Physics, Simulations & Computers30th December 2024
Do we need a whole universe to simulate a universe? No.Physics“Physics is a set of compression algorithms for our Universe.”In a universe where there are no laws of physics, you do need a whole universe to simulate a universe. Randomness personified.But our universe has laws of physics. So we can use those laws and run computations to predict the next state of (a part of) our universe. This is the beautiful thing about physics – it lets us make accurate predictions. We don’t need a whole universe. We just need a powerful enough computer. This is what Elon Musk meant when he said “Physics is a set of compression algorithms for our Universe.”SimulationsCan we simulate our Universe with a computer?That is tricky. I suspect the answer is no. To simulate our WHOLE Universe with a computer means the computer has to simulate itself and it runs into recursions. I don’t know how to resolve those. Maybe it’s not possible. We’ll quickly run out of the call stack of the computer. If you have any insights regarding this, please let me know.Also, the digital computers have a HUGE limitation – the floating point representation is only precise to a certain degree. Put another way, you can’t represent certain real numbers precisely on digital computers. But our universe is filled with real numbers! Imprecise representations of these numbers on digital computers lead to imprecise computations and predictions and ultimately an incorrect simulation. Simulating a 3-body problem is an example of this[1] – Chaos Theory. (You can find simulations of a 3 planet system with slight differences in initial conditions on YouTube and see how wildly varied the outcomes are. The small differences become crucial. Precision matters.)Despite these limitations, what we can do is simulate some other (small) universes. Like video games, for example. Or protein folding by AlphaFold. Or weather patterns of our planet.ComputersComputers are special.Take some sand from a beach. Now, if you arrange the atoms from the sand cleverly, you get rocks capable of running some computations and talking back to you! The device you are reading this essay on is doing exactly that. Dull and unimpressive sand upon reconfiguration does these magical things!Computation capability in our universe increases. How wild is that! You can now simulate (small) universes upon these things. This is why computers are special. Although, computers do a lot more besides simulations.PS – Finished watching Pantheon S2 – a sci-fi show tackling simulations – which prompted this essay.
A shot from Pantheon TV Show
A shot from Pantheon TV Show[1] 3-body simulations with small differences in initial conditions. Code below.
The code to run the 3-body simulations. Show code