Edit: After writing this, my mind returned to the problem and found solutions which undermine all my arguments. See this post for details.
Original post is as follows:
Part One of a Long Post that's been banging around my head for a month
Some few years ago, I was binging a space sim series, when I got annoyed about how there was a hard speed-cap on my vacuum travel. "Not only is it obnoxious," I thought, "it's physically inaccurate! Plus, back in the day, I played [the demo of] an awesome space sim back in the day that had fully Newtonian physics."
But wait. Newtonian physics have been superseded by a model we know to describe our universal mechanics better. And I've never heard of anybody even trying to make a space sim that works on a relativistic model! And so it was, dear reader, that our unsuspecting protagonist fell into a weeks-long rabbit hole where I started thinking through the logistical requirements necessary to simulate relativistic physics with multiple players who aren't necessarily in the same frame of reference.
For the first few days, I was simply haunted by the twintrusive thought "It must can't be possible!" I mean, surely, if a phenomenon can occur, it can be simulated, right? But, simultaneously, I couldn't even begin to figure out how to construct an engine that doesn't privilege one frame of reference as "correct" over any other. And while that problem did yield to scrutiny, it wasn't long until another intractable problem reared its ugly head.
Y'see, while the twin paradox is physically possible, simulating it from both perspectives requires the ability to send data back in time. Alternately, you can achieve the effect by physically accelerating and decelerating the two terminals in such a way that it ceases to be a "simulation" of space travel with relativistic physics. I do not know how to prove this rigorously, but I strongly believe this to be true.
More interestingly, though, this has some implications with regards to the simulation hypothesis. For the uninitiated, the simulation hypothesis is the conjecture that, supposing it is possible within our reality to simulate (a reality within which it is possible to simulate) ... a reality, then the probability that any given reality (including our own) is non-simulated becomes 1 over infinity, a quantity famous for being exactly equal to 0.
Well, if it is true that it's not possible, within our reality's physics, to simulate multiple frames of reference simultaneously without the ability to send information backwards in time, that imposes some constraints upon simulations.
For instance: if our reality is simulated, at least one of the following conditions must be true:
- The simulator can only observe one frame of reference at a time
- All states of the simulation have been pre-calculated (ie: the simulation is deterministic)
- The system running the simulation is no less than the size of the observable universe
- The simulation is not accurately modelling the physics of the external reality.
And, regardless of whether or not our reality is simulated, these constraints do apply recursively to any simulations created within it.
This is one of the reasons I stopped believing our reality is a simulation.
