2024-12-31

It's Impossible To Know The Future

The idea that it is impossible to know the future is quite a simple fact. Yet, I’ve wondered what a definite proof of this would look like. Can it be done?

Simulations

If we wanted to predict the future, one way would be to build a simulation of the universe, and simulate the universe up to some time in the future. But for this to be useful, it would need to go fast enough (no need to predict what happens in 2030 if we need to wait until 2040 to compute the simulation).

Magic computer

Hence, let’s assume, as a thought experiment, that we have some kind of magic computer that can simulate the Universe faster than our reality (that is, at a rate of more than 1 second/real second), we would very quickly reach a point where infinite energy would be required.

Let’s say we started running our universe simulation at time $t_{0}$ . There will be some point at a time t₁ where our simulated universe will be at the time t₀, that is when we started running our universe simulation. This means there is now a simulation inside our simulation. Then at some point in time t₂, the simulated universe will have advanced to t₁, at which point another simulated universe will be created. We now have a simulation inside a simulation inside our simulation. This process carries on like that an infinite number of times.

Infinite energy required

The problem with this is that $t_{2} - t_{1}$ is smaller than $t_{1} - t_{0}$ because, remember, our simulated universe goes faster than the universe we live in, and $t_{3} - t_{2}$ is smaller than $t_{2} - t_{1}$ for the same reason. This continues on and on with $t_{n + 1} - t_{n} < t_{n} - t_{n - 1}$ . What this mean in practice is that there is a point in time where there will need to be an infinite number of simulated universes. This happens as we can safely assume that simulating a universe inside a simulated universe takes no less energy than simulating it in the first place (otherwise, this would mean the universe simulation program could be infinitely optimized, until it takes almost no energy to run it, which is plausibly impossible)

Nonetheless, if we had a way to make a computer that could use an infinite amount of energy, the consequences could be quite intriguing.

Thus, simulating the universe at a faster speed would result in infinite energy usage, which is impossible given the universe has finite energy as long as you consider super-Turing machines do not exist. Therefore, universe simulations running faster than the one we live in are impossible.

What if we could actually predict the future ?

This would cause an infinite recursion. Predicting the future implies that we predict a future which changed depending on what we predicted about the future. So, our prediction of the future depends on the fact that we already predicted the future in the future.

This would only be possible if we suppose determinism and if the prediction was in some “stable equilibrium” such that knowing about the future didn’t change the future. While this doesn’t ring to me as impossible, it seems highly unlikely.

What if the energy cost of simulating the universe in real-time is lower than we think ?

Some people say that by cutting corners, like not simulating things we can’t see, we would be able to simulate the whole Universe in real-time or faster. I’d argue that because of all the inaccuracies it creates, it wouldn’t be our Universe. Think about it: a lot of things do happen when we aren’t looking: a couple hydrogen atoms can trigger a massive chain reaction, and the details of that reaction need to be exactly right in our simulation, which meant statistical means like local quantum mechanics cannot be used.