Teleportation and time-travel

Let’s assume:

1. Faster-than-light travel is metaphysically possible in a special relativistic world.

And let’s assume:

2. In a special relativistic world, no (inertial) reference frames are metaphysically privileged.

Now, if faster-than-light travel occurs, then one travels from space point z₁ to point z₂ during a length of time t < d(z₁, z₂)/c according to some reference frame F₁. The arrival location then is not in the light-cone centered on the departure point (and light-cones do not depend on reference frames). But if the arrival point is not in the light-cone centered on the departure point, then there is a reference frame F₂ according to which the arrival is earlier than the departure. (For the forward light-cone centered on a point a is just the set of points of space-time that are later than or simultaneous with a according to all frames. So if you’re not in the forward light-cone centered on a, you are earlier than a according to at least one frame.)

But no frame is privileged by (2). Moreover, if faster than light travel is possible, then faster than light travel is possible at any finite speed, since anything else would be unacceptably ad hoc. So if faster than light travel is possible according to F₁, it is possible according to F₂. So let’s suppose that you traveled from z₁ to z₂ and arrived −δ units of time earlier according to F₂ (for some δ > 0). Then add another spot of faster than light travel from z₂ to z₁, at a speed high enough to ensure you arrive at z₁ in δ/2 units of time. Then according to F₂, you moved from z₁ to z₂ and back to z₁ and arrive −δ + δ/2 = −δ/2 units of time after the beginning of your journey.

So according to F₂ you time-traveled backwards at the same spatial location. But backwards time-travel at the same spatial location in one reference frame implies backwards time-travel according to all frames (because it implies going into one’s backwards light cone).

So, we’ve argued:

3. If (1) and (2) are true, then it is metaphysically possible to travel absolutely backwards in time,

where absolute backwards time-travel is time-travel backwards according to all inertial frames. (I assume that most people working in philosophy of time know this.)

And there is good reason to believe (1) and (2). Indeed, (2) seems definitional. And (1) seems pretty plausible, especially given an omnipotent God. After all, surely God could make you travel to alpha Centauri and back by Christmas of this year. Note, though, that a part of (1)—and perhaps this is the controversial part?—is the possibility of a special relativistic world.

I am not sure what to make of this.

Three levels of theological models

There are three kinds of metaphysical models of a theological mystery—say, Trinity, Incarnation or Transubstantiation:

• realistic model: a metaphysical story that is meant to be a true account of what makes the mysterious doctrine be true

• potential model: a metaphysical story that is meant to be an epistemically possible account of what makes the mysterious doctrine be true

• analogical model: a story that is meant to be an epistemically possible account of what makes something analogous to the mysterious doctrine be true.

For instance, Aquinas’s accounts of the Trinity, Incarnation and Transubstantiation are realistic models: they are meant to be accounts of what indeed makes the doctrines true. Van Inwagen’s relative identity account of the Trinity or his body-snatching account of the resurrection, on the other hand, are only potential models: van Inwagen does not affirm they are true. And the history of the Church is filled with analogical models.

A crucial test of any of these models is this: Imagine that you believe the story to be true, and see if the traditional things that one says about the mystery (in the case of a realistic or potential model), or analogues of them (in the case of an analogical model), sound like reasonable things to say given what one believes.

For instance, consider a time-travel model of the Incarnation. Alice, currently a successful ultramarathoner and brilliant geologist, will live a long and fruitful life. Near the end of her life, she has lost most of her physical and mental powers, and all her knowledge of geology. She uses a time machine to go back to 2020 when she is in her prime. If we thought this story was true, it would be reasonable to find ourselves saying things like:

• Alice is a successful ultramarathoner and barely able to walk

• Alice understands continental drift and does not not know what magma is

• Alice is young and old

• Alice is in the pink of health and dying.

These things would sound like a contradiction, but the time-travel story shows they are not. However, these claims are also analogous to claims that constitute an especially mysterious part of the mystery of the Incarnation (and I suppose a mysterious part of a mystery is itself a mystery): Christ suffers and is impassible; Christ is omniscient and does not know everything; Christ is timeless and born around 4 BC.

Of course nobody should think that it’s literally true that the Incarnation is to be accounted for in terms of time travel. But what the analogical model does show is that there are contexts in which it is reasonable to describe a non-contradictory reality in terms that are very similar to the apparently contradictory incarnational claims.

Another really weird thought experiment

Suppose we accept a memory theory of personal identity and accept that people can be moved from one set of hardware to another. Now suppose Alice is an internally determinstic person, currently without inputs from the outside world, whose mental state is constantly backed up to a hard drive. Suppose now that Alice is a person who in hardware AliceOne has experiences E₀, E₁, E₂, E₃ at times 0,1,2,3, respectively. Then the initial hardware is destroyed, and the backup from just before time 2 is restored into another piece of hardware, AliceTwo, who goes on to have experience E₂. Then AliceTwo is destroyed, and a backup from just before time 1 is restored into AliceThree, who goes on to have experience E₁, after which all the hardware and the backups are destroyed by a natural disaster.

What is the order of Alice’s experiences? The obvious answer is:

• E₀, E₁, E₂, E₃, E₂, E₁ at times 0−5, respectively.

In particular, when Alice is experiencing E₂ for the second time, if she were informed of what is going to happen, she would be rationally dreading E₁ if E₁ is unpleasant. For E₁ would be in her future.

What makes it be the case that the second E₁ is experienced after the second E₂? It is the order of external time, according to which the second E₁ comes after the second E₂. It is not the order of causal connections in Alice (since the second E₂ comes from first E₁ while the second E₁ comes from the first E₀, and since there need be no causal connection between the hardware AliceTwo and AliceThree).

I think this is all a bit odd. To make it odder, let’s imagine that AliceTwo and AliceThree are in a room that time-travels in such a way that it is first at time 5 and then at time 4. Now, perhaps, Alice experiences the final E₁ before she experiences the final E₂. That’s really unclear, though.

The more I think about various combinations of time-traveling backups and time-traveling hardware, the more indeterminate it looks to me whether the final E₂ comes before the final E₁.

This is not much of an argument. But the above lines of thought lead me to think that one or more of the following is true:

1. Time travel is impossible.

2. People cannot be moved from one piece of hardware to another.

3. One does not survive restoration from a backup.

4. The order of experience does not have tight connections to rationality of attitudes.

5. The order of experience can be quite indeterminate.

Partial amnesia and fission

Some cases of partial amnesia present a prima facie problem for memory theories of personal identity (the theorist will bite the bullet on total amnesia, of course). At 9 pm, Bob starts to drink. At 11 pm, he makes a fool of himself. At midnight, he passes out. At 9 am, he wakes up remembering nothing that happened after 10 pm. Obviously, at 9 am, it’s the same person as the one who made a fool of himself the night before, but there is no chain of memories from the 9 am self to the 10 pm self.

There is a simple solution: don’t talk about chains of memories, but instead talk of chains of memory-links. Memories are unidirectional (you remember later what happened earlier) but memory-links are bidirectional: when at t₂ you remember what happened at t₁, there is a memory link from t₁ to t₂ as well as from t₂ to t₁. And now we have a chain of memory links: the morning-after self is memory linked to the 9 pm night-before self, and the 9 pm night-before self is linked to the 11 pm night-before self (Bob at 11 pm remembers starting to drink at 9 pm). So the morning-after self is the same as the 11 pm night-before self, much as he might wish he weren’t.

But here is an interesting thing. If we think about this scenario, formally this is a case of fission. There are two memory branches:

1. starting at 9 pm, then going on to 10 pm, 11 pm, and up to midnight, and then fizzling out forever

2. starting at 9 pm, then going on for a little bit, then skipping until 9 am.

So, partial amnesia cases like the above are actually cases of fission. And in cases of fission, most people do not want to say that we have the same person in the two branches. The most popular solution is that fission is death, and a second option is a four-dimensionalist one on which the occurrence of fission shows that there were two people there all along. But neither option is plausible for our partial amnesia case. It is absurd to say that Bob automatically dies around between 9 and 11 pm. And it is absurd to say that there used to be two people in Bob’s body all along. Those are extreme solutions that might fit science-fictional cases, but surely are not appropriate for all-too-common cases like Bob’s.

Perhaps we can say this: real fission requires there to be two simultaneous branches. So now our theory is this:

3. when memories branch, and the two branches are simultaneous, then something metaphysically weird happens (either there were two people before the branching or the pre-branching person has died).

But (3) fails in time-travel cases. Suppose Bob owns a time-machine. At 9 pm, Bob goes into a time-machine set for midnight. He keeps on drinking in the machine for two more hours, until 2 am. Then he passes out and loses the memory of the last two hours of drinking while the time-machines auto-pilot pulls him back to midnight and dumps him in his bed. We now have two branches starting at midnight: Bob drinking in the time-machine for two hours and Bob sleeping in bed with loss of memory of two hours of drinking. But it seems wrong to say that by adding a time-machine to the original partial-amnesia story, thereby making the two branches simultaneous, we would get the weirdness of having Bob perish or having always had two persons there.

Suppose you think backwards time-travel is impossible because of the paradoxes that result. You should still think of forwards time-travel as possible. Indeed, non-instaneous forwards time-travel is possible: that’s what happens in the twin paradox from relativity theory. But there is nothing logically absurd about instantaneous forwards time-travel. But any case of simultaneous-branch fission can be transformed into a case of non-simultaneous-branch fission by forward traveling one branch right after branching to a future time after the other branch has perished. Thus, we really shouldn’t treat simultaneous and non-simultaneous branchings differently.

I think this is a serious problem for memory theories of personal identity.

An argument against time travel or for temporal parts or for internal time

Start with this plausible claim:

1. If two objects are composed of the very same particles at the same time, then they have the same shape.

But now consider a statue of a horse that is reshaped into a statue of a tree and then time-travels back to sit besides the statue of the horse. Then the statue of the horse and the statue of the tree are composed of the very same particles at the same time, and yet they do not have the same shape.

I see three ways out of this paradox.

2. Deny the possibility of time travel.

3. Subscribe to temporal parts theory and modify (1) to speak of temporal parts of particles instead of particles.

4. Distinguish external and internal time, and qualify (1) to refer to internal time.

My preference is (4).

Asymmetric temporal attitudes and time travel

Philosophers sometimes use thought experiments concerning the asymmetry of attitudes towards future and past events as arguments for a metaphysical asymmetry between past and future. For instance, the fact that I would prefer a much larger pain in my past to a smaller pain in the future is puzzling if the past and future are metaphysically on par.

Here’s a thesis I want to offer and briefly defend:

• It is not rationally consistent to give use thought experiments in this way and to accept the possibility of backwards time travel.

The reason is quite simple: if backwards time travel is possible, our asymmetric attitudes track personal time, not objective time. If I am going to travel 100 million years back in six minutes, I will prefer a smaller pain in five minutes to a much larger pain 100 million years ago, since both of these pains will be in my personal future and only a minute of personal time apart. But the metaphysical asymmetry between past and future tracks external time, not personal time.

Looping and eternal pleasure

Scenario 1: You experience a day of deeply meaningful bliss and then are annihilated.

Scenario 2: You experience a day of deeply meaningful bliss and then travel back in time, with memories reset, to restart that very same day of an internally looping life.

Scenario 3: You experience a day of deeply meaningful bliss, over and over infinitely many times, with memories reset.

Here are some initial intuitions I have:

1. Scenario 3 is much better than Scenario 1.

2. Scenario 3 is at most a little better than Scenario 2.

But the following can be argued for:

3. Scenario 2 is no better than Scenario 1.

After all, you experience exactly the same period of bliss in Scenarios 1 and 2. Granted, in Scenario 1 you are annihilated, but (a) that doesn’t hurt, and (b) the only harm from the annihilation is that your existence is limited to a single day, which is also the case in Scenario 2. Time travel is admittedly cool, but because of the memory reset in Scenario 2, you don’t get the satisfaction of knowing you’re a time-traveler.

This is a paradox. How to get out of it? I see two options:

4. Deny the possibility of internal time loops.

5. Affirm that Scenario 3 is much better than Scenario 2.

Regarding 4, one would also have to deny the possibility of external time loops. After all, it wouldn’t be significantly all that different for you if everybody’s time looped together in the same way, and so external time loops can be used to construct a variant on Scenario 2.

I personally like both 4 and 5.

Objection: On psychological theories of personal identity, memory reset is death and hence in Scenario 3 you only live one day.

Response 1: Psychological theories of personal identity are false.

Response 2: Modify Scenario 3. Before that day of bliss, you have a completely neutral day. On each of the days of deeply meaningful bliss, you remember that neutral day, but then have amnesia with respect to the last 24-hour period once each blissful day ends. By psychological theories, there is identity between the person on each blissful day and the neutral day, and hence by symmetry and transitivity of identity, there is identity between the person over all the blissful days.

Note: Scenario 1 is inspired by a question by user “Red”.

The possibility of multiple incarnations

A classic theological question is whether it was possible for one person of the Trinity to be simultaneously multiply incarnate. The question is particularly important if it turns out that there are other non-human rational animals--namely, aliens--in need of redemption.

Here is an argument for this possibility:

1. An incarnation of a divine person is possible.
2. If an incarnation of a divine person is possible, multiple sequential incarnations of one divine person are possible.
3. If multiple sequential incarnations of one divine person are possible, multiple simultaneous incarnations of one divine person are possible.
4. So, multiple simultaneous incarnations of one divine person are possible.

Premise (1) is this: according to revelation an incarnation is actual, hence it is possible. Premise (2) is, I think, quite plausible. After all, if an incarnation is possible, it would also be possible for this incarnation to come to an end--a divine person could become incarnate as a mortal being, which perishes qua that kind of mortal being. But then it is very plausible that another incarnation could follow. And so on.

That leaves premise (3). Here I have two lines of thought. The first is the intuition that since God is outside of time, it really shouldn't matter with respect to possibility whether multiple incarnations are in sequence or simultaneous--in each case, the multiple incarnations create a relationship between a timeless being and several locations of spacetime. The second involves time travel. Suppose that there are two sequential incarnations. Then the rational animal that results from the second incarnation could travel back in time and meet the rational animal that results from the first incarnation, and then there would be two simultaneous incarnations.

Death is bad: An argument against cessationist models of resurrection

Consider cessationist models of resurrection. On these, the person who is saved completely ceases to exist at death--not even a core of the person, like a soul, continues to exist. But then some time later God resurrects the person to full existence, an existence that involves complete human fulfillment for an infinite amount of time.

Many Christian materialist models are cessationist. Perhaps God gathers the matter and forms it into something close to what the body was like at death in a way that ensures personal identity. Perhaps God gives the body at death a miraculous power of causing a future body at the time of resurrection. Or perhaps God arranges for the pre-death body (or some part of it) to time travel to the time of resurrection and replaces the original body with a simulacrum which we bury.

Now consider this argument:

1. Death is always a great harm for the person who dies.
2. Death is not a great harm on cessationist models.
3. So cessationist models are false.

In this post I am going to take (1) for granted, even though I know that a number of Christians deny (1). I want to focus on an argument for (2). Suppose Francis dies in his sleep and is resurrected a thousand years later. So: Francis goes to sleep. Next thing he knows, he wakes up resurrected, and much happier than when he went to sleep. Where is the harm in that? Sure, had he not been resurrected, it would have been bad for him. But given that he was going to be resurrected, it wasn't.

Maybe the harm is that there was a thousand years without Francis. But that sounds like a harm for the world, not a harm for Francis. Moreover, there were billions of years without Francis before Francis was conceived, and that wasn't bad for Francis. As far as Francis is concerned, he basically time-traveled by a thousand years into the future (cf. Merricks). Maybe we can worry that his heavenly existence is short a thousand years, but that seems mistaken: it's infinite, after all, and infinity less a thousand is no shorter than infinity.

Let me try to make the point perhaps more vividly. Consider two people, Hyacinth and Agnes. Both of them go to sleep in the evening at age 80, and neither has dreams.

Agnes has a heart attack in her sleep. But at the very moment that she would otherwise have been dead, the resurrection happens, so she never dies. Instead, she wakes up to heavenly life. The badness of death didn't touch Agnes since she never died.

A much more complicated thing happens to Hyacinth. He, too, has a heart attack in his sleep. But one second before he was going to die, he time-travels to a time one second before his conception (or whatever point marks the beginning of a human being's life). He lives for one second then, albeit asleep, and then dies. Eighty years later the resurrection happens. Coincidentally, the resurrection happens the moment right after Hyacinth was whisked back in time.

Hyacinth died but Agnes didn't. However, notice that Hyacinth actually exists at every moment of time from his conception onward. He also has that weird little extra one second of existence before his conception due to time travel. But surely that's insignificant. It doesn't seem that Hyacinth is noticeably worse off--or even at all worse off--than Agnes.

But now compare Hyacinth to Francis, who dies in his sleep 80 years prior to the resurrection without any time travel. Both Hyacinth and Francis die 80 years before the resurrection. The only difference is that for Hyacinth, that death 80 years before the resurrection takes place just before Hyacinth's conception. But surely that doesn't make Hyacinth significantly better off than Francis. Francis and Hyacinth are roughly on par in how well off they are. And by the same token, Francis and Agnes are roughly on par. But Francis dies and Agnes doesn't. So death isn't bad for you on the cessationist model.

What models of resurrection make death be bad for you? I think it's models on which you continue to exist between death and resurrection but in a way that is importantly diminished. For instance, a dualist can say: It's really bad to lose your arms. But when you die, you lose your arms, so dying is really bad. And you also lose your legs, your eyes, your ears, etc. (You even lose your brain though maybe God miraculously supplies the mental functions that we normally need a brain for?) Granted, you are more than amply compensated by union with God, but that a bad is compensated for does not make it not be bad. Similarly, a non-cessationist materialist could think that God snatches your brain out of your body just prior to death, replaces it with a replica, and then makes you literally be a brain in a vat in heaven. Such a non-cessationist materialist would be able to say why it is really bad for you to die, because you lose your arms, legs, eyes, ears and most of your body, except your brain.

Infinite causal histories and causal loops

As I was thinking about causal finitism, the view that nothing can have an infinite causal past, I realized that there were structural similarities between the arguments for it on the basis of paradoxes like the Grim Reaper and Grandfather-like arguments against causal loops. And that led me to thinking whether there wasn't some way to generalize causal finitism so as to rule out both infinite causal pasts and causal loops.

There is. Here is one way. Say that a causal nexus is a network of nodes with partial-causation arrows between them, such that there is an arrow A→B if and only if A is a partial cause of B (or causally prior to? I think that's the same thing, but I'm not sure; or, if there is such a thing, directly causally prior to). Say that a monotonic sequence in a causal nexus is a finite sequence A₁,A₂,...,A_n of nodes such that each node is joined with an arrow to the next: A₁→A₂→...→A_n. The sequence culminates in A_n. Note that if there are causal loops, then a monotonic sequence can contain the same node multiple times.

The generalization of causal finitism now says:

• No metaphysically possible causal nexus contains a node that is the culmination of infinitely many monotonic sequences.

This rules out three kinds of causal nexuses:

1. Infinite regresses: longer and longer monotonic sequences of distinct nodes culminating in a given node.
2. Infinite cooperation: infinitely many arrows pointing to a single node (and hence infinitely many monotonic sequences of length two culminating in it).
3. Causal loops: longer and longer repeating monotonic sequences culminate in a given node (e.g., A→B, B→A→B, A→B→A→B, ...).

The possibility of handling infinite causal histories and causal loops--which I've long thought absurd--in the same framework makes me even more confident in causal finitism.

Living in the moment, literally

Jim lives for a minute. Then he activates the time-and-space machine in his backpack, and travels to position one minute back and one meter back. Then the story repeats, giving Jim a lifespan of 80 internal years, all contained within a single minute of external time.

We could shorten that minute of external time to a second, or to any non-zero length of time, by making him jump back in time even faster.

Bold Hypothesis: We could shorten it to zero.

This works most easily if Jim is made out of ghostly matter that can overlap itself (nothing absurd about this: two photons can be in the same place at the same time), and as we shorten the time interval, we shorten the spatial distance of the jump.

The Bold Hypothesis basically says that just as one can have a time-travel machine, one can have a time-non-travel machine that keeps one in the same place in external time for all one's life.

Given the possibility of time travel, and the possibility of discrete time, it's not hard to argue for the Bold Hypothesis. Suppose at each instant of time, Jim can set the time-machine to determine where he will be in the next internal instant. Then why couldn't he set it so that in the next internal instant he will be at the same external instant as he is now.

Given the Bold Hypothesis, Jim would have a lifespan of 80 internal years, all in one moment.

All this suggests that when thinking about time, we should be careful with moving from our subjective experience of time and change--which Jim would have in his all-at-one-moment life--to claims about what external time is like.

Internal time, external time, probability and disagreement

Suppose that Jim lives a normal human life from the year 2000 to the year 2100. Without looking at a clock, what probability should Jim attach to the hypothesis that an even number of minutes has elapsed from the year 2000? Surely, probability 1/2.

Sally, on the other hand, lives a somewhat odd human life from the year 2000 to the year 2066. During every even-numbered minute of her life, her mental and physical functioning is accelerated by a factor of two. She can normally notice this, because the world around her, including the second hands of clocks, seems to slow down by a factor of two. She has won many races by taking advantage of this. An even-numbered external minute subjectively takes two minutes. Suppose that Sally is now in a room where there is nothing in motion other than herself, so she can't tell whether this was a sped-up minute or not. What probability should Sally attach to the hypothesis that an even number of minutes has elapsed from the year 2000?

If we set our probabilities by objective time, then the answer is 1/2, as in Jim's case. But this seems mistaken. If we're going to assign probabilities in cases like this—and that's not clear to me—then I think we should assign 2/3. After all, subjectively speaking, 2/3 of Sally's life occurs during the even-numbered minutes.

There are a number of ways of defending the 2/3 judgment. One way would be to consider relativity theory. We could mimic the Jim-Sally situation by exploiting the twin paradox (granted, the accelerations over a period of a minute would be deadly, so we'd have to suppose that Sally has superpowers), and in that case surely the probabilities that Sally should assign should be looked at from Sally's reference frame.

Another way to defend the judgment would be to imagine a third person, Frank, who lives all the time twice as fast as normal, but during odd-numbered minutes, he is frozen unconscious for half of each second. For Frank, an even numbered minute has 60 seconds' worth of being conscious and moving, while an odd numbered minute has 30 seconds' worth of it, and external reality stutters. If Frank is in a sensory deprivation chamber where he can't tell if external reality is stuttering, then it seems better for him to assign 2/3 to its being an even-numbered minute, since he's unconscious for half of each odd-numbered one. But Frank's case doesn't seem significantly different from Sally's. (Just imagine taking the limit as the unconscious/conscious intervals get shorter and shorter.)

A third way is to think about time travel. Suppose you're on what is subjectively a long trip in a time machine, a trip that's days internal time long. And now you're asked if it's an even-numbered minute by your internal time (the time shown by your wristwatch, but not by the big clock on the time machine console, which shows external years that flick by in internal minutes). It doesn't matter how the time machine moves relative to external time. Maybe it accelerates during every even-numbered minute. Surely this doesn't matter. It's your internal time that matters.

Alright, that's enough arguing for this. So Sally should assign 2/3. But here's a funny thing. Jim and Sally then disagree on how likely it is that it's an even-numbered minute, even though it seems we can set up the case so they have the same relevant evidence as to what time it. There is something paradoxical here.

A couple of responses come to mind:

• They really have different evidence. In some way yet to be explained, their different prior life experiences are relevant evidence.
• The thesis that there cannot be rational disagreement in the face of the same evidence is true when restricted to disagreement about objective matters. But what time it is now is not an objective matter. Thus, the A-theory of time is false.
• There can be rational disagreement in the face of the same evidence.
• There are no meaningful temporally self-locating probabilities.

Can A-theorists believe in time travel?

I used to think that A-theorists cannot consistently believe in time travel. I think I was mistaken. As best as I can reconstruct my line of thought it was this. Time travel requires a distinction between external and internal time. If I go into a time machine, then maybe in five minutes I'll be a thousand years ago. That's a contradiction given non-circular time unless one distinguishes as follows: internally in five minutes I'll be a thousand years ago externally. But now I think that what I must have been thinking was that in five internal minutes my internal present will no longer line up with the world's objective present, since in five internal minutes my internal present will be about thousand years behind the world's external present. I don't know for sure if that's the thought I had, but if it was, it would have been a howler. For on the view, internally in five minutes, I will be at the time at which the world's external present was about a thousand years ago. Or, to put it from the external point of view, a thousand years ago I was five minutes older than I am now (age is measured internally). Even presentists can say that.

To see that this is coherent, consider a theory that takes external time to governed by the A-theory but internal time to be entirely governed by the B-theory. Thus, superimposed on the external A-series of past, present and future, there is an indexical B-series of earlier-for-me and later-for-me, where these relations are perhaps defined by internal causal relations (earlier states causing later ones). There is no more need for these two series to line up than there would be a need for the two series to line up if the external series were a B-series.

However, while this is coherent, maybe it undercuts one of the main motivations for the A-theory. For if there is a distinction between internal and external time, as there must be for time travel to be possible, all the changes we actually experience are changes with respect to internal time. In other words, they are B-type changes. But the typical A-theorist thinks B-type changes--it (internally) earlier being one way, and (internally) later another--are not what we experience when we experience "real change". Indeed, if time travel is possible, it is possible to live all of one's life at one external time, but moving through external space. Basically, just imagine that at each moment you travel to some external time t₀, but to a different spatial location in it. Maybe you have a backpack time-machine which is permanently stuck on t₀, but with the spatial locations changing. You'd experience change, because your state at internally earlier times will be different from your state at internally later times. But it would be mere B-type change, since it would all be happening at one and the same objective time.

I suppose one could say that in time-travel scenarios, especially the preceding one of living all of one's life at one external time, our experiences of change become non-veridical, for a condition on the veridicality of our experiences of change is that our internal clock lines up correctly with external time, and time-travel causes a misalignment. Maybe.

But in any case, now that we have the possibility of living all of one's life--a life that presumably could have rich causal interconnections--at one objective external time, just moving "sideways" to new spatial locations, I do think that the motivations for the A-theory decrease. For we see that what matters for the diachronic richness of our lives is that our lives be stretched over internal time, not over external time. It also matters that other people's internal times be sufficiently lined up with ours. But that doesn't call for the A-theory, either.

So, all in all, while A-theorists can believe in time travel, thinking time travel through would undercut much of the motivation for the A-theory.

An argument against the possibility of instantaneous causation

Instantaneous causation is causation where the cause and effect both occur at the same instant. It's a species of simultaneous causation, with the added condition that the events are instantaneous.

Suppose that instantaneous causation is possible. Then the following are compossible characters: the Judge, who instantaneously stamps death warrants, and the Executioner, who executes the person listed on the warrant in such a way that the very instant that the death warrant is stamped, the person is dead. Moreover, the Executioner takes no orders from dead people: she only executes people if the Judge was alive at the instant the warrant was stamped, and she executes no one else.

There is no metaphysical absurdity if the Judge stamps a warrant for your death—there is "merely" an injustice. But what if the Judge stamps a warrant for his own death?

Then, instantaneously, the Executioner executes the Judge. But then the Judge wasn't alive to stamp the warrant (and if he stamped it posthumously, then that doesn't count). But with no warrant stamped, the Executioner didn't do anything. And so the Judge both is and is not executed, which is absurd.

Now, we might conclude from this just that it's not possible for the Judge to stamp a warrant for his own death. And we could tell stories similar to banana-peel stories from the Grandfather Paradox: if the Judge were to go to stamp his own death warrant, he'd slip on a banana peel, or the stamp would be out of ink, or some other such thing would happen. But many philosophers are unsatisfied with such stories. It sure seems like it's no harder in principle (though it may be psychologically harder, though only if he knows it's his) for the Judge to stamp his own warrant than anyone else's.

It seems that a particularly good way to explain the impossibility of the setup, without any banana peels, is that instantaneous causation is not possible. In any case, people who think the Grandfather Paradox establishes the impossibility of time travel should think that this argument establishes the impossibility of instantaneous causation.

But what about the intuition one might have that instantaneous causation is possible? Here is a suggestion. Let the date of an event E be the temporal duration between the beginning of the universe and the event. (If the universe has no beginning, choose some other base for dates, with dates before it being negative.) Then our intuition that instantaneous causation is possible can have some justice done to it by saying that it is possible to have causation where the cause and effect have the same date, even though they are at different instants. These instants, then, have no duration between them. Thus, we could have the Judge and Executioner story work like this. There is a duration T (say, in seconds) from the beginning of the universe at which there is an instant, a, at which the Judge stamps his death warrant. And with no temporal gap, no duration in between, there is another instant b, at which the Judge is dead, also duration T after the beginning of the universe. (And between a and b there will be other instants, such as the instant when the Executioner sees the stamping and the instant when she initiates the causal process that kills the Judge. Quite possibly, in this story time is not dense.)

This does some justice to our intuition that there can be instantaneous causation. It's not quite instantaneous causation, but it's causation with no temporal extension, no temporal gap.

Acknowledgment: I got the warrant-stamping from Jon Kvanvig. It works better rhetorically than the instantaneous writing of the warrant that I initially had in mind.

A theory of time

This isn't meant to be a very good theory, but it's a start. The primitive notion I want to explicate is this notion of temporal priority between events: A is at least in part earlier than the start of B. I will abbreviate this to "A is earlier than B". And then we say that A is earlier than B if and only if there is a chain of at least partial causation starting at A and ending at B.

A consequence of this theory is that it is not possible to have simultaneous causation: if A causes B, then A is earlier than B. That's a count against it, but perhaps not a fatal one.

Another consequence of this theory is that it gives no account of simultaneity between events. That may not be such a bad thing.

A limitation is that we have no notion of a time, just of temporal ordering of events. That may be fine. But the costs are adding up.

I am more troubled by the fact that this rules out time travel and, more generally, temporally backwards causal influences. This makes me want to reject the theory.

But I can reprise the theory, not as a theory of the temporal priority between events, but of the temporal priority between accidents (or maybe just modes?) of a single substance. Just say that an accident A of a substance S is earlier than an accident B of S if and only if there is a chain of at least partial causation between accidents of S starting at A and ending at B.

We still have to rule the possibility of temporally backwards causation within the life of a single substance. But that's less costly, I think, than ruling out temporally backwards causation between events in general.

We still have the problem of not having simultaneous causation or any account of simultaneity for that matter. And no notion of times.

We can introduce times as follows. In some worlds, it will happen that there are nomic relationships between the accidents of a substance that are simply parametrized in terms of some parameter t such that accident A is earlier than accident B (in the above causal sense) if and only if t(A)<t(B). In such a case, we can call values of this parameter times. In worlds where there is no such neat parametrization, there may be temporal priority, but no times.

We get divine internal atemporality now as a corollary of the claim that God has no accidents.

But there are still a lot of costs. For one, the lack of a notion of simultaneity makes it hard to make sense of the transcendental unity of apperception. Maybe that's just too bad for that unity?

Punishment, time, and a poor objection to identity after fission

It is a truism that the punishment should follow the crime. Thus, even if you know with enough certainty for court conviction that Smith will commit a crime, that is not enough for punishment.

But we need a qualifier. Punishment only needs to follow the crime in internal time. Smith builds a time machine while in prison and travels to 160 million BC. Now, there is a small police outpost in 160M BC, protecting time-traveling scientists from nefarious time travelers, and there is a small jail. It turns out that backwards time travel is much cheaper than forwards time travel (at any decent speed, measured in the ratio of external to internal time). To send Smith back to his time would be prohibitively expensive. There would be no injustice in jailing him in the year 160M BC, notwithstanding his protestations that he hasn't committed any crimes yet. For that's only true according to external time, since by his internal past, he had committed crimes.

Now, consider an apparent case of a person fissioning, say due to a Star Trek transporter malfunction. I used to argue that it is not tenable to suppose that the result of that is a single bilocated person on the grounds that it would be then be appropriate to punish the person in one location for what their copy in the other location did, which seems absurd. But I now think this argument is mistaken. For on the hypothesis that the person comes to be bilocated, we should now think of the person's internal time as having different branches corresponding to each location (this can best be seen by noting that we can run twin paradoxes between them). But then it is false that the person in location A can be justly punished at t₂ for what the person in location B had done at an earlier time t₁. For punishment should follow the crime in internal time. But since the two internal timelines are parallel, what B did is neither earlier than, nor simultaneous with, nor later than the punishment of A—there is no comparison between these internal times. Of course the external time of the punishment is later than the external time of the crime, but that is irrelevant. If parents took a 14-year-old Hitler for a time-travel excursion to our time, it would be wrong for us to now punish the young Hitler for the crime he had committed in the 1930s, since those crimes would not be earlier than the punishment in his internal time.

So while there might be objections to identity-after-fission, the punishment objection is not very strong.

One qualifier: It would not be wrong to set things up so that the punishment would be simultaneous with the crime, as long as the crime caused the punishment in the right way. So where I say that the punishment should follow the crime, I should include the possibility that the two are internally simultaneous, but with the crime explanatorily prior.

"Wholly present"

Here's something I've been thinking about. I want to start with the technical notion of being located at a region. This notion allows for partial location. If I have one leg in Arkansas and one in Texas, then I count as located in Arkansas and located in Texas. If regions have points, then I am located at a region if and only if I located at some point in the region (maybe that's a more primitive notion).

I'd like to move from the notion of being located at a region to the notion of being wholly present in a region. I am now wholly located in Texas, but if I had a leg in Arkansas and a leg in Texas, I would be wholly located in neither.

I could take the notion of being wholly present as primitive. But I don't want to do because it's a three-dimensional notion, while I think I am a four-dimensional entity, so to me it's a derivative notion.

One obvious thing to say is:

1. x is wholly present in A iff x is located at A and not located outside A.

This rules out multilocation—being wholly present at two distinct regions—by fiat. In so doing, it rules out both my view of the doctrine of transsubstantiation (since on my view, it is literally true that Christ is wholly spatially present in different places[note 1]) and the possibility of backwards time travel (since if you can travel back in time, you could be wholly present in two places, and shake hands with yourself).

A plausible move is to introduce parts or, more generally, features (the blueness of my eyes is a feature but not a part) and their locations (I stipulate that every part, proper or not, is a feature). Maybe, then:

2. x is wholly present in A iff every feature of x is located at A.

While this works for transsubstantiation, it doesn't work for time travel. For suppose that tomorrow I lose a leg, and I travel back to today, so that I am in another room in addition to this one. Then it is false that every part of me is located in that other room, since the lost leg isn't there.

There is another interesting problem with (2) and time travel. Suppose that in ten seconds I travel back to the present, so that I am wholly present in two disconnected rooms, and suppose that in the ten seconds I have neither lost nor gained any features. Let A_L be the left half of the space occupied by me in one of the rooms and B_R be the right half (including the cut line—don't put the cut line in A_L) of the space occupied by me in the other room. Let C be the disconnected region that is the union of A_L and B_R. Then by (2) I am wholly present at C as every one of my features is in either A_L or in B_R or in both. But surely I am not wholly located in the messy region C.

At this point things get difficult. My best solution today is moderately complex (but not as complex as my best solution yesterday). It requires the introduction of two sets of times for a persisting substance. There are internal times, which correspond to the internal development of the substance, and there are external times, which correspond to what goes on in the external world. Normally, the two are nicely correlated. But time travel discombobulates things. If in one minute I travel 24 hours into the future, then in one internal minute I will be 24 external hours forward. And if in a minute I travel 24 hours into the past, then in one internal minute it will be externally yesterday.

Now, take the case where I am right now in room A in the normal way, but in room B due to having time-traveled back to that room after losing a leg. Let T be the present external time. There are two internal times associated with t. At internal time t₁, I am in room A, and at internal time t₂, I am in room B. Moreover, at t₁, I have two legs, though at t₂ I only have one. I guess at the external time T, I have two legs. My being wholly present in B does not require that I have both of my legs in B. It only requires that I have in B all the legs that I have at the internal time t₂.

This yields the following pair of definitions:

3. x is wholly present in A at its internal time t iff every feature that x has at t is located at A at t.
4. x is wholly present in A at external time T iff there is an internal time t of x such that (a) x's internal time t is externally at T and (b) x is wholly present in A at t.

This gives the right answers with respect to (a) transsubstantiation, (b) time-travel and loss/gain of parts, and (c) time-travel and the union of the A_L and B_R regions.

The account does, however, have the consequence that if x is an extended simple with all features spread over all of x (so, x is the same color all over, etc.), then it counts as wholly present at every point at which it is located. This consequence is perhaps not so plausible, but I can live with it.

Time travel and interlibrary loan

The following argument is valid. I don't vouch for soundness!

1. (Premise) If I ought to A, then I can A.
2. (Premise) If I have received an interlibrary loan item, I ought to return it on or before its due date.
3. (Premise) If I can return an item on a date before today's date, then time travel is possible.
4. (Premise) Today I have received an interlibrary loan item due on March 8, 2011.
5. So, I ought to return an item on or before March 8, 2011.
6. So, I can return an item on or before March 8, 2011.
7. (Premise) Any date on or before March 8, 2011 is before today's date.
8. So, time travel is possible.

Premises (3), (4) and (7) appear to be true.

Grandfather paradox

Suppose I went back in time and tried to shoot my grandfather before my father was conceived. Then either I would hit or I would miss. If I hit, absurdity results. What is less discussed in the literature is that if I miss, absurdity also results. Suppose that I miss due to sloppy aiming. (This is the case most favorable to my argument. But I think a similar story can be told for other causes of missing.) Then, my sloppy aiming is explanatorily prior to my grandfather's survival. But my grandfather's survival is explanatorily prior to my existence, and hence to my sloppy aiming. Hence, we get an explanatory circle, which is absurd.

Truth as knowledge in the ideal limit

Suppose that the truth is what is (the optimistic version) or would be (the counterfactual version) known (by beings like us) in the ideal limit. In both cases, it seems there are things I know that aren't true, which is absurd. For instance I know that on the table beside my laptop there is right now a water bottle arranged thus-and-so relative to a used wet wipe.

Or was. For I just threw out the wet wipe, and moved the bottle. In a week or a year, most likely I'll forget how these were arranged. It's already starting to fade a little. I don't expect to tell anybody. So, here is something I knew: The water bottle and the wipe were arranged thus and so at 8:17 am on September 2, 2009. Is this something that would be known in the ideal limit? I doubt it. While the powers of science will grow in the progress to the ideal limit, the facts about the water bottle and the wipe will recede into the past, and their traces will be covered up. For a while, the fact could be pulled out from my brain by careful investigation of the memory structures. But presumably eventually the brain will rot (unless the Second Coming comes first). It may be true that the rotted matter will be slightly differently arranged for this memory. But the difference will be harder and harder to discover as time goes on.

Suppose this argument succeeds. And suppose that I accept the ideal limit theory of truth. Then I should say: "I know p but p is not true." And a theory of truth that implies that is absurd.

There are two ways out of this predicament for the ideal limiter. The first is to deny that the ideal limit for all true propositions is reached at the same time, at the culmination of science. The ideal limit for some propositions, such as that the items on the table were arranged thus-and-so, is reached much earlier, say, now. One way to try to do this is to say that the ideal limit has been reached for p at t provided that p is believed by someone at t, and in the course of progress towards an ideal science, an undefeated defeater for p will never be found. An obvious problem, however, is that I might form a false belief about some really trivial matter, then forget the belief, and the course of ideal science would never be able to recover the situation from the rotting matter of my brain to provide a defeater. A further problem is with conjunctions. For let q be some proposition that is known only when science is completed. Then, p and q are both true, and hence their conjunction is true. But their conjunction is never known.

The second, which Jon Kvanvig offered me, is to say that the ideal limit involves time travel. We even have an argument for the possibility of time travel: Truth is ideal-limit knowledge; it is true that the bottle and wipe were arranged thus-and-so; therefore that they were arranged thus-and-so is known in the ideal limit; the only way this could be known in the ideal limit is by time travel; hence, time travel is possible. Now there seems to be something very fishy about a theory of truth that, when conjoined with trivial observations, implies the scientific claim that time travel is possible. Moreover, it is surely true that nobody is time traveling to my home on 8:37 am on September 2, 2009. But if in the ideal limit there were such time travel, as the hypothesis suggests, then we have a truth that isn't true: namely, that nobody is time traveling to my home on 8:37 am on September 2, 2009.