Friday, 2 December 2011

The Deterministic Universe

“There is a theory which states that if ever for any reason anyone discovers what exactly the Universe is for and why it is here it will instantly disappear and be replaced by something even more bizarre and inexplicable. There is another that states that this has already happened.”
Douglas Adams
The creation of the universe is a mysterious thing (from our viewpoint within its boundaries at least). We can theorize and think ourselves closer and closer to the beginning of time and come up with theories for that beginning that correlate with observations done today. The beginning itself though, and how something could come out of nothing (if it did), could very well be impossible to grasp.

Let us, for discussions sake, create a universe in a state at the start of its time. We will also assume that this state could be exactly described, and that if we knew every underlying parameter we could from it derive the next moment in time. This would mean that the universe was deterministic.

In a deterministic universe we could, assuming that we knew all the input parameters (not worrying about computational limitations) exactly calculate another state that is further along in time. A complication would probably be that if we tried to predict a future state, that state would look different because of us being part of it and thus changing it. Since this is a thought experiment, we will just assume that an observer is able to see the state from the outside without affecting the universe. If this was true then, in a deterministic universe, any passage of time would be a surjective function, where every input state maps to exactly one outcome.

The above version of a universe would not fit very well into the more popular theories of today. In fact everything points to uncertainty being a core principle of the universe. This could very well be true, although it could also be true that the randomness we see is based on some pattern that would only be obvious if we extended our viewpoint to outside the current realm. If there was no way for us to see that pattern, to us the universe would always be uncertain even if the rules controlling it were deterministic.

So let us imagine that the universe has these properties of being entirely predictable from a given initial state. Would that mean that if we started a new universe, the same events would happen and a version of me would end up writing this article again? Well, if we go one step back there is no state before the creation (once again, as far as we know). This could mean that even though the universe would behave the same way from a certain state, it could start from different states (and laws) and such even the deterministic universe is not deterministic if we do not have an initial state.

Time to sum this up. If the universe is deterministic it means that if we have the configuration for a universe at a certain time, all that follows can be inferred from it. If it is not deterministic, then the exact same state could yield something different the second time around. Whichever one it is, from where we stand, it will probably always be unpredictable. Just like the amount of time between these articles some things will always be shrouded in uncertainty.

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