How can you prove you’re not in a computer simulation?

I’ve enjoyed read this article in Cosmos Magazine, that has concluded that we cannot live in computer simulation of the kind indicated in the outstanding 1999 movie The Matrix.

The article reports that two scientists set out to see whether whether it was possible to use a technique known as Quantum Monte Carlo to study the Quantum Hall effect. The Quantum Hall effect is phenomenon in physical systems that exhibit strong magnetic fields and very low temperatures, and manifests as an energy current that runs across the temperature gradient.

According to the scientists, the Quantum Hall effect indicates an anomaly in the underlying space-time geometry, and the Quantum Monte Carlo method uses random sampling to analyse this effect.

However, the scientists showed that attempts to use quantum Monte Carlo to model systems exhibiting anomalies, such as the quantum Hall effect, will always become an impossible task because the complexity grows on an exponential scale when analysing more and more electrons from our universe. Indeed, he scientists worked out that just storing information about a couple of hundred electrons would require a computer memory that would physically require more atoms than exist in the universe!

Their conclusion is that we cannot be living in a Matrix-style simulation because of the impossible amount of computing power in a machine that would an order of magnitude bigger than the universe itself!

What interests me is that, ever since I saw the The Matrix, my own conclusion has been that we are not in a computer simulation because computers cannot create true random number sequences.

Most programming languages have a random() method that returns a number between 0 and 1 with lots of decimal places. As a developer this number can multiplied to create a range of, say, 1 and 49 for a lottery ball selection simulator. This function is known as pseudo-random and can eventually become predictable based on a task as simple as taking a count of each number generated (say a billion times) and spotting that some numbers are consistently more often chosen than others every time you run the simulation.

If we were in a a computer simulation, we would be able to spot these patterns in the the most apparently random of sequences. For example, lottery machines that tumble balls to select the ones for a particular draw would still be predictable! Indeed we would uncover that everything apparently random was always non-random – which would then raise suspicions about our universe.

However, we can prove true randomness in our real universe, and that means our universe is real.