Here’s a thought I had a couple of days ago regarding time travel. Most likely it has been thought of by others, but I’m curious to see what Dopers think the holes in the reasoning might be, if any.
Basically, it seems to me that there can be only one 1995. Not two. You can’t have a 1995 “before” some event happened, and a 1995 “after” that event happened.
The reason is that “before” and “after” only make sense for things that operate within time. They do not make sense for time (or space-time) itself.
So, if you invent a time machine and go back to 1995 and visit yourself, you will have changed 1995, since at the moment, you don’t remember 1995 as a time when you met your future self.
If time travel to the past were possible, there would be two 1995’s. The “first one”, “before” you invented your time machine, in which you went through the whole year without meeting your future self, and the “second one”, “after” you invented your time machine.
If you look at space-time as an “object” that simply exists (it does not change, since change would imply time passing, and time does not pass for the space-time “object” itself), then space-time can contain only one 1995. Since you know that you never met yourself in 1995, you simply cannot travel back to that year and meet yourself.
This relates to a pet-peeve of mine, and that is when people say that something “moves through spacetime”. You cannot move through spacetime. You have a trajectory through spacetime, and that trajectory describes your motion through space, as a function of time.
Anyway, the point is that there is no “later” of “after” for spacetime. So there is no new 1995 “after” you invent your time machine. So, you can’t travel back.
Any thoughts? Any holes in the above reasoning?