Proof by induction:
Suppose, for the sake of argument, that one day somebody invents a machine that lets people travel back in time. That will be a big day in history — the day that travel back in time finally becomes possible!
Here’s the problem: Precisely because it will be such a big moment in history, sooner or later people from the future are going to want to come back and visit that historic day. In fact, since people will be traveling to the same destination from all different eras in the future, that particular moment in history is going to become awfully crowded.
And not all of those visitors from the future will be as careful as they should be. One of them, inevitably, is going to do something that will interfere with the sequence of events that resulted in the invention of the time machine.
When this happens, the time machine will no longer have been invented on that day. That entire future timeline will cease to exist, curious time traveling tourists and all.
Which means that we will enter an alternate timeline. In this new timeline, travel will only be invented sometime later.
But in this new timeline, the same sequence of events will happen, only at a later date.
And so, alas, QED. Nobody will ever invent that time machine.
it’s not that the time machine isn’t getting invented. It is. It is getting invented and uninvented (erased from existence). And if, as you suggest, the cycle is repeating itself, it is not that the machine is invented once and then the alternate path is created and that’s the end of it all. The creation of the machine and alternate path are repeated endlessly. What you mean to say is that the time machine itself is inevitable. You also suggest the inevitability of its erasure…. But do you know know that for sure?
If it happened once it would be:
1 time machine – 1 time machine = no time machine
If it happens forever, it is
(1 time machine -1 time machine ) + (1 tm -1 tm ) + (1-1)…… etc. = 0 time machines
You are assuming that the multiple cycles always have to end the same way. If it cycles only once, that is definitely the end. If it cycles infinitely, don’t you think at least one of those times the cycle will break and the time machine will stay?
I prefer to think that either one, there is a unique timeline in the universe and this the particular one we inhabited; or two, there is an infinite number of timeline and every moments exists with every nanoscopic changes imaginable, a Hilbert’s Grand Hotel of timeline if you will.
One or Infinity, no N.
In this scheme, an infinite number of timeline will never know timetravel or will erased their existence in their future self. And another infinite number will know timetravel and never used it in a way to invalid its very invention.
Let’s just hope than no timeline peasant will find the door of their room and decide to visit the Grand Hotel by themselve, except maybe to binary encode their watch for their daughter or something..
Well, no and no.
No, time travel isn’t possible, for very good relativistic reasons.
But also, no, your logical arguments would not forbid time travel. Imagine that every possible state of the universe is a position in a vast mathematical space. Time travel would only mean visiting a different position with the same t coordinate. Thus the normal passing of time for that traveller would progress through increasing t on a parallel track. The original track is no longer reachable.
Thanks for all the very thoughtful comments on this post!
Anais: Yes, I agree that in the fictional scenario that I set up, there would indeed be an infinite number of time machine inventions. I’m just saying that they would all be unstable. Each of those timelines would eventually collapse.
PhilH: The mathematical hypothesis underlying your analysis is certainly very reasonable. Then again, there is no no empirical evidence for the kinds of multiple universe theories that we are discussing. So any of these hypotheses are reasonable in their own way.