Can we know if we are actually living in a computer simulated universe? New physics research gives us some possible clues about how we might tell and how hard it would be to artificially create the world we experience. This work is at the fine border between scientific speculation and speculative science. Keep in mind that it is about as far from practical and testable as physics can get.
The heart of the matter is to determine whether the space we live in has infinitely small distances. What do I mean by that? Everyday intuition tells you that you can take one step, or half a step, or half of a half of a step, or a half of a half of a half (1/8) of a step, and so forth. The universe, so far as we know, probably allows you take smaller and smaller steps forever (infinitely).
However, when a computer simulates reality, it does things differently. It can't use infinitely small space because it can only store a limited (finite) number of things in its memory. This places a limit on the very smallest step you can take. So, if we were living in a simulation, we might find out that trying to take too small of a step is impossible!
One of the very best current computer simulations of reality is lattice QCD. QCD is the quantum theory of the strong force. It describes what protons and neutrons are made of and how they interact to form atomic nuclei and carry out nuclear processes. Computer simulations of QCD must use space with a limit on how small the size of a step can be. These simulations assume that space has a smallest possible step to move (or set of positions that you can occupy). Currently, the smallest step is somewhere around one tenth to one twentieth of a femtometer (10-16 m = 10-1 fm). This is about one hundred times smaller than the nucleus of an atom (2-15 fm).
To simulate a cube of space the size of the period on this page, you would need roughly 1035 possible steps you can take or locations you can be at in that space. Right now our fastest computers could never do this in a trillion years.
Lattice QCD simulation (Brookhaven National Laboratory)
This work analyzes extremely high energy bursts from outer space, called cosmic rays. Based on the energy of these rays, physicists claim that the space they come from must have steps at least as small as one millionth of one billionth of a femtometer (10-27 m = 10-12 fm). So if we are being simulated by some future computer, it must be incomprehensibly powerful to be able to analyze this many possible steps. (Think trillions of years to simulate the size of an atom.)
This raises a new question. Is it even possible to build such a computer and carry out a simulation this powerful? While we have been experiencing approximately 50 years of unbelievably high (and consistent) increase in computer power, it would take centuries (or millennia or more) of growth continuing at the same rate for this to be possible for us. Furthermore, there are certain other problems, like whether there are enough atoms in the universe to build such a powerful computer, which no one has any idea about.
While this new evidence gives us something to think about, we are still back to essentially the same ancient conundrum. Before the computer age, philosophers wondered if we could all be living in someone else's dream. Like that old puzzle, the new practical conclusion is that we still can't tell, and so we might as well not worry about it.