A critique of the replacement theory of time travel
The replacement theory of time travel was developed by Mark Joseph Young to sort out various anomalies appearing in time travel stories. It is described in detail on his website Temporal Anomalies in Popular Time Travel Movies and illustrated by logical reconstructions of many complicated movie plots. The author recently had a lively email exchange with Mr. Young on the subject of time travel. On his suggestion this critique is posted here for comment and discussion. The article is self-contained, but the reader will benefit (and have fun) from reading Discussing Time Travel Theory section on the Temporal Anomalies website. The site also contains some previous discussion between Mr. Young and the author concerning time travel and the replacement theory (see A Critique of the Spreadsheet Theory).
Replacement theory
The gist of the theory is that if the past is changed by a time traveler from an original timeline, causes of changes must be replaced within the resulting new timeline. In particular, there has to be a person in this new timeline, who travels into the past and makes the changes that created it. Every time trip into the past, say from 2030 to 2000, terminates the original timeline at 2030 and rewinds the history back to 2000. The traveler then has until 2030 to re-justify his appearence in 2000 within the new timeline, e.g. convince his younger self to repeat the trip in 2030.
Otherwise, time snaps back to 2000 again to avoid a causality violation. Snap-backs are the main enforcement mechanism in the replacement theory and they are instrumental to its claim that a time traveler impacts his own life. Mr. Young sees this last point as a distinctive feature of true time travel as opposed to parallel dimension jumps. I will take up both ideas here and express my reservations about them. At the end, I will outline some approaches to modifying the theory.
By his own bootstraps
To get a feel for the replacement theory let us briefly illustrate how it deals with the classical time travel paradoxes. In cases with a single time trip to the past there are two basic types of them, often called bootstrap and grandfather paradoxes.
In a typical bootstrap paradox a traveler (Oldie) gives his younger self (Newbie) a book describing construction of time machines. Newbie reads the book, builds a time machine and goes back in time to hand over the book to himself. Where did the book come from? This is not a logical contradiction, but there is a mystery of that self-existing book with all its knowledge, which is forever trapped in a time loop.
The replacement theory is at its best in handling such bootstrap scenarios. In our example, it postulates existence of an original timeline, where Newbie invented time travel without Oldie’s help and wrote a book about it. Intending to save himself the trouble he travels to the past as Oldie and hands over the book. The original timeline is aborted as soon as he arrives at the past and time restarts from that point. In the new timeline, Oldie instructs Newbie to close the loop by returning the book to himself, and goes back to the future to live the rest of his life. This is the bootstrap timeline we started with. The genuine cause in the original is replaced by circular causality in the final timeline.
The entire process, called N-jump, can be pictured as a zig-zag of the original timeline terminating in 2030, snapping back to 2000, and continuing undisturbed into the future. Most of the reconstructions on the Temporal Anomalies website feature an iterated version of N-jump, where the first Newbie fails to close the loop, but after several intermidiate snap-backs one of his successors does.
Killing yourself the hard way
But suppose Newbie disregards good advice, throws out the book and turns his mind away from time machines. Or perhaps, Oldie discourages him from pursuing them. Then time is forced to snap back again from 2030 to 2000, the original timeline is replayed with invention of time machines, trip to the past, snap-back, new timeline with no time machines, snap-back, etc. This is replacement theory’s infinity loop that traps time forever between 2000 and 2030.
This is also a variation of the grandfather paradox. Classically, a time traveler goes back to kill his grandfather and prevent his birth, but we can do just as well with him killing himself. This is a true contradiction since he can kill himself if and only if he does not kill himself. To get what happens under the replacement theory simply replace ‘build a time machine’ with ‘kill yourself’ in the above example.
In fact, all grandfather paradoxes result in infinity loops and trapped time. Although the contradiction is removed, perpetual snap-backs do not give an appealing resolution. If time travel functioned according to the replacement theory it would likely trip up our universe soon after being discovered. If original inventors experiment with sending an ice cube one minute into the past and see it appear one minute prior to scheduled sending, they may well decide to see what happens if they do not send it after all. The result will be an entire universe forever trapped in a one minute infinity loop.
Time also gets trapped in more general situations, where instead of endless repetition there is endless production of new timelines, all aborted. These are called sawtooth snaps. In fact, iterated N-jumps ending in bootstrap timelines are the only scenarios having a satisfactory resolution. They are also the ones most commonly encountered in time travel movies and literature. But there are serious logical issues with the entire mechanism of snap-backs, which we discuss next.
Dead timeline walking
Time always moves from the past to point A and beyond to point B; at point B, when Traveler leaves time and heads to point A, time ends; but Traveler cannot arrive at point A, because he could not have been there in the original time line… The instant Traveler reaches point A, he destroys point A, replacing it with point C… Time will now continue to point D.
In this passage point A is year 2000 in the original timeline, point B is its year 2030, points C and D are counterparts of A and B in the new timeline. A time jump at B triggered a snap-back to C. The AB timeline has been aborted, obliterated, metaphysically erased. In my opinion, once AB sinks into oblivion its former existence should exert no influence over CD except through the traveler’s presence, which is available at C in the entirety of its relevance. One would think that time would not ‘know’ any different if the traveler simply popped out of nowhere as a result of some spontaneous fluctuation in space. After all, AB timeline is no more, vanished into the metaphysical past. In other words, one would expect time to be metaphysically memoryless. Not in the replacement theory.
Time has to make sure that traveler’s appearence at C is not a miracle, that it is supported by the new timeline. And there is a deadline for compliance — 2030. For an N-jump to occur the matters at D must stand as at B ‘in every pertinent way’, otherwise time snaps back again. In other words, time has to raise B from its metaphysical grave, compare D to B, decide if the differences are sufficiently pertinent and then snap-back or continue. There does not have to be any time travel attempt in 2030 for this to happen. When time is trapped in an infinity loop, no time machines are ever built in CD and nothing special happens in 2030. Somehow, AB timeline extends a dead hand from its grave and snaps time back. I understand the intent to preserve causality, but I do not see through what physical means such a snap-back might be accomplished.
Even if we accept that ‘nature abhors causality violations’ and the time traveler must reproduce circumstances of his appearence in 2000, why is he only afforded 30 years to do so? From CD’s point of view this due date is completely arbitrary. Oldie has left the scene, Newbie has better things to do, there are no time machines around. All that matters is that the traveler’s appearance in 2000 must eventually have a cause within the same timeline. This cause may be a time jump from 2030, or 2050, or 10327. At some point down the line the traveler or his clone must make a trip to 2000 to save causality, but other than that there are no restrictions. Perhaps, time patrol from a distant future will uncover the wrinkle, clone the time traveler, instruct him accordingly and at the appropriate age send him back to 2000. There is no immediate cause for the snap-back in 2030 within the CD timeline, which defeats the purpose of saving causality.
This is like a bill that comes due eventually but the payment can be deferred indefinitely into the future. Of course, in practice this means that the bill never comes due. The miraculous appearence in 2000 may remain a spontaneous act forever. There is no physical mechanism in the replacement theory to prevent that. Forcing a snap-back in 2030 is simply a deus ex machina.
Banana peels
This is not the only problem with spontaneous snap-backs. What if after dissuading his younger self from pursuing time machines our older traveler decides to visit 2040? Under the replacement theory there is no 2040 in this timeline, so no 2040 for him. But why? He would have had no trouble making the trip under the N-jump scenario, and his younger self still has time to change his mind and enact it. According to Mr. Young, travel to the future is benign and should raise no red flags on Time’s radar screen. But to stop the traveler, not only should CD know in advance that the history will end in a loop, it also has to keep diligent watch for any future travel attempts.
And what if after reaching whenever instead of 2040 our traveler decides to return and convinces his younger self to build the time machine after all? The timeline recoheres and 2040 that he allegedly did not reach exists. Then he did reach it despite what we thought before. If we maintain that the trip can happen then there is no snap-back in 2030. If it can not happen we need what is called a ‘banana peel mechanism’. There must be a strategically placed banana peel in the CD timeline, upon which Oldie slips, bumps his head and loses his memory before he can jump to 2040. We saw this mechanism at work in the fixed timeline theory. To paraphrase Mr. Young, Time is a very clever gentleman if it can do all that.
Replacement causes
It isn’t time travel unless the traveler arrives in his own past. That means he can impact his own life; and that means we need a theory that addresses what happens when someone impacts his own life.
In a bootstrap scenario a traveler does change his own life, but only to make it what it was. What one really wishes is to change the course of events into something other than what is remembered. The challenge is to make new events happen to the same person that made the changes, to transmute the time traveler into his younger self. What is vaguely imagined is exiting the flow of time, improving events in the past and then re-entering time as the same person under new circumstances. There are two visions of this re-entry. You can relive your own life from the time the changes were made, or you can skip part of it and slide back into the new you at a later date.
Both scenarios miss the target. Someone has to live through the new life, and if it is not you the only way to slide into it is to displace that new person. If on the other hand, you regress back into childhood and relive your life, then it is the old self that is displaced. In this version of the dream the memories of time travel vanish but its effects linger on. Perhaps, they retain some supernatural influence reminiscent of reincarnations in Buddhism with forgotten past lives and karma. But dreams have the luxury of ignoring logic. In the light of day, it what is asked can not be delivered, it is a logical impossibility. But it can be approximated.
Parallel worlds do the next best thing. They duplicate a person into a changer and a changee: the older traveler makes changes that affect his younger duplicate. This duplication destroys the possibility of changing own past even if you start with exactly the same past. The replacement theory tries to mitigate the problem using snap-backs. In my opinion, it does not succeed.
Duplication still happens as attested to by descriptions of infinity loops and sawtoth snaps, where the older and the younger self have separate origins. Spontaneous snap-backs are unleashed to save the appearences by preventing a meeting between them when they are of the same age. In N-jumps replacement causes are generated to make it look like the older and the younger self are one and the same. But all of this is smoke and mirrors. Having observed the original timeline, we know better. The true old self is gone, vanished into oblivion. The younger traveler growing up, jumping back and changing himself is a sleight of hand, an optical illusion like wheels of a car appearing to roll backwards in old movies.
In a way, the replacement theory fails better than its alternatives. If duplication does not produce an illusion of transmutation the entire timeline gets punished by being aborted at the original travel date. The replacement theory is a crime and punishment story with causality as the victim, time traveler as the perpetrator and Time itself as the police, the judge and the executioner. Many oddities of the theory can be traced to this forcing of Time into roles that it fiercly resists to perform.
Identity crisis
The time traveler in the timeline that marks the final, stable history of the world knows nothing about any previous history of the world… This time traveler has no first-hand knowledge of the original history; that version of him was erased…
It is rather mysterious how exactly the old traveler transforms into his replacement. In the new timeline everything is done by the new traveler who originates in it. The old one is shut down as soon as the old traveler steps out of it. So where exactly did he go, or rather wherewhen did he perform the changes that created the stable timeline with everything performed by his replacement? This is supposed to be explained by the spreadsheet illustration: “Although the cause of the value at A1 has changed, the value itself has remained the same, and all the values springing from it are likewise preserved”. If it means what I think it means, we have another optical illusion.
In the ‘first run’ along the new timeline it was the impostor (as in visitor from another timeline) that instructed the authentic youngster on the fine points of building time machines. After that he conveniently leaves the scene. As the youngster grows up and jumps back we get a ‘second run’. He ends up ‘having the same value although not the same cause’ as the impostor, and now instructs himself on the subject. Of course, we are not allowed to think about it this way, because the timeline is complete in its eternal glory and there are no ‘runs’.
As a result, there is no particular occasion at which the replacement happens or a process by which it happens. This reminds me a common experience of making two lampposts look like one by keeping them in the same line of sight. Identity of indiscernibles hardly applies to physical objects. Besides, I would argue that even metaphysically entities with different causes are discernible.
The curse of parallel worlds
Mr. Young sees duplication as a hallmark of parallel worlds and dismisses them as non-time-travel. Although I agree that traditional parallel worlds are probably not time travel, this broadening of the concept goes too far. According to the strictures of Mr. Young’s definition, his own theory is not time travel. Let me demonstrate.
Consider an N-jump: the original timeline terminates in 2030 and the jump takes the traveler back to 2000. This is the branch point. Replacement timeline then proceeds unhindered into the future. Since the original timeline is gone into oblivion the traveler can not return to it, but he can travel freely along the new timeline. Sounds familiar?
One may object that in parallel worlds the old timeline still exists, while here it is obliterated. First of all, in some versions of parallel worlds only one timeline can be active. But more importantly, if it is impossible to access the old timeline the question of its existence is a moot point.
In parallel worlds you could go back to the branch point and reactivate the abandoned timeline. You simply need to undo the changes made there. Well, under the replacement theory you can also jump back to 2000 and undo what you did. This will reproduce the old timeline in its fullness including the snap-back in 2030. Technically, this is a ‘new’ timeline while in the parallel worlds you reactivated an ‘old one’. But you will be none the wiser unless you are a philosopher preoccupied with identity of indiscernibles. I trust that the reader can perform similar analysis on infinity loops and sawtooth snaps.
Of course, 30 years into the new timeline our brave new traveler will go back to the branch point to satify the N-jump requirement. Then he can finally rest and admire his(?) handiwork. But do we really know that? Or perhaps, he deactivated the new branch and created a newer one just like it? Who knows, and more importantly who cares. In one respect, admitting the second and subsequent branches is an improvement since it would resolve the identity crisis discussed earlier.
As long as two theories make the same predictions their differences are irrelevant. In terms of predictions, the replacement theory is a variant of branching parallel worlds (broadly construed) with return to the branch one creates.
The only remaining distinction are the snap-backs that cap failed branches, but they are not particularly vital. The spirit is preserved if failed acausal branches are allowed to play out, they are just second class citizens.
Temporal kinetics
The idea of replacement causes seems to be the right one for time travel. If the past can be changed and existing causes removed the only way to preserve causality is to replace them. But the enforcemant mechanism of snap-backs is not only incompatible with relativity and quantum mechanics, but also almost inevitably leads to the pathology of trapped time. Snap-backs themselves should be replaced by more plausible physical processes.
A close analogy is the Le Chatelier principle in chemistry: if a system at equilibrium experiences a change, then the equilibrium shifts to counter-act the imposed change. Le Chatelier principle can predict outcomes of chemical reactions but it does not explain them. To explain the shift one needs to understand physical mechanisms that enforce it. Taken at face value, the principle seems to ascribe to a chemical system a mind of its own. In reality, it is a corollary of perfectly mindless equations of chemical kinetics. Now replace a system at equilibrium with a causal timeline, a change with a causality violation and counter-action with snap-backs that seek to establish a new equilibrium. To wit,
Le Chatelier principle of time travel: If causality is violated by a time travel event, then the timeline shifts to counter-act the violation.
This is the driving motive of the replacement theory, but its implementation there is only a first approximation. To continue the analogy, shift in the chemical equilibrium is not instantaneous. If we solve the kinetic equations we discover that in the process of shifting the system undergoes transient stages that are not equilibria. We can also trace chemical forces that drive the shift.
Temporal kinetics is what I am after. Non-equilibria are acausal timelines that appear as intermediate stages between causal ones. Mr. Young has such high intolerance of them that he is aborting them in the womb at the cost of spontaneous snap-backs with all their dubious physics and supernatural baggage. I am not so radical: as transient objects acausal timelines are not that threatening. We also have to account for a possibility that a new equilibrium can not be attained. In this case I would rather have a succession of acausal timelines than endless snaps and trapped time.
But most importantly, I would like to trace the mechanisms by which time polices itself. Anthropomorphic detection of causal violations with abrupt abortion of the violators at an arbitrary date is hardly satisfactory. It is plausible that in the extended theory we will see key features of the replacement theory reproduced, but the point is that they ought to be explained. Resistance of time to causal violations can not be postulated, it has to be derived. We need a mechanism by which time drives events within timelines towards restoration of causality.
Middle course
In the article Toward Two-Dimensional Time recently posted on Outpost Mr. Young suggests a possible alternative to the replacement theory. In the new theory once root changes are made in 2000 the entire timeline instantly changes to incorporate their consequences. If you kill yourself back in 2000 you will produce a history where your time machine was never built, and your murderous trip never took place. Time will follow through on all the consequnces and wipe out the old you from 2000 as well. But then who is going to kill the young you? Do we get an endless oscillation between two timelines again? Mr. Young himself finds this theory wanting.
But the problem with it is exactly the opposite of the previous one. In the replacement theory timelines are too rigid and snap back if time travelers fail to promptly replace uncaused causes. In the two-dimensional theory they are too flexible with no regard for existing events. There is no resistance at all to making changes, they can be made at will and spread across time instantly. In the replacement theory there is so much resistance that any residual violation snaps time’s back. Perhaps we should follow Daedalus’s advice to Icarus and fly the middle course.
The idea is that there ought to be temporal resistance to changes that do not conform with the future already in place. A good model of such resistance should explain how acausal timelines manage to recohere themselves. If a traveler or his successors fail to restore causality on their own there ought to be a mechanism that compels them or others to do so.
Let us apply this idea to the grandfather paradox. If you go back and kill yourself the timeline will start incorporating this change. Taken to the extreme, it should erase your presence completely. However, the previous history where you were in place, will resist alteration. Since time is not a reasoning entity it will likely take a path of least resistance, i.e. make minimal changes that restore causality. Your spot may be filled by others, they replace you as causes of events already in place. Since you conveniently removed yourself from the timeline in 2030 this does seem like an economical solution. Your double presence in 2000 remains a wrinkle to be smoothed out, but again someone else may take your place as your childhood killer.
This holds assuming that you did not go back after the self-killing but put a gun to your own head. Your return would change things. Now you are alive before 2000 and after 2030 but not in between. This will not do. It makes sense that the wave of changes is strongest near the point of origin, by 2030 it loses some of its strength. In contrast, your return to 2030 triggers a much stronger backlash wave. The two will have to balance out on events between 2000 and 2030. In the final stable timeline your childhood wound is not fatal and you recover to make your ill-conceived trip in 2030.
Working out a physical mechanism behind the time waves is beyond the scope of this article, but it does seem to be a worthy undertaking. It will allow a better reconstruction of time travel plots that do not easily conform to a bootstrap scenario. This includes stories where time seems to resist travelers’ efforts to change it as in the movies Deja Vu and Time Machine. It will also handle multiple interlocking time jumps more robustly and perhaps satisfy our curiosity as to what history ends up persisting. An example is the Terminator series, where the replacement theory predicts infinity loops over minor inconsistencies and does not tell us who ultimately has the timeline, the Skynet or John Connor.
