1MileCrash said:
But if that starting event did occur identically, would the results not be identical? And any results stemming from those results?
If all factors are identical, how can there be a new result?
You're thinking of a
deterministic universe, deterministic meaning that it is governed by a set of equations that determine the evolution of systems with time, so that if you know the initial conditions, and you know those equations, you can predict the behaviour or state of those systems at all subsequent times. Say you know a classical particle's initial position and velocity, and you also know its equation of motion. You can then determine its trajectory (i.e. you know its position at all future times). This is sort of true on large scales for objects that behave in a manner described by classical physics.**
When you get to the subatomic world, quantum mechanics is the relevant physics. The point of quantum mechanics is that things (e.g. quantum particles) are not deterministic -- properties like their positions and their momenta are not governed by such equations. Those properties are random variables whose probability distributions are given by things called wavefunctions. The
wavefunctions evolve deterministically with time, but unfortunately they don't themselves say anything direct about the physical observables (i.e. the quantities that we measure, like position or momentum). All they can tell you is what the
likelihood is that a measurement of particle's position will result in a particular outcome. In this sense, quantum mechanics is inherently
probabilistic (as opposed to deterministic). The same particle in the same state doesn't have to do the same thing twice (it's random). In fact, if you had an ensemble of systems that were prepared to all be in exactly the same quantum state (e.g. maybe each system consisted of a particle described by exactly the same position wavefunction), and if you performed a position measurement on each one, you'd get a different answer every time (EDIT: okay sometimes the results would repeat, but that's expected for a truly random situation). In fact, that's one way to think of what the wavefunction is -- it describes the
statistical distribution of results that you would get when performing position measurements on such an ensemble of identical quantum systems.
**EDIT: I should also mention that even for systems whose individual components evolve deterministically, if those systems are sufficiently
complex[,i], it may be impossible to predict their behaviour, not only because doing so is computationally infeasible, but also because the system manifests some sort of emergent behavour (i.e. the whole is somehow more than the sum of its parts). This emergence is a really interesting aspect of complex systems that I must confess I don't know too much about. But it's the reason why, for example, we can't really predict the weather too well (not on timescales longer than a few days) and it is also related to that "chaos theory" stuff. Again, I'm getting into territory here where I don't really know what I'm talking about.
