Is it possible?Without getting too philosophical:
I believe yes, theoretically it could be. If you consider that the universe and everything within it is the result of interaction between particles (of some description) and forces, then yes it could be modelled. Providing that you know the initial state, and precisely how everything interacts.
Practically, no it couldn't. We don't have the computational power, nor complete enough understanding of the 'system' to do it.Getting very philosophical:
We have an initial state S and a function f that transforms the current state into a future state. f contains therefore the complete laws of physics of that universe.
Don't you find this very, very interesting? This leads me towards the belief that choice is an illusion, and that whatever has happened in the past was always going to happen, given the current values of 'S' and 'f' of the universe in which we currently exist. Not in a 'predetermined fate' kind of way (although I guess it is related), but in a 'we have multiple choices, but we were always going to make the choice that we made' kind of way.
I once saw it explained with a snooker analogy in some strange popular science video. If you could set up a snooker game so that the balls are in the exact
same position at the start of the game, the environmental conditions are the exact
same, and you break with the exact
same application of force, then the balls will move the exact
same way each and every time. I.e. the outcome is the same, given the exact same initial state and influences. Could this not then be extended to the universe? If you could 'reset' the universe to time = 0, give it the exact same state as our current universe, then let it run its course again, there is no reason to suspect that the outcome would be any different to now. I.e. I'd still be sitting here and writing this post, you would be sitting here reading it, I would've had the same thing for lunch, so on and so forth.