A few years ago I read “The Universe is not a Computer”, an interesting paper by Ken Wharton. The part of his argument that I took away was: (i) physical systems can be described either in terms of their initial conditions, and then their behaviours projected into the future, or they can be described in more global terms, with boundary conditions at different times, and their behaviour calculated under these constraints; (ii) computation is essentially of this initial condition form: we say what the system is like now, and compute its behaviour over time.
He was arguing that we are privileging the initial condition form of our physical theories, because of the fit with the restricted computational approach, and this is what is making quantum mechanics difficult, as it doesn’t readily fit this formulation. (Read his full paper for the full argument; it is very readable.)
I found this an intriguing idea, but felt it was lacking in its computational approach. That’s a very classical model of computation, and I’m interested in more unconventional models, including using physical systems to compute directly (which raises questions of its own). So about a year ago, when I was invited to write a paper for a special issue of a journal, I decided to write one arguing that maybe unconventional computation didn’t need these restrictions either.
Meanwhile, way back last millennium, I read David Deutsch’s lovely book The Fabric of Reality. There is much to enjoy there, but the piece relevant here is the way he takes universal computing seriously: that is, he works through the consequences of it really being universal. One of those consequences he unwrapped was to use Turing’s classical model of computation to infer that time travel is impossible: because there is no way to build a “universal virtual reality renderer” to model a consistent physical reality containing time travel, that is, to compute time travel, then physics can’t implement time travel. (I think that’s the gist of the argument, but it is a decade and a half since I read it.)
Recently, I was describing Deutsch’s argument to someone. And then his argument and Wharton’s argument banged together in my head. Hang on a minute! Does my response hold for both? Deutsch’s argument is using classical computing. What if instead, we used an unconventional computer, maybe one performing direct physical computation as it time travelled? Could we then use it to compute the time travelling behaviour, to nullify Deutsch’s argument?
I think we can. This doesn’t prove time travel exists, of course. It merely says the classical computing argument against it doesn’t hold. Maybe we can’t prove it one way or the other. Maybe it’s the case that if time travel is possible, then we can use a time travelling computer to build a virtual reality with consistent time travel; and if it isn’t, then we can’t. The answer lies in the physics. But the door is still open.