A Time Travel Dialogue
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5. Friday

It is 9:00 am. Tad enters the lab where Dr. Rufus and Willie are already halfway through their cups of coffee. Tad smiles smugly as he makes his way to the coffee pot.

Carlene: What’s got you so chipper this morning?

Willie: Do you mind, Tad? It’s far too early for that.

Tad: Okay, so I’ve been doing a little research, and I spent last night brainstorming about our tricky little test subject, especially the result from yesterday.

Carlene [listening carefully]: Please continue.

Tad: I still think that one-dimensional time travel is impossible. How can someone go back into the past and change it when that would change the future? So on and so forth. It would create direct contradictions.

Willie [shaking his head]: Well, no, Tad, because, even if someone were to travel to the past, the past would have already occurred the way it did; it would have included the arrival of the time traveler and his or her actions.

Carlene: Do we really need to debate the grandfather paradox again?

Tad: Bear with me a minute. I finally found an answer that makes sense to me. Willie, do you remember on Monday when you mentioned the possibility that time isn’t one-dimensional? The way around the paradox is to drop the idea that time has only one dimension!

Willie: Tad, I meant only to suggest that we can’t even begin to make sense of films like Back to the Future without supposing that time is multi-dimensional. I meant to introduce to the discussion the possibility that time permits more than one timeline or branch of a timeline, but I never meant to suggest that time might actually be multi-dimensional. What are you trying to get at?

Tad: What if on one timeline my grandfather lives a normal life? He dies of old age, and then I decide to go back in time. My arrival is on a closely related timeline, but not the original timeline. And there you have it! I can kill my grandfather. The murder would have no effect on my birth because my birth isn’t on this new timeline; my birth is only on the original timeline.

Willie: Yeah, I get the idea. It’s a fun idea, Tad, really. But as far as the grandfather paradox is concerned—and as far as I’m concerned—your multiple timelines are gratuitous metaphysical musings.

Tad: Look, all week I’ve been searching the internet for information on time travel, and last night I came across this site, timetravelphilosophy.net, which a professor and his students assembled. It’s got some really good stuff; it even puts forth some models of multi-dimensional time and discusses how the past could be changed. I can tell you where the particle is coming from!

Carlene: You have my attention.

Tad: The website got me thinking: what if I decide to travel back to Willie’s tenth birthday party?

Willie: That would be awesome. The time travel, I mean, not you at my party; my parents and I would have been more than a little creeped out to have this unfamiliar graduate student crashing my party.

Tad: Hey, it would be a blast; I even know how to juggle! Anyway, if I decided to travel back to your tenth birthday party, I wouldn’t be traveling back to an event exactly like you remember, Willie; I’d be traveling to the party along a different dimension. The party I would visit would include my arrival. The original timeline—the one we’re on right now—would branch as I arrived, with the original timeline going the way you remember it did, and another branch including my arrival. As one timeline plays out, I didn’t arrive at the party; as the other plays out, I did. On this model, a time traveler to the past is bound to change the past.

Carlene: Does this model really let the time traveler alter the past, though? It sounds like you would arrive at a very similar but distinct party, not the party of Willie’s past.

Tad: I’m not sure that matters very much to our results.

Willie: Probably not, but I’m inclined to think that it could be the same party along the two branches. The party along each branch stands in causal and spatiotemporal relations to events that are identical along parts of the timeline prior to the branching, which seems to me to be sufficient for the identity of me with my younger self, my parents with their younger selves, and the continued existence of the party that started before Tad made his arrival. With one-dimensional time travel to the past, one person can be at two places at once, so why not one person along the original timeline and also along the alternate timeline? There could even be one event partially along the original line and partially along the branch; for example, this would be the case with the party.

Carlene: I’m having a hard time visualizing this.

Tad [taking out some paper]: Okay, take a look. The t-axis represents normal time along the original timeline, and it indexes the normal times. A person born at (t0, L0) who never time-travels will live her life along the t-axis. Now, the L-axis keeps track of branches off the original timeline; L1 will be the first branch. I’ll graph the birthday example. Willie, what year were you born?

Willie: I was born in 1970.

Tad looks surprised. Dr. Rufus smiles briefly.

Tad: Hmm, you’re older than you look. So, let’s have t0 represent 1970, and we’ll tick off intervals of ten years. I was born in 1990, so my birth is here at t2.

Willie [interrupting]: Tad, I didn’t realize you were just a kid.

Tad: Come off it, Willie! Try to focus. So, if I decide in 2010 to depart in my time machine set to travel back 30 years, to your tenth birthday in 1980, my departure would be from (t4, L0), a point along the original branch; I would cross back and arrive at (t1, L1), which is 1980 on the arrival line. If I stay along that timeline for 40 years, I’ll be about 60 at (t5, L1). Here, I’ve highlighted my life on the graph. (See Figure 5.1)

Fig. 5.1 The Life of Tad1

Carlene: So (t5, L1) would correspond to 2020 along the arrival branch rather than the departure branch. You would lead your life, missing 2015 along the departure branch but being a part of it along the arrival branch.

Tad [smiling]: ‘Departure branch’, that’s good. Don’t you think this is really shaping up?

Carlene: Why did you say you’d be about 60 in 2020 on the arrival branch, rather than exactly 60?

Tad: Well, you’ve got to consider whatever amount of time I experience during the trip, here along the diagonal.

Carlene: Tell me a little more about this diagonal part of the trip.

Tad: Well, there are a couple of ways time travel could go: you could either skip over all the time between the departure and the arrival, or move through all the time between the departure and the arrival.

Willie: Right, that’s the difference between discontinuous and continuous time travel. On a discontinuous trip, the time traveler leaves one time and instantaneously appears in another, without the traveler experiencing any time between the departure and arrival; this is the way things appear to go in Back to the Future when the DeLorean gets up to speed. On a continuous trip, however, the time traveler leaves one time and has to travel through the time and space between the departure and the arrival, to the effect that, as Tad suggested, time passes for the traveler between the departure and the arrival; the time machine in H.G. Wells’ The Time Machine travels in this way. Time travel in The Time Machine is one-dimensional, and we’ve clarified that time travel in Back to the Future only begins to make sense if it’s multi-dimensional. So far, that’s the Wellsian time machine’s one-dimensional continuous travel and the DeLorean’s multi-dimensional discontinuous travel, but what you seem to be describing, Tad, is multi-dimensional continuous time travel.

Tad: Right, like the boxes in Primer.

Willie: Oh, so you’ve seen it?

Tad: Yeah, the website on time travel suggested it; I watched it last night.

Willie: It’s a good one. Tell Dr. Rufus about it.

Carlene: Oh my.

Tad: Primer is a movie about two engineers, Aaron and Abe, who discover a way to travel backwards in time. They build boxes out of PVC pipe and who-knows-what; they turn these boxes on, and then later they can get inside and travel back to the time when the boxes were turned on. The catch is that they have to wait inside the boxes while they travel through all the time between getting in and getting out. As Willie said, the movie depicts multi-dimensional time, so they can change the past; they make big bucks buying stocks that they know will do well at the end of the day, and all kinds of other stuff.

Carlene: So, figuratively speaking of course, you think that the psi-lepton is traveling in a Primer box?

Tad: You’ve got it, Professor.

Willie: This makes a certain amount of sense, but I’m not sure why they don’t end up along L2 or even L1/2 for that matter.

Tad: I put the arrival branch along L1 because I’m thinking of it as the branch on which the traveler stops traveling—and begins, once again, to experience the ordinary passage of time—after her first trip. If she left that branch, she would end up on L2, and so on. When exactly along the arrival branch the traveler arrives depends on the settings of the time machine: 30 years back, 80 years back, or 80 years forward. Make sense?

Carlene: Do all time travelers departing from L0 arrive on L1? What if they set their time machines to arrive at different times in the past?

Tad: Let’s keep it simple: at most one time-travel departure for each line or branch and exactly one time-travel arrival for each branch. For every departure of a time traveler, there will be an arrival and this arrival is the beginning of the new branch off the departure line or branch.

Carlene: What about the times along L1 prior to your arrival at t1? What events take place then?

Tad: As Willie hinted earlier, the events on L1 before t1 would be the same events that happened before t1 on L0; in general, the events before the arrival time on the arrival branch are the same events that happened before that time on the departure branch. On the graph, L1 looks separated from L0 both after and before the arrival time, but that’s just a flaw of the visual representation. I intend for the events along L0 prior to t1 to be the causal and spatiotemporal antecedents of the t1 and post-t1 events along both L0 and L1.

Carlene: Okay, Tad, you’re right; this really is starting to shape up. But what does it mean for our research? Are you saying that every time the trigger happens, the psi-lepton travels to a different timeline? What observations might we expect with your hypothesis that time is multi-dimensional?

Tad: Well, that depends on which branch we’re on. Are we on the branch where I show up at Willie’s tenth birthday party or the one where I don’t show up? Here’s what I think: every trigger occurrence represents a departure of the psi-lepton. With multi-dimensional time travel, there are many more possible outcomes than with one-dimensional time travel. In multi-dimensional time travel, depending on which branch you’re on, you’re going to see completely different things on the printout.

Willie: It’s like what I said my parents would observe at my tenth birthday party: along the departure branch there’s nothing unusual, but along the arrival branch there’s a creepy graduate student.

Tad: I’m glad you understand the model, Willie.

Carlene: How about our observations? What’s going on with the psi-lepton?

Tad: This is going to get tricky in a minute, but we can start off simply enough. If we’re considering the psi-lepton as the time traveler on the departure line, let’s make t0 be zero nanoseconds and tick off intervals of one nanosecond; so t5 is at five nanoseconds where the trigger occurs, if it occurs at all. Now, let’s consider something like Trial 16, where the trigger doesn’t occur. Here’s what the graph would look like. (See Figure 5.2)

Fig. 5.2 An Ordinary Psi-Lepton: No Time Travel

Willie: No trigger, just normal psi-lepton behavior, living for seven nanoseconds and decaying at t7 on the graph.

Tad: Right, but that’s only the most straightforward case. Next we need to consider what the graph looks like when the trigger occurs at t5. Keep in mind that we’re making these observations from L0. Also, remember we’re working on the supposition that the trigger causes the psi-lepton to depart on a trip that’s a case of inter-timeline time travel.

Willie [interrupting]: 88 miles per hour! It would look to us like the psi-lepton just vanishes, just like the DeLorean when it gets up to speed. The graph would show the psi-lepton existing only from t0 to t5. Why don’t you draw that? (See Figure 5.3)

Fig. 5.3 A Time-Traveling Psi-Lepton as seen from the Departure Branch?

Tad: Calm down, Willie. And remember we’re using the Primer-box metaphor, not the DeLorean. Think of it as Abe getting into the box. But you’re right because, as far as we could tell, the particle’s life would just end at five nanoseconds.

Willie: We haven’t seen a trial with this behavior, have we?

Tad: Well, you haven’t, but Dr. Rufus and I have.

Carlene: Have we?

Tad: Yes, Trial 12.

Willie: Trial 12? You haven’t mentioned that one; I assumed it was one of the early successes, a single particle that behaved according to your theory.

Carlene: Of course, Trial 12! Willie, it was the beginning of our unexpected results. I had already dismissed it; we thought it was just a mishap of some kind since the results were never duplicated.

Tad: A mishap of some kind, but not exactly in the way we thought then. Here, Willie, take a look. (See Figure 5.4)

Fig. 5.4 The Disregarded Results

Willie: Are you sure the trigger occurred? It doesn’t appear to have occurred because there’s no second particle.

Tad [pulling out the data tables]: As you can see here, there was a B-field disturbance at t=5.

Carlene: I remember now how strange I thought that was; it couldn’t have been due to decay because the particle hadn’t lived nearly long enough.

Willie: What does the disturbance have to do with anything?

Tad [trying to contain excitement]: Okay, let me explain what my theory says. First of all, the trigger is causing the psi-lepton to time-travel.

Willie: We’ve always had that as part of the hypothesis.

Tad: Give me a second, Willie. The occurrence of the trigger causes the psi-lepton to travel backwards across timelines. Remember that each step into the past changes the past. Traveling across timelines surely takes some energy, which has to come from somewhere, so the trigger draws it from the B field in the chamber; that’s where the disturbance is coming from. During Trial 12, we observed a psi-lepton hit the trigger at t=5, at which point it got some energy from the B field, and it left our timeline. Always, the first question we need to consider is whether we’re on the departure or the arrival branch. Here we’re on the departure branch.

Carlene: So, an equally important question is whether the trigger is on or off on our branch.

Willie: That’s nice, Tad, but what about Trial 15? There are two particles, and there was no magnetic field disturbance. What about that?

Tad: There are a lot of different factors to consider. Depending on which branch we’re on and—you’re right, Professor—whether the trigger is on or off, there’s a variety of possible outcomes. The behavior exhibited during Trial 15 is one such outcome. Let’s take a look. (See Figure 5.5)

Fig. 5.5 A Time-Traveling Psi-Lepton as seen from the Arrival Branch?

Willie: I hope you’ve got something good.

Tad: Just hear me out. On our timeline the trigger is on; the psi-lepton travels normally until t=5, at which point it hits the trigger and leaves our timeline. Meanwhile, at t=3 there appears a psi-lepton from another timeline; on that timeline the trigger must have been on, too. Based on our previous time-travel hypothesis, the second path was the same psi-lepton traveling backwards in time; on my hypothesis, it’s a psi-lepton from a different timeline, and it’s traveling forward in time. It arrives at t=3 and moves towards the psi-lepton that originated on our timeline. Good so far?

Willie: So far, so good, I guess.

Tad: Now, you asked why there was no B-field disturbance during this trial. It’s because the psi-lepton that arrived on our timeline decays! It lives the first five nanoseconds of its life on its timeline—its departure branch—and it lives the last two nanoseconds of its life on our timeline—its arrival branch—at which point it decays, here at t=5. The energy released from this decay supplies the energy for our psi-lepton to depart; it doesn’t need to get it from the B field!

Dr. Rufus’s eyes widen. Willie looks excited but nervous.

Willie: Remember when we were talking about your time-travel trip to my tenth birthday party? You said that after staying on the arrival branch for 40 years you would be about 60 years old. The psi-lepton has an extremely short lifespan. How is it living for five nanoseconds on its original timeline and two nanoseconds on our timeline when it must have spent some of its life during the diagonal trip across timelines?

Tad: I’m way ahead of you. We don’t know what might be going on during an inter-timeline trip, but I think it’s safe to assume that the physics is a nightmare. Now, the predicted lifetime of the psi-lepton is really a mean lifetime; it may live just a little bit less or a little bit more than seven nanoseconds. So, if the psi-lepton experiences less than two nanoseconds during its trip—and, for all we know, this is a possibility—then it’s possible for it to live another two nanoseconds after it arrives.

Carlene: This is clever, Tad, but I have one more question: if the psi-lepton that arrives on our timeline at t=3 nanoseconds is moving forward in time, why is it moving towards the lower part of the chamber, towards our psi-lepton? The path made sense when it was the same psi-lepton moving backwards in time—from its perspective it never changed direction in space—but I’m not sure about this.

Tad: That troubled me for a while last night, which is when I decided to take a break to watch Primer. I know this is kind of lame, but what if the psi-lepton has to turn around to get out of its Primer box to stop time-traveling? What I mean is this: what if every time the particle stops time-traveling, its direction in space is reversed?

Carlene: It’s a stretch, Tad, but it makes enough sense to me, at least for now. What do you think, Willie?

Willie: I don’t know. On one hand, it makes some sense of the data, like you said. On the other hand, why introduce so much tedium? Trial 12 aside, we had a pretty good and simple hypothesis about what we’d observed. Unless your theory can explain Trial 20 from yesterday, I don’t see why we need it.

Tad: That’s the thing, Willie; it does explain Trial 20! It explains every trial!

Willie: Okay, so show us. Here’s the printout. (See Figure 5.6)

Fig. 5.6 Trigger-On Departure, Trigger-Off Arrival,
as seen from the Arrival Branch?

Tad: After all I’ve just explained, it’s a piece of cake. Remember that the program we were using during Trial 20 was set to turn the trigger off just in case a second psi-lepton was detected, and that the trigger was initially on. So, our psi-lepton is traveling along, and at t=3, the second psi-lepton appears from another timeline, which turns the trigger off. The second psi-lepton decays at t=5, and our psi-lepton—since there’s no trigger anymore, remember—keeps moving until it decays as expected after about seven nanoseconds. The most important thing to notice here is that on the second psi-lepton’s departure branch, the trigger never got turned off; otherwise it wouldn’t have traveled to our timeline. The set-up on that departure branch would have had to be the same as ours—the same program running and all—but this is fine; all that means is that on the departure branch no second psi-lepton showed up to turn the trigger off.

Carlene: What about the magnetic field disturbances we recorded yesterday?

Tad: That’s easy. Since our timeline isn’t a departure branch, when the psi-leptons decayed, they didn’t have anything to feed their decay energy. The decay of the particle that arrived on our timeline at t=3 should have disturbed the B field at t=5, and it did. Our original psi-lepton—the one we created at t=0 on this timeline—should have decayed and disturbed the B field at t=7, and it did. Both disturbances are here.

Willie stares blankly for a moment before smiling.

Willie: So, on the departure and arrival branches of Trials 15, 17, and 19, the trigger was on, and we were on the arrival branch. But during Trials 16 and 18, the trigger was off, so there was no departure or arrival. During Trial 12, we were on the departure branch, which had the trigger on. And during Trial 20, we were on the arrival branch with the trigger off, but the departure branch had the trigger on. Damn, Tad, as crazy as it all seems, I’m impressed. I never really doubted the possibility of multi-dimensional time, but I never saw why it might be needed; it seemed ontologically irresponsible to assume it about our universe. I never thought there could be empirical evidence that spoke in favor of multi-dimensional time over one-dimensional time, but it looks like you found some. These models have to be taken more seriously than I ever thought. If we grant that the psi-lepton is time-traveling, our evidence favors it time-traveling multi-dimensionally rather than one-dimensionally.

Tad [smiling]: Thanks, Willie. But yeah, our recent trials are all evidence of time travel. The trigger always sends the psi-leptons back in time, and we’re here sometimes to collect them and sometimes to watch them go.

Willie: I’ve got to take my hat off to you, Tad; you’re now reasoning like Dr. Rufus was on Monday, looking for explanations that would make sense of the data. And I guess you have my hopes up a little that we’re really witnessing time travel. I never liked multi-dimensional time; I never saw the point.

Tad: Is it too soon for me to buy a rifle and take after Gramps, or better yet Hitler? Too soon to check out the mid-cap stocks and make my fortune? Too soon to take a trip to the past in order to step around any blades of grass I well please?

Carlene: Hold your horses, Tad. As incredible as all this seems, no one’s time-traveling or even leaving this room until we get more results; we only have one example each of trials like 12 and 20. Are there any additional experiments we need to run?

Willie: Yeah, getting more results like Trials 12 and 20 would be great. But I want to look into something I just thought of. Tad, where’s the printout for Trial 19? Ah, here it is. (See Figure 5.7)

Tad: What about it? The results are the same as Trial 15 and the others.

Fig. 5.7 A Challenge for Tad’s Multi-Dimensional Hypothesis

Willie: The results were the same, but the experimental set-up was unique. We started Trial 19 with the trigger off, but the program was designed to turn the trigger on if it detected two particles in the chamber. Supposing time is one-dimensional, my explanation for the results was that this was one of two perfectly possible results, neither of which was determined by the conditions prior to three nanoseconds. The results were explained by a causal loop; the time-traveling psi-lepton in the upper part of the chamber was detected, which turned on the trigger, which sent the psi-lepton in the lower part of the chamber back to t=3 when it was detected.

Tad: Yeah, but that makes no sense to me. I don’t believe in the possibility of causal loops just like I don’t believe in the possibility of time-traveling to the past without changing it.

Carlene: Oh, Tad, but that’s the issue, isn’t it? If there was no causal loop, what’s your explanation of the results of Trial 19?

Tad: That’s the beauty of my theory; I don’t need a causal loop. The results of Trial 19 are consistent with the trigger occurring on the arrival and departure branches.

Willie: Be careful. The experimental set-up couldn’t have been different on the departure and arrival branches; you said so yourself when you were talking about Trial 20. For Trial 19, the set-up was such that the trigger doesn’t occur on the departure branch unless there are two particles in the chamber before three nanoseconds; the trigger was programmed to turn on if and only if the second particle was detected. Your model doesn’t allow intra-timeline time travel, so how does the departure branch get the trigger turned on? It seems that a causal loop in one-dimensional time is the only way to make sense of the results. You realized yesterday that on your view the psi-lepton shouldn’t have time-traveled during Trial 19. Unfortunately, it looks like it did.

Tad: Maybe we just can’t explain these results. Maybe the second particle spontaneously appeared, and spontaneously decayed before it should have, and, hey, it’s no worse than the causal loop, which you said might be inexplicable!

Willie: I suggested that the causal loop itself might be inexplicable, but the loop does allow for the results we got.

Tad [grabbing at the air]: Well, what if there was an infinite regression of branches, each one receiving a particle that turns its trigger on so that it can send its particle to the next branch

Willie: What about those branches, then? Are we on each one to infinity and beyond? One of the virtues of your model was that it allowed you to make predictions that could be observationally confirmed, but an infinite regression of branches? How do we confirm that? This is an ad hoc addendum to your hypothesis, Tad, and to be honest I felt similarly about your idea that the psi-lepton turns around in space after time-traveling. The rest was great, though; I’m sorry it doesn’t work out.

Tad: I’m not sure what to say, Willie. I can’t make sense of Trial 19, but you can’t explain Trials 12 or 20.

Willie: We need more results. Carlene, what do you want to do next? Do you want the trigger to turn on only when there are two particles? I could also leave it to turn off only when there are two particles. We have a fair amount of choice.

Carlene: Both Trials 19 and 20 raise interesting issues, and we’ve run those experiments only once each. Let’s just leave the program from Trial 20 running for now. Maybe we’ll get results like Trial 12; that would help out Tad’s hypothesis.

Tad: I’d love anything in my favor. You ready, Willie?

Willie: Yeah, I’m all set. Don’t get your hopes up for a repeat of Trial 12, though.

Tad: What do you think the chances are?

Carlene: We’re scientists. This is Jefferson National Laboratory.

Tad: Meaning?

Carlene: We wait and see.

1 To see an animation of any of the Friday illustrations online visit www.openbookpublishers.com/isbn/9781783740376#resources.

http://dx.doi.org/10.11647/OBP.0043.05