The self-consistency principle always seemed to me like a ridiculous handwave born of a limited notion of causality.
Except the self-consistency principle isn't something anyone came up with to explain what would happen in case of time travel. It's how
all of physics works, and applying it to time travel is just saying there's nothing special about closed timelike curves, and they should be treated like any other situation.
The laws of physics aren't an algorithm. They don't say "In this state, this is what will happen." They're most easily expressed in terms of relations across a plane: Cut the universe in half along a 3D hyperplane,
regardless of what angle that plane is oriented at, and what physics will tell you is how the conditions at one side of the plane relate to the other side. This is most obviously true for past-future, but you can apply the exact* same rules to left-right, up-down, or any other way you care to slice it.
Put another way, the equations of the laws of physics let you decide what the contents of one side of the cut must be, given complete*** knowledge of the other side. Though again, it's not an algorithm -- there isn't a computer program you can run, there's just equations that either add up, or not. "f(A) = f'(B)", you know A, so what is B? ...unfortunately, "f" is immensely difficult to compute at all, let alone reverse. If you can guess at B, you can check if the equality holds, but guessing B is difficult.
For instance... let's pretend we have a mirror. We'll cut the universe in half, past-future: That is to say, we do the usual thing and try to compute the future based on the past. Or vice versa, actually; the laws are time-symmetric, and really don't care. But in this case we're computing the future.
A photon hits the mirror. The photon bounces off. You get to watch yourself shaving.
In the above case, we had both the incoming photon and the mirror itself as part of the equation's left-hand side, the "past" half of the universe, and this constrained the right-hand side quite well. Sometimes, things can be less determinate. Let's say we cut the universe in half, west-east and right above the surface of the mirror. Our left-hand state now contains both the past and future of the photon...
What will the laws of physics let us figure out? There's a photon appearing to bounce
right at the hyperplane, so in fact you can use pretty much the same mechanism as you used to compute that the photon would bounce off a mirror, to compute that there
is a mirror. There also might just be another photon crossing over, though. If that was all you knew.
See, actually I'm understating it slightly. Your left-hand side contains a lot more: It contains half of planet Earth, and half the universe, and quite possibly the company that made the mirror. Physics will tell us absolutely everything there is to know about the right-hand side; the complete state of the universe. There's no difference between this case, and the past-future case.
Alternately, let's rotate** the situation slightly. We'll keep the hyperplane at past-future, like the first case, but instead of having a photon bounce off a mirror we now have two photons -- the past and future of the original one -- that are both coming from the past, and hitting the same spot on our hyperplane. Assuming they're high enough energy, what you'll see is the photons mutually annihilating and turning into an electron-positron pair...
(It turns out that positrons are electrons moving back in time, or vice versa, although that's a separate arrow of time from the thermodynamic arrow of causality.)
Now turn the universe upside down, or else your equations. Instead of matter creation, you're looking at matter annihilation.
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What's my
point?
All of these situations are, in fact, the exact same situation. You can rotate the universe, or you can rotate your hyperplane, but the laws of physics remain the same regardless. Consistency constraints is how they work, and
nowhere in physics, except for geometry, is the time dimension special. There is that metric asymmetry, yes -- we live in Lorentzian space, not Euclidean -- but that barely suffices to ensure thermodynamic causality, and thermodynamic causality appears to be an emergent phenomena, not something fundamental.
So I'd be astonished to see a resolution to time-travel that isn't just "the universe remains consistent", because this sort of consistency is how it always works.
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*: Modulo the dimensional asymmetry between space and time, which has a fairly minuscule effect so long as you stay well away from null geodesics. Unfortunately photons... but I like the mirror example too much to stop.
**: Rotation of this sort is impossible to carry out physically, but perfectly fine on a diagram. Specifically, it's impossible to rotate
smoothly across the speed of light -- hence matter cannot become tachyonic, or vice versa, as all real-world processes are smooth. For the purposes of presenting a different physical scenario, we can just do a jump-cut.
***: "Complete knowledge" means complete knowledge of the universal wavefunction, not just the non-interacting decoherent branch of it that the experimenter is sitting in. This can be a problem. In experiments it isn't much of one, and in the real world, thermodynamic causality allows you to estimate
reasonably well what the past half of the universe practically looks like, since the other branches which you can't see will have a negligible impact on the future.
It does mean you can't actually figure out the contents of the east half of the universe by reading the complete, big bang to big rip, Akashic history of the west half, because you can't acquire said history... but that's not really any more true just because decoherence
also gets in the way. Plenty of other things already did.
