So the Simulation Hypothesis, from what I've heard, is not scientifically testable because it is not falsifiable, which makes perfect sense to me and is the viewpoint I have always adopted.
Yet recently I have come across an argument from Michio Kaku on the topic of simulation hypothesis, and he has this to say about the concept:
I do not think we live in a computer simulation. No digital computer can compute all the motions of molecules in a simple object, e.g. the weather. The smallest object which can simulate the weather is the weather itself. When you add quantum corrections, then no digital computer on earth can simulate the quantum effects in the weather. So no digital computer can possibly simulate reality as we know it.
I mentioned that a digital computer cannot simulate even a simple reality, since there are too many molecules to keep track of, far greater than the capabilities of any digital computer. We need a quantum computer to simulate quantum reality, and hence, once again, the weather is the smallest object that can simulate the weather. Therefore, I don’t think we live in a simulation, unless the simulation is the universe itself.
Similar arguments are made regarding how the universe is too complex or large to simulate, such as this argument from Doug Bonderud:
Despite solid philosophical and theoretical arguments, a team from Oxford University has found reasonably solid evidence that our universe is more than a mobile application. The proof? Attempting to model specific quantum phenomena such as the Hall effect quickly gets out of hand — according to Cosmos, modeling just a few hundred electrons using the quantum Monte Carlo technique requires more atoms than exist in the universe. As noted by Fast Company, storing just 20 spins of one particle using this model would require one terabyte of RAM.
So I understand that, according to our known laws of physics (particularly the Bekenstein bound, which implies Bremermann's limit, which in turn is a consequence of the Uncertainty Principle) that trying to simulate an exact copy of our universe in our universe is impossible. But simulation hypothesis, at least how I understand it, is not asking about if it is possible to simulate our universe inside our own, but if there could be another reality "above" our own.
Why does the universe "above" ours have to conform to the same physical laws as our reality? Nothing in simulation hypothesis says this has to be the case; and it certainly doesn't seem like it is a logical impossibility. There doesn't seem to be any reason why, if we're in a simulation, the universe "above" our own couldn't have a much denser Bekenstein bound, or perhaps even none at all; the Uncertainty Principle may very well not apply to a higher reality. It may even be the case that such a reality is not "quantized" like ours, and is infinitely divisible, and thus an infinite amount of information can be "packed" in a finite space (in turn, allowing for processes like supertasks, possibly Super-Turing computation?). Obviously it would be impossible for anything like this to physically exist in our universe, but nothing seems to rule this out for a "higher" reality. The only requirement seems to be that any "lower" universe must be less powerful than the one above it.
However, could there be an argument that demonstrates the impossibility of the simulation hypothesis not with empirical testing, but with a proof by contradiction? i.e. Assume the universe is a simulation. Then A (rigorous proof details left as an exercise to the reader), which implies ~A, thus the universe cannot be a simulation. Does this kind of proof make sense when applied to a philosophical argument? It's definitely something I'm curious to know more about.