While reading Gödel, Escher, Bach, on the chapter covering formal systems and their relationship to well-formed strings ( see The p-z problem ), the author briefly mentioned the debate of whether the universe operates deterministically or not. This particularly interested me following my work with differential equations and chaos theory, where I learned that even simple systems can exhibit chaotic behavior, making long-term predictions impossible despite being deterministic in nature. However, was this just because of the complexity of the systems I was studying, or could it be that the universe itself is not deterministic?
Now obviously this is an unsolved question, but I wanted to explore the topic a bit more and see what arguments exist for both sides.
If the universe is deterministic, then the question would follow of finding the “initial conditions” of the universe, which would allow us to predict the future state of the universe. This is similar to how we can predict the future state of a chaotic system if we know its initial conditions. This has been a quest for physicists for centuries, however the introduction of quantum mechanics has thrown a wrench in the works, questioning if such answers would even be useful.
If the universe is not deterministic, then it would imply that there are some fundamental limits to our ability to predict the future state of the universe, similar to how we cannot predict the future state of a chaotic system without knowing its initial conditions. This would also dip into philosophy a bit with the question of free will, as if the universe is not deterministic, then it would imply that our actions are not predetermined and we have some level of control over our future.
Obviously, this is not something that can be answered definitively at this time, but it is an interesting question to ponder.