The Simulation Hypothesis holds that alien races (or future versions of humanity) will eventually get the computing power and programming techniques to simulate the whole universe and that when they do, they will probably do so millions of times, meaning that most universes are simulations, and thus the odds that this universe is not a simulation are vanishingly small.
Oh my God are there a lot of problems with this argument. Such as: why is it foreordained that computer science will eventually attain the power to simulate whole universes, including autonomous, conscious beings? There is no way to predict whether you are standing on the upslope of a power-law curve or an S-curve that's about to level off, until you get farther along the curve.
Then there's the assumptions about the inevitable conduct of alien races with vastly more advanced computing power than us. This isn't a falsifiable hypothesis, it's a mere fancy. I can conceive of alien races that engage in lots of conduct that doesn't end with simulating the Earth, let alone millions of them. Elon Musk's ability to found a company that makes self-driving cars does not give him the ability to make sound predictions about the aspirations of hypothetical alien races in the distant future.
Finally, there's the statistical card that's being palmed there. Here are some other versions of this argument: the likelihood of your parents meeting and the specific sperm and egg cell making rendezvous are infinitesimal, compared with all the other possible outcomes, therefore God ordained that you would be born, because the probability of it happening on its own is vanishingly small.
Here's another version: the universe's timespan is unimaginably long. The human lifespan is comparatively so small that it barely exists. The likelihood that you are alive at any given moment is thus a tiny number divided by a number so large that the result is largely indistinguishable from zero, and remains zero-ish unless you are actually immortal.
Therefore you are immortal.
But let's put those quibbles aside and dig into some physics, shall we? Theoretical physicists from Oxford just published Quantized gravitational responses, the sign problem, and quantum complexity in Science Advances, in which they document the geometric complexity of computing the location of particles that make up the universe. It turns out that figuring out these particles' locations scales at n^2, meaning the amount of computing power needed doubles with each additional particle, which means that "storing information about a couple of hundred electrons would require a computer memory that would physically require more atoms than exist in the universe."
So unless this is one of the tricksy rules set up by our hypothetical alien Matrix-crafters, we are not living in a simulation.
You are, however, immortal.
The researchers note that there are a number of other known quantum interactions for which predictive algorithms have not yet been found. They suggest that for some of these they may in fact never be found.
And given the physically impossible amount of computer grunt needed to store information for just one member of this subset, fears that we might be unknowingly living in some vast version of The Matrix can now be put to rest.
Physicists find we're not living in a computer simulation
[Andrew Masterson/Cosmos] (site currently down, Google cached copy)
via Naked Capitalism)