A recent paper on Closed Time-like Curves has editors the world over asserting that paradox-free time-travel is now possible! Readers have gotten pretty excited too….
Fantastic! If we travel back in time and cause an accident, we’ll still exist when we get back!
Well, no. Or at least, not quite. These headlines are inaccurate: a more accurate headline might be “Paradox-Free Time Travel Possible, Provided Closed Time-like Curves (CTCs) Exist (in our universe)”.
It’s a bit wordy, and loses some of the buzz, so one can understand why editors have opted for click-bait.
Notice the conditional in there, the proviso? If CTCs exist - or can exist - in our universe, then we get safe time travel. But that is a huge “if”….
CTCs are a set of possible solutions to the equations of General Relativity (GR). The equations of GR are non-linear and it is not always possible to produce analytic (complete) solutions, so physicists often use approximations to get close to a solution. If a solution is interesting, e.g., T=0, it is studied further (oh, the Big Bang (literally: T=0, everything starts)). One can also make assumptions about some elements of the equations (if we set this to P…) and see what pops out (oh, Big Bang! oh, CTCs!).
The equations of GR are studied as much for how interesting is the math as for their potential physical value. CTCs have been studied for over a century, in part as an intellectual exercise (oh, these are weird, could things really work this way), in part to learn if their study can inform open problems in physics.
One such open problem is that GR and Quantum Mechanics (QM) are inconsistent with each other. For example, GR assumes continuous functions and continuous values (it is a classical theory, in that limited respect) while QM assumes that observations can take on only discrete values and, as a result, functions used in QM are those amenable to treating discontinuous ranges of values. This is where the term “quantum leap” comes from: An observable leaps from one value to another without having any of the values in between; in classical mechanics and GR, this just isn’t allowed. (Fundamentally, the maths of GR and QM don’t even share much commonality; I saw a great graphic about this years ago, and I regret not saving it.)
Cosmology is informed by both QM and GR: GR tells us more or less how to interpret the structure of the universe at a large scale, over large time frames (was there a Big Bang; is the universe expanding; is there dark matter; how do stars evolve and black holes form; etc.) while QM gets us the smallest scales and tells how information behaves in the universe, e.g., is information lost at the event horizon of a black hole, can physical processes be irreversible, etc.
One of the most important aspects of this is that of the four fundamental forces (the electromagnetic, the strong and weak nuclear forces, and gravity), three are described by QM (the first three) and form part of the Standard Model (in which every force is transmitted by a “particle”, e.g., the photon for the electromagnetic force, and from which many incredible predictions have been made, e.g., the existence of the Higgs boson, recently confirmed at CERN). The fourth fundamental force, gravity, the most important to the overall structure of the universe, comes from GR. In particular, there is no “graviton” that carries it (or at least not yet).
When physicists talk about a Grand Unified Theory, they are hoping to reconcile GR and QM, e.g., to make quantum gravity. Or more accurately, to quantize gravity.
Since CTCs are a pure-GR thing, whether or not they can exist should depend on whether or not they are consistent with or violate QM. For example, the paper cited above does include as one of its references a paper arguing that CTCs would violate the Heisenberg Uncertainty Principle, which is pretty much as fundamental to QM as the constancy of the speed of light is to GR.
Where things get really interesting is when one combines CTCs with computational complexity….
If CTCs exist, Aaronson and Watrous have shown based on work by Deutsch that quantum and classical computers have exactly the same power - provided that one could engineer a classical computer to operate in a CTC (I’m going out on a limb stating that, a lot of Aaronson’s work makes my head hurt). Deutsch’s work isn’t universally accepted either.
So. What is the article saying?
If CTCs can exist in our universe (if they are consistent with our most-successful-ever theory, our most tremendous intellectual artifact, QM), then paradox-free time-travel can exist.
But that is a very, very, very large IF. Like 96 point bold underlined flashing neon.
What’s the point, then?
The more we learn about GR and what it allows and forbids, and the more we learn about QM and what it allows and forbids, the more clues we obtain to what is wrong with either and what a future synthesis or replacement theory might look like.
Studying paradox-free time-travel via CTC may provide theoretical insights or it may actually predict observables, either confirmatory (if we see it, CTCs are real) or contradictory/falsifiable (if we see it, CTCs cannot be).
So we don’t know anything more for sure, yet. But we have a better idea of how things might be, provided other things are. We just don’t know what those other things are yet.