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For this question think of the times of past, present, and future as $T_{-1}$,$T_0$, and $T_1$, respectively. There is a man named Jim, currently in $T_0$, so lets refer to him as $J_0$. $J_0$ is a very smart man and at some point between $T_0$ and $T_1$ he invents a time machine. His future self, $J_1$, uses this time machine to travel back in time from $T_1$ to $T_0$. At this point, $J_1$ tells $J_0$ to not build the time machine. This in turn sends the timeline from $T_0$ to $T_{1A}$. However, without the time machine, $J_1$ cannot tell $J_0$ to not build the time machine, therefore creating a paradox.

Here is a visual example:

1 - Normal Timeline with $J_0$ at $T_0$. 1 2 - $J_1$ goes back in time to $T_0$ from $T_1$. 2 3 - This creates an alternative timeline starting at $T_0$ to $T_{1A}$. 3

Now what happens next? $J_{1A}$ cant go back in time like $J_1$ did because he had no time machine and would have no purpose to do so anyway. Therefore, would the universe reset to the original timeline or will something else happen?

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    $\begingroup$ @IonLee. If you use a notion of proof of plausibility, it must be very different from any notion of logical proof. (Why use a notion of proof of plausibility anyway? As William Blake put it, "Man by his reasoning power can only compare & judge of what he has already perceiv'd".) I'm not sure whether you are aware that Gödel proved time travel to be compatible with Einstein's theory of relativity; but if in your terms time travel hasn't been proved plausible, surely it hasn't been proved implausible either. $\endgroup$ – h34 Mar 25 '15 at 8:13
  • $\begingroup$ I thought in the first time T0 J1 is in there but i cannot tell J0 to not invent the time machine because in my opinion time is convergent structure and it is constant.Thinks like that ; there is x, y z dimensions right. If we count time as a another dimension every point we can see is constant and do not move even a bit in 4d universe. $\endgroup$ – oknsnl Mar 25 '15 at 12:33
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If your universe allows time travel to split the timeline into two, I think your choice to splitting it only based on whether the time machine is built is incorrect. The right place to split the timeline is at $T_{-1}$, just before $J_1$ arrives in "his" past.

In one branch, at $T_{0A}$, a $J_1$ from "the future" appears. In the other branch, at $T_0$, he does not.

Thus, when $J_1$ tells a "past version of himself" not to build the time machine, he's really telling $J_{0A}$, an alternate version of his past self, not $J_0$.

I quoted some of the phrases above, because of the alternate realities involved. $T_{0A}$ isn't really $J_0$'s past, nor is he really from that timeline's future.

Bad ASCII diagram:

T-1 ----------------> T0 --------------------------> T1
  \       (J0 invents time machine)           (J1 uses machine)
   \                                              /
    \             .-------- J1's journey <--------
     \            V
      --------------> T0A -------------------------> T1A
       (J0A doesn't invent the machine)  (J2 and J1A live happily ever after)
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  • $\begingroup$ I never even thought of it that way. +1! $\endgroup$ – GamrCorps Mar 25 '15 at 4:38
  • $\begingroup$ This is the only form of "time travel" that I've ever seen make sense. Anything else goes into paradox really fast. Note that this isn't really time travel though, it's travel to alternate dimensions at a different time point in that dimension. $\endgroup$ – Tim B Mar 25 '15 at 17:00
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I think the established term for this is known as the grandfather paradox.

From a story in which a time traveller ventures into the past and kills his grandfather. Since it seems to defy all known laws of the universe there's no way to say for sure what would happen. I'd like to think that time travel would result in creating two parallel dimensions that the traveller "jumps" between. Since he's from another dimension, it doesn't really matter if he has a grandfather in the current dimension he's in. Or does it?

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    $\begingroup$ +1 for this. There's actually a scientific theory, postulated by this guy, which says there are two dimensions of time. Add that to the mix and things get even more complicated, though it does make time travel look more possible. $\endgroup$ – Rand al'Thor Mar 25 '15 at 1:11
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    $\begingroup$ Two time axes have also been conjectured by those working in fractional calculus, e.g. Igor Podlubny. $\endgroup$ – h34 Mar 25 '15 at 8:27
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The theory I usually go with is that each possible timeline is also part of a multidimensional universe of timelines. When $J_1$ goes back in time to create $J_{0A}$, he's not actually going back to tell the same $J_0$ not to build a time machine, since that's impossible by causality, but just one in an equivalent timeline up to that point.

$J_1$ and $J_{1A}$ coexist in different timelines, one with the time machine, one without, and never then able to communicate to each other again because they can't travel to the exact same timeline anymore. If $J_{1A}$ were then to invent another time machine between $T_1$ and $T_2$ and try to go back in time to $T_1$ to tell $J_{1A}$ not to make the time machine, he'd be telling $J_{1B}$ not to make it, not $J_{1A}$.

So the universe doesn't really reset, it's just a copy of it that gets affected.

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You invented a time machine. As you are about to use it for the first time, you excitedly enter the room. You place yourself in the seat, and you're about to press the launch button, when you notice a piece of paper, jammed into a previously invisible crevice in the machine. You open it up. It's clearly a page torn from your pocket notebook, in your own handwriting, albeit in a very shaky script. There is only 1 word on the paper:

$$\huge{Don't}$$

You ponder this for a minute. You tear a page from your notebook, and, in a shaky script, write: "Don't". You set the time machine to Present Time -1 hour, 0 minutes. You press the button. You quickly stuff the paper in the appropriate crevice, and go silently hide in a nearby cupboard. An hour later, you breathe a sigh of relief, come out, and take a large crowbar out of your toolbox. You turn towards the machine.

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  • $\begingroup$ Why wouldn't you notice the second time machine in the room? $\endgroup$ – user867 Mar 16 '16 at 5:18
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There are several different theories on how a Grandfather Paradox would resolve itself.

Split Reality: The time traveler creates an alternate dimension in which that time machine is not invented. The time traveler returning to his home time/reality may or may not be possible.

Stable Time Loop: The past and future cannot be changed and are immutable. If you went back and time and told yourself not to build a time machine, then you were told not to build one by your future self, built the time machine anyway, and then went back to tell yourself not to. That is how it always happened, and it cannot be altered. This is a favorite of a lot of shows (like Doctor Who...for a good example of a stable time loop, see the episode 'Blink.')

Timey-Wimey Shenanigans: You are told not to create a time machine, then your future self ceases to exist, and you are left with that information despite the fact that it couldn't have been delivered. See: Marty McFly disappearing from existence as a result of his actions, from Back to the Future.

Chronal breakdown: Congrats, you just broke reality. Maybe time freezes, maybe you wink out of existence, maybe the whole universe vanishes in a puff of logic.

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