My thoughts on the simulated universe

Today I had one of those days in which I have an active mind. Even considering the fact that I slept only 5 hours to assist an absurdly long 4-hours-lecture on Introduction to String Theory. I decided to invest most of such precious brain activity in making memes about Greta Thunberg, one of the most prolific activities of our age. However, during the day I also reserved some time to think a bit about the pop-science theory that suggests that we live in a computer simulation, presumably run on a computer of a hypothetical advanced civilization. I made a survey on my Instagram account and most of my physicist colleagues voted a sound “NO”. So yeah, the theory isn’t very popular among my circles. I’m going to throw some of the thoughts I had today about it.

First, we shall (although it doesn’t really matter) differentiate between three different scenarios:

1. The computer that runs the simulation is classical and the physical laws of the universe that contains it are the same as the physical laws of our simulated universe.
2. The computer that runs the simulation is quantum and the physical laws of the universe that contains it are the same as the physical laws of our simulated universe.
3. The physical laws of the universe that contains the computer that is simulating our universe are different from the physical laws of our simulated universe. Therefore we cannot say anything about the nature of the computer.

Let's now try to discuss each of the scenarios.

Scenario 1: Classical simulation in an equivalent universe

This scenario is probably the easiest one to argue, although I don’t think that to completely dismiss it by empirical arguments is possible. Supposing that the classical computer is deterministic (yes, there are also probabilistic classical computers) a sufficient argument to dismiss the scenario would be to dismiss determinism. This is a very old and long discussion in Physics, initiated by Laplace, continued by Einstein and Bohr and that even today we can find famous theoretical physicists discussing (in a not very friendly way) about it. I’m not going to replicate here the discussion “determinism” vs “randomness” of quantum mechanics, Google can do the work for me.

However I want to point out one of the arguments that came out in the answers of a famous StackExchange post by the physics Nobel prize winner Gerard 't Hooft. Hooft is a physicist who put a lot of effort into trying to build a solid deterministic quantum theory (like the cellular automata interpretation). In this post he asks the Physics community “Why do people categorically dismiss some simple quantum models?” (and by simple he means deterministic). The most voted answer to this post is from no other than Peter Shor, one of the founding fathers of Quantum Computing. In his answer Shor states: 

“Regular quantum mechanics implies the existence of quantum computation. If you believe in the difficulty of factoring (and a number of other classical problems), then a deterministic underpinning for quantum mechanics would seem to imply one of the following:

•  There is a classical polynomial-time algorithm for factoring and other problems which can be solved on a quantum computer.
• The deterministic underpinnings of quantum mechanics require 2^n resources for a system of size O(n). 
• Quantum computation doesn't actually work in practice.

None of these seem at all likely to me.”

However, if the reader stops to think for a moment about those arguments, he/she will notice that none of them invalids the simulation argument. The perception of time inside the simulation has nothing to do with the time outside the computer. To see this, suppose that you have a very slow computer and you want to play The Sims 3 and the game performs so poorly that your frame rate is 1 frame per second. To the sim people in the game, it is irrelevant the frame rate at which you are running the game, they will perform exactly the same actions. Shor, who is probably one of the smartest people alive, also thought about this possibility and that’s why later in his post he points out:
 

“For the second, deterministic underpinnings of quantum mechanics that require 2^n resources for a system of size O(n) are really unsatisfactory (but maybe quite possible … after all, the theory that the universe is a simulation on a classical computer falls in this class of theories, and while truly unsatisfactory, can't be ruled out by this argument).”

Here we can already see the difficulty of dismissing even the easiest scenario of the three. And even if we gathered enough empirical evidence to dismiss this scenario (or any of the three) beyond any reasonable doubt, we still could say that all experiments that we run are determined by the simulation and therefore couldn’t be used to dismiss it. This is what I call the “superdeterministic” argument. 

As a personal note, I find this scenario very unlikely. I don’t think that in an equivalent universe (and by equivalent I mean with same physical laws and comparable size and timescale) is it possible (or sensible) to build a classical computer that simulates our universe before the original universe reaches an entropic death or some equivalent fate.

Scenario 2: Quantum simulation in an equivalent universe

This argument is even more difficult to dismiss because now we don’t have the time constraints that we had in the classical simulation. Since the simulating computer is quantum, it could reproduce our quantum experiments in polynomial time and all the previous arguments start to fall apart.
However, it seems unlikely to me that a civilization could reach the point of such a vast computational power and the will to run the simulation. The main concern I have here is that supposing an equivalent universe, it is probably not possible to simulate our universe in a time faster than the time of the external universe. To state this more clearly: supposing that a civilization reaches the point in which they can simulate our universe, I think they only will have the resources to simulate it with a time rate no smaller than the time rate of their universe. In the same way that is proven in complexity theory of chaotic systems that we cannot classically simulate faster than our universe chaotic systems like a double pendulum. But I haven’t done the proper math. So, take this statement with caution.

Scenario 3: Simulation in a non-equivalent universe

We run simulations of systems that obey physical laws that are different from the ones of our universe, for example running a simulation in which the bodies don’t behave according to Newton’s laws of motion. This can be done easily with MatLab, Python or similar platforms. Why then should we constrain ourselves by thinking that the greater universe that contains the computer that runs our simulation has the same physical laws like the one that is simulated?

This supposition opens infinitely many loopholes in which you can still maintain the simulation theory, so it is completely impossible to dismiss by any logical or empirical argument.

Final thoughts

What I want to leave clear now is that I’m not defending here the simulation theory but pointing out that it is a theory impossible to falsify (and therefore, non-scientific in the most rigorous sense of the word). Scientific theories need for empirical signs to motivate further considerations. However, gathering empirical signs that we live in a simulation is at least as difficult as dismissing that we live in a simulation. We can only wonder how powerful must be and in which universe must exist a computer that can simulate us.

But all this nonsense doesn’t really matter for all practical purposes. We, humans, make models of the universe that allows us to predict some properties of it. All models that we can build consist of a limited amount of information that describes the universe. Any model could be translated to a binary version of it since all information can be expressed as a sufficiently large binary string. In the end, every model of the universe that we obtain could be translated to a grid of 1s and 0s switching according to some rules. Is that so different from a computer simulation?