by some physical mechanism or law of nature. The constraints are fulfilled by any logically possible time travel scenario, regardless of the physics involved. One helpful way of understanding how these constraints work is to consider an analogy from literature. Suppose a novel begins with an old character relating her memories of critical, formative events of her life. This novel, if it is consistent, will not honestly describe certain types of events. She will not die of pneumonia at age 12. She will not permanently lose her ability to remember. The reason she wonít is not because these things are physically impossible. Itís because they are incompatible with the fact that she is at some stage of her life old and remembering. I cannot stress this point enough because it has been implicitly and sometimes explicitly denied by some prominent writers, e.g. Krauss, in The Physics of Star Trek, and Stephen Hawking. These authors think that some heretofore unknown physical laws or constraints must be true in order to avoid the paradoxes of time travel. This way of thinking is entirely misguided because it is logically impossible that an inconsistent time travel story will ever be true. Obviously, if something is logically impossible, it is physically impossible, no matter what the laws of nature are. So we donít need to trouble the physicists with a demand for them to find a prohibition for time travel. What we should do, is trouble science fiction writers for interesting explorations of some of the oddities allowed by time travel. Here are some possibilities which may strike you as counterintuitive.

Information Paradox

There are some interesting physical behavior in worlds where time travel occurs. To see this, consider the following story. You go back in time with a copy of Shakespeare's complete works. You travel to England, look up Bill and hand him the text. Bill, being unscrupulous, copies the plays and poems by hand and submits them for publication. They get published, produced, become famous, and editions containing his complete works are published, allowing you to buy a copy before you travel back in time to hand them to Shakespeare.

One may ask at this point, ďWho wrote the plays?Ē One answer is simply that no one did. One of the oddities of time travel is that plays can come into existence without having been written. The lack of explanation in this case conflicts with some philosophical principles which have been put forth. Most famously, Leibniz held that nothing ever comes about unexplained. Everything that happens, happens for some sufficient reason. The principle of sufficient reason seems to conflict with the apparently unexplained history of the play. Of course, each stage of the playís existence does have an explanation: namely, the stage of the playsí existence immediately preceding it in personal time. If one traces back along a chain of explanation, one ends up traveling in a circle. So while each of the stages of the playsí existence are explained, there is no explanation for the existence of the entire loop. There are two things worth mentioning at this point. First, one may debate whether having an explanation for all of somethingís stages is tantamount to having a full explanation. Second, the lack of full explanation may be traceable to a demand we typically make of these types of explanation: that they track dependence of one stage of the world on some previous stage(s) of the world. Typically, time travel involves a breakdown in determinism. This determinism is in some sense worse that the indeterminism one finds in certain interpretations of quantum mechanics because in the quantum mechanical case, one can determine in principle the likelihood that any given state will follow. In the time travel case, no information could possibly be found in 1478 AD which could indicate what the likelihood of Shakespeareís plays springing into existence. Time travel loops enter the world completely unannounced, crashing whatever party it finds.

Gift-giving Paradox

Suppose you go back in time and give yourself a drawing on a sheet of paper which you (the younger) keep until you go back in time. On may wonder, ďIf paper yellows and deteriorates with time, how does the paper get handed to you in good condition?Ē If one tracks the personal time of the sheet of paper, it must return to its exact microscopic state upon completion of its loop. Thus, either it maintains its condition, or it must undergo some transformation which restores its condition. This apparently is at odds with the second law of thermodynamics. The second law is commonly presented as making the claim that the entropy (some measure of disorder) of any system tends to increase. The law, if it may be so called, under contemporary understanding, does not make the claim that entropy must increase, but that there is a very high likelihood that it will increase for any large enough system for any large enough amount of time. The constraint that the existence of the paper places on the world forces one of the unlikely evolutions of the world. Some extremely atypical thermodynamic behavior must occur for the book to make it around the loop. Is this a reason to think time travel itself is unlikely to occur? I leave that to the reader to consider.

Sexual Paradoxes

Here is a puzzle presented by Jonathan Harrison in Analysis 1979--Jocasta Jones discovers an ancient deep freezer containing a frozen young man. She thaws him out and asks him his name. "Dum," he replies. Dum carried with him a book with details concerning how to build a time machine and a freezer. They marry and have a son named Dee. When Dee grows old enough, he reads his fathers book and builds a time machine. Dum and Dee get into the time machine and travel far into the past (with the book). When food supplies run low during the time travel trip, Dee kills his father Dum and eats him. Dee arrives in the past, destroys the time machine, changes his name to Dum, and builds a deep freezer and jumps in. He is revived by a woman, namely Jocasta JonesÖ. The puzzle question posed to the public is ďDoes Jocasta commit a logically possible crime?Ē There are a couple of additional things to consider besides the possibility of time travel itself. Incest is not typically applied to cases in which the purportedly incestuous act is the act which generates the son. One may also ask whether Dee commits murder or not, his act of killing being possibly an instance of suicide. I note in closing that there are other interesting things for time travelers to do with their sex lives. For some ideas look at Robert Heinleinís short story All You Zombies.

For an excellent source of commentary on time travel stories and an accurate analysis of the logic of time travel paradoxes, see Paul J. Nahin's Time Machines: Time Travel in Physics, Metaphysics, and Science Fiction.


 All questions and comments should be directed to Douglas Kutach (kutach@rci.rutgers.edu)

Last updated: November 13, 1995.