My understanding is that you can only travel from the future back to the time when you invent the time machine. However, sometime in the distance future we may find an alien time machine on a distant planet that was invent previous to our time machine, then you will be able use that time machine to travel back to the date it was invented (with your interstellar spaceship) and travel back to the earths far past.
I’ll personally stick with the many-worlds hypothesis, thanks. So if you travel from 2008 back to, say, March 1, 1995 at 8:00 a.m., you cause yet one more branching of the space-time continuum, and from the moment you arrive in 1995, you’re on a different branch of time than the one you came from.
The branching you left continues merrily on its way without you, presumably forever.
The branching you’ve just created is one that neither you nor your 1995 self has ever been to before. You can do anything you want in this branching, because it hasn’t happened yet. You can kill your 1995 ‘self’ on March 1, 1995, at 8:01 a.m., and nothing will happen to you, because he’s no longer your previous self.
He was you, up until the instant you showed up - then he bifurcated, like everything else, into two separate timelines: the one you came from, and the one you’re in now. The self you were on March 1, 1995, at 8:01 a.m. is on the timeline you left; you can’t kill him because you can’t get there from here.
I’ll confess that the troubling question of displacement of matter between timelines is beyond me, though.
That’s what I get for writing so slowly - Cal, you beat me to the ‘many worlds’ interpretation. And brought up the ‘grandfather paradox,’ of course - care to resurrect a certain former sig line of yours? 
I could be wrong but my understanding of the Many Worlds interpretation is not that you create a new timeline by moving around. That branch of events has already happened. There is a universe to represent every possibility ever.
Which if right I take to mean that rather than actually time traveling you are more traveling to different parallel realities where things worked out that you appeared there when you did.
True dat. I was being careless with my description. Yours is accurate.
Hmmm. The thing is, they’d be the same reality up to the point you jumped back to, at which instant they’d diverge. So you’re really doing both - you’re time-traveling back to a point in your past, but from the instant of your arrival, you’re no longer in your own past but in the parallel/branching/whatever realities. (Plural because they keep on branching, of course, but in ways that have nothing to do with your time travel.)
Space being the ability to have height, depth and width, space-time is that plus ability of change. There is no “moving to a time” to because time is movement. More precisely, time is the magnitude of movement. Movement in any direction is just movement so there’s no “going back in time”. “1995” is a count of movements our planet made around its star since an certain event. (Which, if it happened at all, didn’t happen then.)
Since Cal is taking his time, here’s his old sig line:
Movement through what? And why can’t we move in the other direction?
Movement through space. We can move in any direction space allows. Doing so is time.
Time travel is possible, and it is possible to change the past. But each time you change the past, the past is changed. So there have already been innumerable time travellers who travelled back to the past and changed things. But each time they changed things they also changed the future such that the new past creates a new future. And each time someone travels through time a brand new future is created. This means that the time-space fabric is radically unstable.
Until it reaches equilibrium. And there is only one equilibrium state…one where time travel never happens to be invented. And therefore, that must be the universe that we live in. Time travel can work, it’s just that if someone invents time travel in our timeline, then our timeline will be destroyed. Since our timeline exists, it must be one that won’t be destroyed. Therefore, that proves that no one will invent a time machine in our timeline.
Oh, I thought I covered that in my explanation. Further, note that re-entering the time machine, rather than living through time, places you back on the original track.
There are other perfectly consistent solutions than just “time travel is never invented”. For example, see 12 Monkeys, Bill & Ted’s Excellent Adventure, most of the handling of time travel in the Hitchhiker’s Guide to the Galaxy, …
Or, just ruminate on, say, the following history of the universe:
Big Bang - 2009: Pretty boring
2010: A man shows up in Chicago and, after some inexplicable dalliance with pies, begins to tell people how he is from 100 years in the future.
2011 - 2109: Pretty boring again. The story of the piemaker in Chicago is perhaps preserved in collections of kooky news, but almost nobody actually lends his claims much credence.
2110: Renowned pie chef John Q. Gomez, bored to his wits’ end, sits down one day and invents a time machine. He programs it for 2010, perhaps in accordance with the century-old urban legend he once heard reference to as a kid, hops in, and disappears.
2111 - forever after: Nobody ever discovers John’s time machine or rediscovers the principles of time travel. The universe is boring again.
Not the most interesting history of the universe, but it does show how you can have “equilibrium” even with time travel.
Martiju recommended The Time-Traveller’s Wife, which I haven’t read, but which now sounds very interesting
The Time-Traveller’s Wife’s take on time travel is similar enough to the Hitchhiker’s Guide’s ‘it all fits together, like a jigsaw’ approach as to make no never mind, AFAIAC.
OTOH, it’s a wonderful story. They started filming the movie in September, and it’s currently due to come out towards the end of the year.
… of course, there was that afternoon when every chrononaut from every alternity arrived to see what really happened to the dinosaurs. The simultaneous manifestation of several million iridium-infused ceramic travel cages was equivalent to an asteriod impact.
Something similar happened when the imaging systems of a butt-load of Viewers all took a snapshot of a single afternoon’s events in the Near East around 34 ad. The amount of light captured made the natives see the sun dim in the middle of the day…
I find it interesting that the OP explicitly rejects metatime; why should we do that? Just because we’re not aware of it?
The problem with “consistent solutions” to the time travel problem, e.g. the story you mention above, or any other story where the result of the time travel is consistent with observed history, is that it puts enormous limits on what you can do with a time machine.
In the example above, I imagine this sort of discussion between renowned pie chef John Q. Gomez and his friend Fred.
John: “Hey Fred, check this out, I invented a time machine”
Fred: “Cool, let’s use it to go back to see the dinosaurs or the Kennedy assassination”
John: “Well,…, we actually can’t. Only I can travel with it, and I can only use it to travel back to May 21, 9:43am, 2010 in Chicago”
Fred: “…, OK, why don’t you buy lots of HugeBank stocks, and get rich? Or visit now-deserted Las Vegas, I heard it was pretty cool?”
John: “Well, …, I can’t do any of those things. When I go back I have to stay in Chicago, open a pie shop on June 18 2010, and then on December 15 2010 I have to tell people I am from the future”
Fred: “That’s not a very useful time machine you have there John”
See, that’s the problem with time travel: Any self-consistent solution puts so many unreasonable constraints on where you can go and what you can do when you get there, that it does not jive with the reality of how humans operate once they are present in a given point in space-time.
What exactly is metatime?
Of course, outlawing time travel altogether imposes even more constraints on where you can go and what you can do when you get there.
Incidentally, though only begbert2 can speak for himself, my assumption would be that “metatime” is supposed to be like a second dimension of time; for example, rather than just locating events in spacetime with a single temporal coordinate, we can imagine there to be both a time and a, let’s say, “sime” axis. For example, if one were to “change the past”, the way this would be realized would be saying things like that at time-my-birthday-1995 and sime-16, I wore a red shirt, while at time-my-birthday-1995 and sime-17, I wore a blue shirt. (I.e., changing the shirt I wore on my birthday took one year of sime, but, of course, was entirely localized to just one moment in time).
The many-worlds solution sounds more like science fiction and fantasy than science.
I would like to see some scientific evidence of the existence of other universes that branch out of our own, or exist parallel to our own, before we use the many-worlds solution to prove that time travel is possible.
What I would like is a discussion on how possible time travel to the past is, using only what has been scientifically proven to be the case about our universe.
e.g. with special relativity theory, which has been experimentally verified, you can essentially time travel to the future if you go close to the speed of light.
For going back to the past, we could posit a whole strange set of circumstances under which it will be possible, e.g. our universe is the dream of some guy, and in it, he dreams of someone going back in time and changing things. So, in that sense, time travel to the past would be “possible”, but I’d like to see it shown using proven scientific theories, and not fantasy like dreams or the many-worlds hypothesis.
(BTW, even if there were multiple universes branching out from each other or existing in parallel to each other, I still think that there are several remaining issues with time travel to the past, but I’m no expert on it, so I’ll just leave it there)
Lost the edit window: You could come up with interesting mechanics for such a metatime system as well, and speak in an entirely logically consistent way about it, but for whatever reason, I still find the “just one dimension of time” approach much more aesthetically pleasing. Obviously, others preferences will differ.