Time: Different from space
I missed this the first time around, but it’s interesting and touches on a whole slew of issues. The first is that, unlike what you may have heard but as we always expected, time really isn’t just another dimension like the three in space, not even in the theoretical framework of modern physics. (Apparently the difference comes down to a minus sign.) It then metamorphoses into an argument about algorithmic complexity, of all things. I really believe that continually challenging yourself by reading stuff that is partially, but not wholly over your head is good for you, and on that note, I’ll readily admit that I don’t understand the connection between how the best algorithms scale with the size of the problem in a world with time travel and the difference between time and space. But then comes something that I’m having trouble wrapping my head around, but which sounds deep: a novel solution to the Grandfather paradox of time travel:
So is there a better way to treat time as a reusable resource? I believe that there is. We can have a parameter that behaves like time in that it “never changes direction”, but behaves unlike time in that it loops around in a cycle. In other words, we can have a closed timelike curve, or CTC. CTCs give us a dimension that (1) is reusable, but (2) is also recognizably “time” rather than “space.”
Of course, no sooner do we define CTCs than we confront the well-known problem of dead grandfathers. How can we ensure that the events around the CTC are causally consistent, that they don’t result in contradictions? For my money, the best answer to this question was provided by David Deutsch, in his paper “Quantum Mechanics near Closed Time-like Lines” (unfortunately not online). Deutsch observed that, if we allow the state of the universe to be probabilistic or quantum, then we can always tell a consistent story about the events inside a CTC. So for example, the resolution of the grandfather paradox is simply that you’re born with 1/2 probability, and if you’re born you go back in time and kill your grandfather, therefore you’re born with 1/2 probability, etc. Everything’s consistent; there’s no paradox!
It seems to work by embracing the paradox rather than dissolving it. I’m not sure if it’s satisfying but it sure is interesting.
