More detailed technical article: "Constraints on an external reality under the simulation hypothesis", pdf
One of my long-running interests is thinking about how to build a virtual world to go with our future neural interfaces. It’s not just a software engineering challenge: there are real physics problems hidden in it.
Separately, some of my friends are enamored with the simulation hypothesis — briefly, that we are living in, and our entire universe is, a computer simulation — and so I’ve ended up spending a fair amount of time thinking about that, and specifically whether it’s possible to say anything concrete about the probability that it is actually true.
A little while ago I realized that if you turn the build-a-virtual-world problem inside-out, you can start making fairly interesting statements about the simulation hypothesis in the form of constraints that must be imposed on any “containing” universe. Importantly, these arguments have nothing to do with the amount of available compute power, which felt like a significant advance. (It avoids the handwavery that comes from believing you can approximate any otherwise intractable problem reasonably fast if you have a sufficiently powerful machine, which seems to be an oft-used escape hatch.)
Long story short, we can pretty much rule out the conclusion that we are living in a simulation and that the external universe at all resembles our own.
If we ourselves have any connection to the external reality, it is possible that we might be far apart in spacetime here but sitting right next to each other in the “real world,” which would cause all kinds of problems. (Though a game can obviously simulate travel through space, it is impossible to simulate travel through time with multiple players in a way that has any meaningful consequences and not end up with paradoxes.)
But even if we don’t have any possible existence in the external universe, the same problems arise for a simulation influenced by multiple external agents that share a common sense of time, since its physics must still be invariant over arbitrary informational connectivity. This immediately implies properties like an infinite speed of light, which is not the case in our universe.
Things might work if there is only one possible external agent peering into our simulation, but either way, we can bound that only one of our universe and a containing universe can be relativistic, and since we know that ours is, the outside universe cannot be. At this point I think the simplest thing to do is to discard the simulation hypothesis, but it is true that an alternative is to just take this constraint and run with it in terms of imagining what the outside universe might be like. It would be very different from anything we’re capable of imagining, completely lacking a space-time connection, and that’s probably only scratching the surface of this line of reasoning.
On the other hand, the Star Wars, Star Trek, and various Marvel universes — where space is apparently just space and time is apparently just time — are all seemingly perfectly valid subordinate universes to ours (though not vice-versa) under this analysis, so that’s exciting.
These arguments do require making a couple assumptions, but in my opinion they end up being pretty mild. The two critical assumptions are that we have to believe that any universe must be internally consistent to exist, or at least talk about describing; and that the creators of a simulation have to end up with some way of interacting with it. If you could build a virtual world full of simulated organisms, but to you it would look like a black hole, why would you bother, much less let it consume your resources?
I flesh this out a fair amount more in a short unreviewed preprint, Constraints on an external reality under the simulation hypothesis, for those who want to have this debate with finer resolution.