In short, we don’t know. But let’s explore the problem a bit deeper.

What is meant by a “simulated universe” is that our universe, the one that we experience as our reality, is actually a simulation being run on a fantastically powerful computer, presumably designed and built by a race profoundly more technologically advanced than ourselves. In the movie, The Matrix, most humans were plugged into and experiencing a simulation of the entire Earth. This movie is often brought up as an example of a simulated universe, but it’s not quite what we mean. In the Matrix, humans still had a physical existence. Their brains were just plugged into a simulation. In a simulated universe, however, we would be entirely simulated ourselves, not really floating in a bubble of liquid while information is being fed into our non-simulated brains.

There are several basic approaches to this question – philosophical, theoretical, and empirical. The Rationally Speaking blog recently tackled the philosophical approach to this question. In that series of posts David Kyle Johnson writes:

The simulation hypothesis suggests that the world we inhabit is a simulated world and that we are simulated persons. And Nick Bostrom has argued this hypothesis is much more likely than you might think. His argument goes like this: If we do create a simulated world, we won’t stop there. We won’t just create one. We didn’t stop with one iPhone; we wouldn’t stop with one simulated world. Once Pandora’s box is open, you can’t close it. If there is one, there will be thousands. And beings in simulated worlds could even advance enough to create their own simulated worlds within their world. So a physical universe with a single simulated world isn’t a very likely scenario. Thus, when we consider the possible physical universes that could exist, we realize the following: either there is one real physical universe and in that universe no simulated world is ever created, or, in the one physical universe that exists, thousands upon millions upon billions of simulated worlds are created.

Therefore, some philosophers conclude, it is highly likely that we are living in a simulated universe, since most universes would be simulated. However, there is one massive “if” in that chain of logic – if we create a simulated world.

Is the current universe we are experiencing simulated? Could we empirically demonstrate its simulated nature if it were? It seems that the answer to both questions may lie in an aspect of physics known as lattice-gauge theory. At its most fundamental level the universe is made of fields of energy. The question that is relevant to the simulated universe is this – are those fields ultimately continuous or discrete? Another way to state this is this – is the universe ultimately analog or digital? If digital, then that opens the possibility of simulating the universe in a computer, and therefore that the universe itself is a simulation.

Think of the lattice as a grid, with spacing representing the smallest interval that energy fields can possess, and the increments as advancing time. Physicists have been able to describe the strong nuclear force in terms of such a lattice. If the lattice theory is correct, then nothing can exist that is smaller than the spacing between two points on the lattice. This provides an opportunity to test the lattice theory – as explained in a recent MIT technology review article:

The question that Beane and co ask is whether the lattice spacing imposes any kind of limitation on the physical processes we see in the universe. They examine, in particular, high energy processes, which probe smaller regions of space as they get more energetic

What they find is interesting. They say that the lattice spacing imposes a fundamental limit on the energy that particles can have. That’s because nothing can exist that is smaller than the lattice itself.

So if our cosmos is merely a simulation, there ought to be a cut off in the spectrum of high energy particles.

It turns out there is exactly this kind of cut off in the energy of cosmic ray particles,  a limit known as the Greisen–Zatsepin–Kuzmin or GZK cut off.

They further propose that there will be an asymmetry in the direction of observed cosmic rays, and that they can look for this asymmetry to confirm the existence of the lattice (and therefore a digital universe, and possibly a simulated one).

The same line of reasoning, however, leads to the opposite conclusion – that the universe is analog – when the weak nuclear force is considered. So far (as explained in a recent Scientific American podcast) physicists have been unable to place the weak nuclear force on the lattice. George Musser explains that our current inability to place the weak nuclear force on the lattice may simply be due to the fact that it is a very complex problem that no one has yet solved. The argument that we are living in an analog universe because physicists have not explained the weak nuclear force in terms of the lattice, therefore, is an argument from ignorance. According to Musser, physicists have not proved that the weak nuclear force is analog, they have only been unable to prove that it is digital.

But, he argues, it is possible that this problem has not been solved (despite extensive attempts to do so) because it is insolvable – because at its most fundamental level the universe is analog and not discrete.

Even if some aspects of quantum electrodynamics, chromodynamics, and the standard model of particle physics are ultimately discrete (can be placed on the lattice), if any aspect is not then the universe cannot be simulated.

Conclusion

At present the current answer to the question of whether or not our universe is simulated has no definitive answer. The physics questions above address the question of whether or not it is theoretically possible for our universe to be simulated. If it turns out that the answer is that it’s impossible, then of course our universe is not simulated. If it turns out that the lattice-gauge theory is correct and applies to all of physics, then it will be theoretically possible to simulate our universe, but we still won’t know if our universe is in fact simulated.

That leaves us with the empirical approach – is there any observation that we can make that would demonstrate our own universe is simulated? I think the answer to this is no. In a simulated universe we would be part of that simulation. How could we make an observation from within such a simulation that would demonstrate it’s a simulation? Further, at that level, what’s the difference between a “real” universe and a simulated one (from the perspective of someone inside the universe)? Even if simulated, what we experience is just the universe.