In particular, it would be really expensive to simulate physics. If the simulators wanted to make the world accurate for the observations that people make, they'd have to go down to the quantum level, because people do make quantum-level observations. But this would be prohibitively costly. Think of how much computing power we'd need to simulate a single quantum particle accurately. Simulating a quantity X of physics probably requires many times X amount of computer hardware. So unless the simulation is running in a basement universe that's much bigger or allows for much easier computation, the simulation is unlikely to have quantum-level fidelity.
But then how do we explain the consistency of our observations of quantum physics? Here's Bostrom's suggestion from his original paper:
The skipping back a few seconds would only work before people became aware of the contradiction, because once a simulated experience is run, it "happened," even if you undo the memories later. Some fraction of observer-moments would still consist of observing the wrong thing.Simulating the entire universe down to the quantum level is obviously infeasible, unless radically new physics is discovered. But in order to get a realistic simulation of human experience, much less is needed – only whatever is required to ensure that the simulated humans, interacting in normal human ways with their simulated environment, don’t notice any irregularities. The microscopic structure of the inside of the Earth can be safely omitted. Distant astronomical objects can have highly compressed representations: verisimilitude need extend to the narrow band of properties that we can observe from our planet or solar system spacecraft. On the surface of Earth, macroscopic objects in inhabited areas may need to be continuously simulated, but microscopic phenomena could likely be filled in ad hoc. [...]
Moreover, a posthuman simulator would have enough computing power to keep track of the detailed belief-states in all human brains at all times. Therefore, when it saw that a human was about to make an observation of the microscopic world, it could fill in sufficient detail in the simulation in the appropriate domain on an as-needed basis. Should any error occur, the director could easily edit the states of any brains that have become aware of an anomaly before it spoils the simulation. Alternatively, the director could skip back a few seconds and rerun the simulation in a way that avoids the problem.
Keeping track of the belief states of all minds seems like a lot of work. Maybe it wouldn't require vast computing power, but it would be a challenging software problem, because you'd need a classifier to map from brain-state data to a semantic label that "Harry believes X," which is a different level of abstraction.
In any event, the implication of all this is that if we're in a simulation, the physics that we observe is just made up. Maybe it's approximately correct to a degree that's cheap to compute, but it's probably not correct down to every quantum particle, or even to every cell. The cheapest experiences to create would be just brains with very shady input from the environment.
And, by consequence, it seems unlikely that our simulation is a near-exact replica of the way things were in the real basement universe, because it's too expensive to compute how things really were. Of course, people kept history books and took video recordings, and those could help stitch together a rough picture. But our simulated experiences would then be akin to a movie reenactment of the fall of Julius Caesar: The costumes and events and environment might be about right, but the simulation would be making up the gaps that were lost to history.
Timeless decision theory suggests that even if we are in a simulation, our choices can still matter a lot if they correspond to choices that our same brains made in the basement universe. But if we're not an exact simulation of the basement universe, then it seems our ability to influence the basement is less than we might have thought. Still, if there are lots of simulations of minds close to what was in the basement (e.g., people narcissistically creating vast copies of their former selves with approximately realistic environments), the correspondence may still hold enough to matter, but I don't know how much it's weakened. Perhaps the simulation is only being held on the right track to correspond with historical reality through artificial revisions, because the environment and choices of the simulated mind really aren't close enough to what happened in the basement due to butterfly effects resulting from the insufficient level of detail?
In view of this, my estimation of the power of our minds if we're in a sim is slightly lower than before, which means that it's slightly better than I previously thought to act as though we're not in a sim, because if we're not, then we potentially have much greater power. That said, the mind experiences generated in sims may be replicated astronomically many times, and to the extent that actions still have physically reasonable consequences in the sims, then our choices still do still matter both to ourselves and to our plentiful copies -- even if we don't control anyone in the basement.