A Tale Of Two Spocks, pt.2

So I've been thinking about time and time-travel today, thanks to watching the Star Trek film on the weekend and a conversation I had with a friend on the way to the train station last night. I tried to explain my understanding of space-time, complete with Einsteinian relativity and Lorenz dilation/contraction, and all it served to prove was that I don't have it straight in my own head!

Time-travel is an old sci-fi standby, used everywhere from Back To The Future to various incarnations of Star Trek to H. G. Well's classic "The Time Machine" (if you haven't read this one yet, avoid the movie and read the book -- seriously). Accordingly, there are many different mechanisms for time-travel -- flux capacitors, 4-dimensional hypercubes, "slinging" around a nearby star at greater than Warp 10 -- and just as many warnings, side-effects or admonishments against altering "the" timeline -- but maybe time is more resilient than that. In any case, let's have a recap on what we know about time (and space).

Time? Space? What's this 'space-time' malarkey?

Our universe (or Bubbleverse?) probably started off as a Planckoscopic[1], high-density, enormously energised region -- maybe it quantum-tunnelled into existence, or maybe it "bounced" from a previous Universe collapse (a "big crunch") ... or maybe something else altogether. It's a bit hard to tell, because before[2] the "big bang" there was neither space nor time -- and questions like "what was there instead" are fundamentally incompossible, like asking a non-synaethesiac what the colour blue tastes like.

So. Some time "after" the big bang our fundamental forces and dimensions established themselves. It looks like we've probably got 3 "unfurled" spatial dimensions -- normal "3D" living -- and only one "temporal" dimension (a.k.a. time). Apparently observed effects like gravity and electromagnetism don't work without this 3+1 dimensional arrangement, but dammit, I'm a computer programmer, not a physical mathematician.

Thing is, these 4 dimensions are not solid, fixed planes as we here in the well-below-light-speed world tend to think of them -- Einstein showed that space and time (probably[3]) curve, bend, stretch and compress in relation to each other and the speed of light. Matter matters, too -- curving space-time and (maybe) creating gravity, although I think the jury is still out about the whole gravity thing. But the stretching and compressing seems to be pretty well-understood, and has even been confirmed with experiments involving an atomic clock and a really fast jet.

Einstein and others predicted that an object moving at a sizeable fraction of the speed of light would appear fore-shortened in the direction of travel (a  Lorenz transformation) -- space has actually contracted in that direction. The effective mass of the object also increases. Even worse, time is dilated -- the object appears to "slow down" because the temporal dimension is warping. The icing on the relativity-cake (the cake is a lie!) is that for constant velocities there's no way to tell who is "moving" and who is "stationary" -- so to you, it looks like time is slowing down for your light-speed-approaching friend; for her, it looks like YOUR time is running slow.

Acceleration is even more fun, and is what was tested with the atomic clock and jet -- the extremely accurate clock placed into the jet, which then accelerated to a speed fast enough to register a temporal slow-down. Sure enough, get the clock back and it is no longer synchronised with it's control clock on the ground. So you can slow time down by accelerating really fast! (You don't personally notice the time dilation -- to you, accelerating through space, the poor little plebs on Earth appear to be leading frantic, sped-up lives.)

My quite possibly flawed idea of this is that the sum of our velocity through all four dimensions equals the speed of light. You speed up in a spatial dimension, you slow down in a temporal dimension -- so at our current relative speeds we are falling through time at almost light-speed!  (This would also mean that light in a vaccuum is travelling through space but not time -- the photon that excites the cones inside your eyeballs today is the same age as the first photon formed in the big bang.

Let's do the time-warp (again)!

Cool, so we can slow down time by accelerating close to the speed of light, but what about going backwards? If we could accelerate above the speed of light, would that mean we were going backwards through time? Conventional wisdom (er..) says yes, but it's not possible -- an object accelerating up to light-speed would develop an infinite effective mass, and space would contracted to zero, and time would stop. But accelerating an infinite mass takes infinite energy ... so it's a hard limit.

(This doesn't stop there being some surreal particles in existence that are already travelling faster than light (FTL) -- we haven't found any such "tachyons", but that hasn't stopped us including them in sci-fi!)

It kind of sounds false  to me just now -- if time is a dimension, why can't we move backwards and forwards like in the other three spatial dimensions? Maybe we don't need to travel faster than light to travel backwards, we just have to get UP to the speed of light to stop our fall through time. That, or figure out what is drawing us so quickly in one direction and create its opposite to slow us, then reverse our direction of travel.

So yeah, even if time is one-dimensional (not multidimensional like I suggested in a previous post) I think travelling backwards should only be as hard as, say, generating anti-gravity to stop us falling down a well.

[1] A microscope made entirely of plankton[1.1].
[1.1] Come on, a plankton microscope would be cool! But in this case I really mean "smaller than Planck length". Might've made that word up, yep.
[2] Yeah, concepts like "before" get a bit silly when there the temporal dimension doesn't yet[2.1] exist.
[2.1] "Yet" is also silly at this point. Probably so is "at this point", come to think of it.
[3] That's science -- nothing is ever final, certain. And we LIKE it that way!

A Tale Of Two Spocks

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.