The simulation hypothesis is quite simple: we could be living in a simulation. Nick Bostrom makes this more concrete. Since simulating realities appears to be physically possible, either intelligent species (like future humans) choose not to simulate worlds (for some reason), or else the number of simulated worlds (and thus simulated minds) is probably quite large. In that case, most entities with experiences like ours are actually in a simulation. So, statistically, we are in a simulation.
The argument is simple enough to be persuasive. Of course, there are many counter-arguments. Here, I just want to consider some consistency aspects.
Physics
In order to bolster the simulation hypothesis, people sometimes point to aspects of our reality’s physics. For instance, they note that if space and time are discretized at the quantum level (as they might be under quantum gravity or even QFT), then this sounds a lot like the partitioning one would need to make reality computationally tractable. Others note that the speed-of-light partitions the universe into causal regions, which is convenient if you’re trying to simulate it across a set of servers running in parallel. Others sometimes point to the weirdness of physics (quantum collapse of wavefunction, etc.) as evidence of the limits of the simulation. These arguments are often made semi-humorously; but they point to something real.
There is a problem with this kind of thinking. Specifically, the arguments implicitly assume that the base reality used to simulate our world has similar physical laws. But this is strange. There are two possible cases:
(1) Either the base reality has different physics from our, in which case we can’t really infer anything about their reality (or ours) from how our reality is being computed. For instance, the base reality could be computationally parallel such that they don’t actually need to impose information-propagation constraints to make our reality tractable.
(2) Or the base reality has similar physical laws as us (including separated causal regions, etc.). This means their attempts to computationally simulate our reality are limited in expected ways. However, this also means that you can’t point to those same features as evidence that you’re in a simulation. After all, the people in the base reality could make the same argument (but they would be wrong).
Overall, looking at our physics doesn’t seem to tell us anything about whether we are in a simulation. Or rather, it may well provide clues; but it does not allow one to construct a self-consistent argument and thus it doesn’t provide any believable evidence one way or the other.
Boltzmann Brains
Let us take a detour into Boltzmann brains. The idea is that if you have a bunch of hot matter churning randomly (gas at equilibrium, or whatever), then it could eventually (by random chance) happen to coalesce to form a brain just like yours, including all your memories and current thoughts. Of course this is low-probability and it would dissipate near-instantly, but for a brief moment that brain would think itself real and moreover would have evidence (based on false/random memories) that it lived in a proper universe with a meaningful personal history.
However, this creates a problem. If the universe has more “random equilibrium gasses” in it than “real proper brains”, then you, as an observer, should actually statistically conclude that you are probably a Boltzmann brain and not a real person. If we look at our actual universe, we find that our current time period (of non-equilibrium stars emitting energy, creation of complexity, conscious observers) is quite fleeting. The universe is predicted to expand without bound and enter a heat death that is effectively an infinite-long equilibrium. This means that the amount of space/time for Boltzmann brains is much larger than the space/time for real brains. So you’re not real.
There might be reasons why Boltzmann brains don’t arise in quantum universes. But even if they could arise, there is an additional philosophical problem: cognitive instability. Suppose you find the arguments convincing, and you thus accept you are a Boltzmann brain. Well, upon accepting that, you should doubt your own memories are authentic. Your understanding of physics (and even math/logic) cannot be relied upon now that you believe your memories are just random generations. There is no reason to assume your logic is correct. So you’ve undermined your own belief in being a Boltzmann brain. Since there is no way to consistently believe to be a Boltzmann brain, you must instead (as unsatisfying as it may be) assume that you are one of the special cases of being a real brain.
Simulated Consistency
A similar instability argument can be levied against the simulation arguments. If one believes there is convincing evidence that we are in a simulation, then one must immediately begin to suspect the evidence, physics, our memories, etc. If we are being simulated, what reason do we have to be confident that our memories are trustworthy? What reason do we have to believe that the physics we infer is telling us something meaningful about “reality” (whether that means the hardware/software simulating us, or base reality, or whatever)? What reason do we have to believe that base reality is a collection of sentient entities choosing to run a simulation? Whatever arguments you bring to bear will rely upon evidence (memories) and logic (calculation of your simulated mind); whose very reliability we should now question.
So being-in-a-simulation is cognitively unstable. That doesn’t make it wrong. But it means that one cannot provide believable evidence for it.
Conclusion
The point is that we may well be in a simulation. But it is very difficult to provide believable evidence for the same. Whereas it is at least possible to construct a consistent understanding that we are real entities in a consistent physical universe.