Dee and I watched the Star Trek movie this weekend. Today at work we're having a ... philosophical (since it's about technology and knowledge that doesn't (yet) exist) ... discussion about the whole "Spock situation" -- can you interact with your future/past self and neither create a paradox nor annihilate into photons[1]?

The physics answer is, of course, maybe.  But the "maybe" hinges on  a) whether two different timelines correspond to two different "realities", and b) whether it's possible to move from one to another.

What is "singular reality"
Better start with this, I suppose. In a single-reality model there is one true reality: one definite past, one present, one future. Our observed 3 dimensions is the whole show (or at least the other spatial dimensions are either two tightly furled to affect us, or they act just like our observable three).

Except that with a single reality, quantum physics is hard to explain. Electrons suddenly smear across space, then "collapse" when they arrive at an "observer" (whatever that means).  But hey, maybe it's a true representation of reality.

What are "multiple realities"?

Whilst we don't have any direct evidence of alternate realities (or "parallel worlds"), there are a few different theories of how they might exist, with the corresponding supporting physics (and mathematics). It may be possible that our habitable part of the universe is just a little "bubble", and that outside our bubble are innumerable other "bubbles" in which the the initial conditions or even the laws of physics can be fundamentally different. In an infinite Bubbleverse there could be an infinity of separate bubbles, and at least some of those would support life (as ours does).

Each bubble could have bubble-local time and space, but travelling between two bubbles is probably "non-trivial".

Alternatively (sic), we can interpret the results of quantum mechanics as evidence of "many worlds". In this interpretation the probability wave function exists because, actually, every nanosecond sees us diverging into different parallel realities -- in one, the electron went one way; in another it took a different path. (What fun; an electron can interact with itself from another reality!)  It is the sum of all possible/parallel realities that gives us the probability wave.

(You might not like the idea of the continuous splitting of reality into infinite parallel worlds. I don't either. To me, it makes a lot more sense if you just think of another spatio-temporal dimension that we're travelling through. So perhaps time is not one-dimensional (we only travel forward) but 2D -- and our conscious "choices" serve to move us "left and right" towards possible futures. No arrogant, ego-centric "splitting" of reality when we decide to walk rather than take the bus; instead, both futures exist and happen with equal "realism", we just only get to "tune into" and experience one of them.

It doesn't have to be "time", of course, but it's easier to understand and imagine.  (Happy to find through Wikipedia that I'm not too nuts: this "experiential" view is akin to the "many minds" interpretation of Professor Zeh!))

So, what about time travel?

At this point you can probably realise that the "singular reality" leads to all sorts of tricky time-travel paradoxes, including the old standard, "Go back in time {10} and kill your (self, parent, ancestor). So you never existed. So you couldn't go back in time {GOTO 10} ..."  But it's easy enough to prove that you probably wouldn't explode in a shower of hot photons if you, say, shook hands with an earlier self (as that venerable thespian Van Damme in Time Cop might suggest).

We are all recycled. Every atom in our bodies was created in the hot core of a star, ejected out into space, integrated into a planet, a biosphere, an atmosphere, a living creature, a meal. We are what we eat, what we breathe and ultimately what we breathe out (and defecate) becomes the building blocks for a future generation of flora, fauna or mineral (depending upon what you eat and happenstance). Furthermore, we replace our cells -- and therefore our particular atoms -- all the time.  Today's skin is tomorrow's dust. And that dust could be a meal for a mite and ad infinitum up the chain.

So: even if there was some thermodynamic/entropy preserving force that would annihilate "import" atoms when they came in to contact with their former selves, Spock has more chance of exploding when he vaccuums under the bed then when shaking hands with his former self.

The case for multiple-worlds is even better -- if a future version of you from one reality somehow found it's way through a singularity[2] and started messin' with the ol' timeline ... well, that would just change YOUR perception/reality, not his! (Or hers.)  So his (or her) memories wouldn't change spontaneously, and he (or she) could do anything she liked -- up to an including killing you! -- with no effect upon it's own existence.

Think about it from the two different perspectives:

"In one future, I went back and killed myself.  In another, I did not."

"In one past, I was killed. In another, I lived well into the future ... where I went back and ..." you get the point. In the multple-worlds scenario, each perspective is equally valid and (more importantly) independent.

Ah, this post is already long enough. Next time I'll ramble about travelling through time and between realities, promise.

[1] I kid you not; this is the expected behaviour according to a sci-fi head at work. He was deeply upset by the Spocks' final scene.

[2] Yeah, that's probably the dodgiest bit of sci-fience right there. Travelling through a black hole? Hello, spaghetification?? Massive crushing forces? Space compacted to near-zero dimensions? Maybe a photon (or quark) could travel "through" a black hole, but good luck to it.