As you've probably suspected all along, there's a slim but real possibility that the entire universe is just one big simulation being run on the computers of hyper-intelligent pan-dimensional beings. Seriously. This is coming from scientists, people! The good news: there may be a way that we can find out.
The theory behind this whole "universe as a simulation," uh, theory, is actually not that hard to understand, even for us normal people. It goes like this: right now, physicists are capable of simulating the entirety of one infinitesimally small part of the universe. They need a supercomputer to do it, and the simulation is only of an area a few femtometers across, which is really freakin' small. But, the simulation is of everything: particles, energy, space, time, the lot. This means that, fundamentally, the simulation cannot be distinguished from the real thing: if you measure the simulation, you'd get all the same results as if you were measuring a piece of real space the same size.
Now remember, this is stuff we can already do. And it's not hard to imagine that, in the future as computers get faster and more powerful, the amount of universe that we can simulate will get a little bigger. If we can upgrade from a femtometer simulation to a micrometer simulation, say, an area of fake universe large enough to simulate a single cell. If (or when) we do that, the behavior of that cell and any measurements we make on it would be completely indistinguishable from that of a real cell. If they aren't, then the simulation needs more work, but there's no reason why (with enough computing power) this wouldn't be possible.
So now pretend that you're a hyper-intelligent pan-dimensional being equipped with the sort of computer that hyper-intelligent pan-dimensional beings tend to have lying around. This computer works just like the computer that kinda-intelligent less-pan-dimensional humans are using to simulate a femtometer-sized region of the universe, except that, instead, it can simulate the whole damn thing. All of it. And that simulation would be impossible to distinguish from something "real."
Or, nearly impossible, anyway. There is a way to tell.
In any simulation of the universe, you have to simulate space and time. You can make this simulation as detailed as you want, but you can't make it infinitely detailed, and at some point, if you look closely enough, you'll be able to see the "pixels" of any simulation. Now, we have to assume that if our universe is a simulation, it's a pretty darn good one, and if those pixels are out there, they're going to be awfully small. While the pixels might be smaller than we can see directly, we might be able to figure out if they're there by measuring high-energy cosmic rays, which exist in smaller and smaller regions of space as their energy increases. If the universe isn't a simulation, cosmic rays should be able to have as much energy as they want, while if the universe is a simulation, the cosmic rays would be limited in energy to the size of the simulation's pixels, and there'd be a cut-off point.
As it turns out, there's a cut-off point. It's for a different reason, related to cosmic microwave background radiation — so you can stop freaking out — but there are some other rules that cosmic rays would have to obey in a simulated universe made of pixels: basically, the cosmic rays would preferentially travel straight along the axes of the pixels instead of diagonally across them, meaning that there wouldn't be an even distribution of cosmic rays in every direction.
This is something we can measure right now, and if it turns out that we don't see an even distribution, we might even be able to figure out what the orientation of the axes of our simulated universe is. In other words, we could measure which way is actually "up."
We should mention that there are a lot of assumptions to this model, and it's entirely possible that either the universe isn't a simulation, or the universe is a simulation, but it's far more detailed or constructed much differently than the physicists have suggested.
Either way, just to be safe, I have a suggestion to make for the good of humanity and our potentially simulated universe: we drop everything that we're doing and devote ourselves to constructing a message a million miles high out in space that simply says "DO NOT UNPLUG."