Superficially, this is little more than the philosophy "Brain in a Vat" thought experiment. It has some interesting uses for those interested in the subject of ontology, but it makes for awful science.
At its most fundamental level, it's bad science because it is unfalsifiable. A little like the question of "does God exist?", testing it requires the ability to inspect our universe from outside. So far, we have no means of even describing how that might happen, much less making it actually occur. This is one of the reasons that any hypothesis that ends with "and therefore God" (or some variation thereof) is fundamentally not science. The minute you can invoke an unknowable external entity which has no meaningful description, you are simply not engaging in science.
Since I am not a theoretical physicist, I'm not going to go after the idea that we live in a simulation through that lens. I'm fairly certain that people who are a lot smarter than me can explain just how problematic the idea is in understanding the universe. The physics of the universe are complex and only partially understood today.
From a computational perspective, it's much easier for me to critique.
Limits of Current ComputingAt its most fundamental level, current computer architectures are not adequate for modelling the kind of complex, dynamic system that our universe clearly is. Digital computing is finite and deterministic in its processes - everything ultimately must produce a discrete result. Our universe is quite different in this regard. It tends towards equilibrium, which is an analogue state of relative stability. This is, of course, miles removed from what is readily modelled in a computer. Even modelling an integral in a computer is at best a coarse approximation.
As yet, we have not been terribly successful in modelling even the most fundamental aspects of biology in computing. Attempts to model intelligence have given us such wondrous sounding technologies as neural networks, but even those cannot be said to accurately model their biological counterparts.
Analog computing might eventually provide us with modelling that extends beyond the current limitations of digital computing, but progress in that domain has been limited, overshadowed by the rapid pace of development in the digital computing domain.
Practically speaking today, we would have great difficulty building a simulation of an analogue universe which would approach the level of complexity needed to describe the complex universe we live in.
A Thought ExperimentHowever, for a moment, let's engage in a thought experiment. Assume that we could create a simulation that describes a "digital universe" which would work within the frameworks of our current computational abilities. Further, let us assume that this universe forms a digital equivalent of Abbott's Flatland - call it DigitLand. We can "peer in" to this universe and observe the goings on in DigitLand.
Just as the physical nature of our universe makes it impossible for us to step outside of our universe, the virtual nature of DigitLand would render it impossible for the inhabitants of DigitLand to step out of their own universe. Any program that runs in a computer is only able to reach beyond that computer to the extent that the computer itself has connected inputs that it can access. So, on that basis alone, it is impossible for the inhabitants of DigitLand to test the idea that there is some metaphysical (metadigital?) world beyond their universe.
Just as the Halting Problem makes it abundantly clear that writing "code to inspect other code" is deeply problematic, so is trying to break out of your current universe using the laws of that universe. Godel's Incompleteness Theorems serve quite nicely to generalize this principle beyond the Halting Problem. Formal systems have limits, and it has been well demonstrated that you cannot use a formal system to prove the completeness of itself ... bad things happen when you try.
So, even if we are part of a "giant computer simulation", the idea that we "prove" this within the laws of our universe seems highly unlikely. It would be impossible for the denizens of DigitLand to reach out of whatever computer their universe was hosted in, and we are similarly limited in our universe if it were part of some kind of grandiose simulation.