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With time travel and the Grandfather Paradox (where you go back in time and kill your own ancestors), a fiction author can define whatever rules make the story work, but ideally, those rules are logically consistent or you get a "story by author fiat". If there is going to be a single, mutable timeline, then there are generally two options that logically work:

  1. a time travel deletes all later arriving travellers (implicitly resetting the timeline to the state before all changes of them occurred) or
  2. the arrival of a time traveller is a kind of fixed point. That means that after several changes the timeline will be full of arrivals from no longer existent timelines.

I don't like either of these two possibilities. In fictional works about time travel I know (who are single mutable timeline) these problems are ignored (or do not occur due to the story). But I don't want to ignore it.

So is there another option I miss how this can be handled in a logically consistent way?

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    $\begingroup$ "Does every travel back in time..." Yes, if that's how you define your rules/laws for time travel in your world. I'm confused about what you're looking for from the community. $\endgroup$ – Frostfyre Jan 12 '17 at 13:33
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    $\begingroup$ In the known universe there is no such thing as time travel. Therefore if in your story some characters are time-travelers then how exactly time travel works is defined by you, the author. You make the rules, you follow them and you break them if you want to. $\endgroup$ – AlexP Jan 12 '17 at 13:36
  • $\begingroup$ Well, it's time travelling stuff is always timey wimey wibbely wobbley, but if time travel in your story works like this... your world, your rules. $\endgroup$ – Alexander von Wernherr Jan 12 '17 at 13:37
  • $\begingroup$ Your grandgrandfather must have been a horrible child. $\endgroup$ – Mike Clark Jan 12 '17 at 16:27
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    $\begingroup$ "Does every travel back in time "overwrite" and "delete" any later arrivings of time travellers?" In a single mutable timeline, yes earlier actions will always overwrite later ones. This can be conceptualised as a series of nested temporal superpositions. Keeping track of the causality is an absolute nightmare. $\endgroup$ – a4android Jan 13 '17 at 0:58
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There is another option I have never seen used in fiction: understand what the time machine is really doing with respect to conservation of matter. The reason that time travel paradoxes arise is that we focus on macroscale elements, like a person (who may not be conserved), instead of microscale elements, like atoms (which definitely will be conserved by Conservation of Matter laws).

Let's consider a single atom going back into time first.

At 3pm, there's a single atom, Alpha, happily bouncing around. At 9pm, John sends Alpha back to 3pm. Now there are two Alphas bouncing around. Let's call them Alpha+0 and Alpha+6 since the second one is subjectively 6 hours older. Six hours later, the time is 9pm again.

If Alpha+6 didn't change history, then John sends Alpha+0 into the past -- no paradox, no complication. After 9pm, Alpha+6 is now the only instance of Alpha in the world.

But perhaps Alpha+6 did change history and John isn't around any more to run his experiment. Now what happens? In my idea, Alpha+0 STILL GOES INTO THE PAST. Alpha+0 might not be at the machine, and John might not be around, but Alpha+0 still exists somewhere in the world. In my idea, once John has created a wormhole-like connection from the present to the past, that connection exists, regardless of how the past changes. The wormhole endpoint is moved around such that at 9pm, it is always in the location of Alpha+0 and so Alpha+0 always goes to the past, even if Alpha+0 is part of some other molecule in the new timeline.

Let's say Alpha+0 was an oxygen atom. In the original time, it was a free oxygen, not part of any molecule. In the new time, because of Alpha+6 interference, Alpha+0 gets bonded with two hydrogen to become water. Doesn't matter. At 9pm, that wormhole opens up and swallows the oxygen, cutting the two hydrogen loose.

Now, let's consider sending a person back. At 3pm, John and Mary have tea. John convinces Mary to be the first time traveler. Mary drinks her tea and agrees. She comes to the lab. At 9pm, John sends Mary back to 3pm. There are now two Marys in the world... Mary+0 and Mary+6.

If Mary+6 wanders off somewhere and doesn't interfere with her own timeline, then eventually it is 9pm again, and John sends Mary+0 into the past, leaving Mary+6 as the only Mary in the world once again. Great!

BUT... what happens if Mary+6 does interfere with her own past? Mary+6 goes to that tea -- before they drink their tea -- and tells Mary+0 that John is not to be trusted. Mary+0 runs away, and she's so sick to her stomach from fear that she vomits on the sidewalk. She drinks some water to clear the taste. John has to find a new candidate. What happens then?

Well, at 9pm, the atoms that make up Mary+0 all fall into wormholes and travel back to 3pm. Not just those atoms. But also the atoms of the tea that Mary+0 would have drunk. And the atoms of the vomit that were originally in her. But NOT the water that she drunk in the changed time. All the atoms go back in time and arrive at the same point that they were sent originally -- which means they arrive configured like Mary+6, with all the memories of Mary+6.

No matter how much Mary+6 changes the past, the atoms that make up her will always travel back in time and arrive arranged as Mary+6.

There's no change she can make that will alter that fact. We get caught on paradoxes because MARY isn't conserved -- she can be disrupted from one timeline to the next. But we can get out of the paradoxes because THE ATOMS THAT MAKE UP MARY are conserved. The only way those atoms don't exist in the alternate timeline is if they somehow undergo fusion or fission. It is trivial to add to our time travel physics the rule, "Any atom entangled with a time-travel wormhole has enough energy to maintain its coherence... you can heat or pressure it as much as you want, but it won't undergo fusion or fission while it has a date with destiny."

Important: This conservation of atoms concept means that even if time is changed to prevent the time machine itself from being constructed, the time travel will still occur. All the machine does is open the wormholes. Once they're open, they stay open.

It also means that if the time traveler changes history enough, his/her atoms could be a part of important things in the new present, things that will suddenly have holes in them for no apparent reason when those atoms are pulled into the past. There's a lot of story potential there.

If you use this idea in a story, I really want to read it. I've tried to make it work but never quite got it working right. :-)

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    $\begingroup$ Time travel that respects the conservation of matter. In that case, let me direct to the works of William Tenn who wrote several time travel stories where the conservation of matter was involved. Most especially, "Winthrop was Stubborn" where this was a key part of the story. $\endgroup$ – a4android Jan 13 '17 at 0:50
  • $\begingroup$ I will check it out! @a4android $\endgroup$ – SRM Jan 13 '17 at 0:54
  • $\begingroup$ It's 1950s SF, so the scientific details are more relaxed. Precisely how it works is left open. But, at least, he recognized the problem. $\endgroup$ – a4android Jan 13 '17 at 1:02
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    $\begingroup$ Great improvement! This really clarifies the concept. I'm familiar most time-travel concepts, but this is quite new. Definitely plus one. $\endgroup$ – a4android Jan 13 '17 at 7:33
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    $\begingroup$ @everybithelps Yes. That is EXACTLY the consequence. :-) $\endgroup$ – SRM Jan 13 '17 at 16:35
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If your grandgrandfather is killed and you're in a self-righting timeline you could just get assigned a new one. For instance:

1)Other Time Traveler shows up in X - 50 and kills some kid that would have been you're great-grandfather.

2)Rubber band timeline kicks in and you original great-grandfather's brother end up marrying your great-grandmother.

3)They have a kid who is in terms of genetics, upbringing, and temporal placement almost indistinguishable from your original grandfather, who will (if allowed to live) grow up to have a child with your original grandmother who will grow up to have you with your other original parent.

4)You show up at X and kill this child.

Most people are replaceable to some degree, so if the universe needs to "draft someone in" to make sure both you and the other time-travelers action are possible it shouldn't be hard.

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    $\begingroup$ You have failed to grasp the point this is time-travel in a single mutable timeline. This answer deals with self-consistent determinism (more or less). $\endgroup$ – a4android Jan 13 '17 at 0:52
  • $\begingroup$ @a4android it can be a single, deterministic, mutable timeline. There's no dichotomy in that. $\endgroup$ – user32063 Jan 13 '17 at 15:20
  • $\begingroup$ Your model is basically a deterministic timeline.. Something like Fritz Leiber's Conservation of Events concept. This is self-consistency where that are an infinite number of pathways to achieve a given outcome. This evades mutability. What if a third traveller shows up & kills both time travellers & all male and female great-grand relatives? How soon will you run out of replacements? David K Lewis considered something would always happen to stop the past changing including your replacement model. $\endgroup$ – a4android Jan 14 '17 at 4:44
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In time travel it's important to keep track of causality. That is, what is it that causes these seeming paradoxes to happen?

In your example, if you go back in time and kill your grandfather, you are without cause. There is nothing in the new universe that leads to your journey to the past, because 'you' never actually existed. From this, I can see two options:

1 - There can only be one time travel at a time. That is, when you go back in time, the universe is set up, and runs from there as it would normally. If another time traveler has already made the journey, they still exist, but anyone who would have come later cannot exist, because there is nothing in the universe that causes their existence.

2 - Time travels are 'baked in' to the universe. In this version, the journeys through time are weaved into the timeless fabric of the universe. If you go back to the 40s to kill Hitler, you will in all possible iterations of this universe go back to the 40s to kill Hitler, regardless of whether or not someone else kills him first. The problem with this approach is that there is a vanishingly small chance that you will go back to your own past. As the number of time travels approaches infinity, so too will the versions of yourself, appearing in different versions of wherever you were trying to go. In fact, assuming that the universe resets itself each time, every time traveler would appear in the universe created by the last time traveler, which would be a universe where time travel does not happen. Potentially someone went back to the beginning of life on Earth and destroyed it, leading all time travelers to suffocate on a dead planet.

I'd recommend the first option.

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    $\begingroup$ You have failed to grasp the point this is time-travel in a single mutable timeline. This answer deals with self-consistent determinism (more or less). $\endgroup$ – a4android Jan 13 '17 at 0:53
  • $\begingroup$ Your answer is exactly what the original question said were unacceptable answers! :-) I have edited the question to make this more obvious. If you have a better solution, edit your answer to answer the actual question. $\endgroup$ – SRM Jan 13 '17 at 7:28
  • $\begingroup$ @SRM My answer attempts to explain that a 'single mutable timeline' is going to have problems either way. Sometimes the right answer is that it just won't work. In fact, I think my answer shows the issues with the currently highest-voted answer. $\endgroup$ – DaaaahWhoosh Jan 13 '17 at 14:23
  • $\begingroup$ @daaaahwhoosh I agree you highlight the problems, but our challenge from the OP was to find a way around those problems. Your answer #2 is essentially the same as my answer, but the "baking in" occurs at the level of atomic physics, thus allowing for mutability at the human scale. $\endgroup$ – SRM Jan 13 '17 at 15:20
  • $\begingroup$ @SRM I would like to point out that I posted my answer first. And that I don't think your answer adequately addresses the concerns I raised. But your answer is accepted, and I think mine is valuable enough to not delete, so I'm willing and/or prepared to leave things as they are. $\endgroup$ – DaaaahWhoosh Jan 13 '17 at 15:32
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There are a lot of possibilities in the way time actually is (we don't know what is true).

  1. There are models saying that everything is predetermined, so sort of static
  2. It could be non-deterministic and just one line, so traveling back in time makes it so you don't have the intention to travel back, because it already was changed, so it isn't changed at all (we don't know which state will be true in the end)

That is the way I would think of your time theory to develop, I don't really get how a single timeline is changeable by a big deal as any thing that you do in the past stops you from having the intention in the future -> no time travel.

The only why I could image it is your time traveller self getting destroyed as soon as you change the past as that consciousness of yours doesn't exist in the timeline anymore and only the changed one will live on (none as you would not be born). So you will come out of thin air and be thin air after the change. You would not notice the other person killing him first as you don't exist.

For a normal person he might see some person appearing out of thin air, but don't notice any "changes" because he only knows the changed way.

  1. The way I like the most is the branching model, in which every decision creates a new branch, that can or cannot recombine (some models say yes others no)

To explain what would happen in the branching recombining one: You making the decision to eat X to breakfast will split the timeline, but not for long as it mostly wont have consequences and thus recombine with the timeline where you ate Y, but having you kill your grandfather will create a timeline in which he his dead and so your father/mother is never born and you aren't as well.

These two timelines might recombine in the future if your existence doesn't make a difference anymore as there aren't any information about it. In your home timeline nothing will have changed, your grandfather will still be there and not killed, so you would have to live in a different timeline to experience change.

These theory makes there be a big (you can't think of how big it actually is as it is just mind-blowing) number of branches, so it would make it very difficult to travel to "the" future, as there are in your timeline alone many possibilities on where to travel to. Whether you are allowed to travel to a different timeline than your past (the timeline you started to exist and are "thinking on") is not yet chosen by my own liking.

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    $\begingroup$ You have failed to grasp the point this is time-travel in a single mutable timeline. This answer deals with self-consistent determinism (more or less). $\endgroup$ – a4android Jan 13 '17 at 0:53
  • $\begingroup$ Branching is explicitly ruled out in the original question. I have edited the question to make that more obvious. $\endgroup$ – SRM Jan 13 '17 at 7:25
  • $\begingroup$ I'm a big fan of time-travel with branching timelines too. The pity is that the question blocks it out. Look forward to seeing more answers and questions from you in future. $\endgroup$ – a4android Jan 13 '17 at 7:38

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