Heisenburg says we can't MEASURE a particle, it says nothing about SIMULATING them. It would, however, be quite impossible to simulate our own universe.



Just because quantum physics appears non-deterministic to us now does not mean that it actually is. It could be that it is deterministic under a set of laws we just haven't discovered yet.

I believe this applies to EVERYTHING.

There are zero inputs and there are an infinite number of states.

The original question was whether or not you could predict the future if you could simulate the Universe. If quantum mechanics is correct you cannot. It's a difficult concept to grasp because we tend to visualize particles as something concrete like a baseball, but they don't behave that way. Humans are hard-wired to view the world in terms of classical mechanics.

Simulation is measuring. To simulate something you have to mimic the behavior of something. The case of atoms and its constituent particles, you have to simulate their behavior which requires knowing how the original behaves exactly. HUP says you cannot know its momentum precisely.

Dash_Rendar wants to know if a supercomputer can predict the future with absolute certanty. My (dwindling) understanding of quantum mechanics is that you cannot, only make probabilities.

Well, yes, but you said nondeterministic, which is different. A finite state machine can be nondeterministic.

Also, state machines can be infinite, sort of.

Cough:
http://en.wikipedia.org/wiki/Laplace's_Demon

Remember when I made a thread about the double slit experiment?

Is the double slit experiment the one with photons?

I don't know much about advanced physics and things... but I think I'm gonna go with what JM said. If there's something that seems random, it's because we don't fully understand everything that's going on.

Consider a system with a set of initial conditions, which is then set in motion and eventually reaches some final state. If we vary these initial conditions a little bit and set the system in motion again, there are two things that can happen.

The system can reach some final state that is only a little bit different from the first one. The variation in final states is proportional to the variation in initial conditions. This is a classical system and is perfectly described by Newtonian mechanics. The usual examples of this are the simple pendulum, mass on a spring, pendulum on a spring, mass on a spring on a pendum (on a conveyor belt), whatever.

Or, the system can reach some final state that is very different to the first one. The variation in final states is proportional to the exponential of the variation in initial conditions (the constant of proportionality is called the Lyapunov exponent). Changing the initial conditions a little bit causes a very big change in final states. This is a chaotic system, and a particularly nice example is that if a pendulum on a pendulum. If you swing the first pendulum hard enough, the second pendulum goes crazy. This system is still deterministic, in that the final state is completely determined by the initial conditions, but the final state is very sensitive to a change in initial conditions. This is chaos.

When we want to study the very small (or even the large, at very low temperatures), we have to remember Quantum Mechanics. In QM, there is always a necessary uncertainty in measurements given by the Heisenberg uncertainty relations. In the old quantum theory, this was understood as an interference between observation and the experiment (in order to observe the motion of a particle, you have to bounce a photon off of it and this will deflect it and change its trajectory). This is a very pleasant semi-classical interpretation of QM, but some very clever variations on the double slit experiment (using a delayed observation) have shown this to be highly inadequate. In the quantum realm, uncertainty is a necessary part of reality. A particle is 'spread out' across many possible positions, into a 'wavefunction'.

So if we have a quantum system that experiences chaos, we have something that is truly very random indeed. The system is very sensitive to changes in initial conditions, but there is an inherent uncertainty in the initial conditions. The particle could be in one of various different positions (it is actually in all of them, all at once), and its behvariour is inherently random across its small range of positions. The chaotic system is very sensitive to these changes, and so this causes random behaviour across a very large range of final states.

This effect is very irritating for cosmologists. And also for anyone trying to build a computer to accurately simulate the entire Universe (or even any system significantly smaller than that). This effect is also significant for large particles (like atoms) in a strong magnetic field.

When you think about it we shouldn't be suppressed when randomness, we should be surprised when we see order. We observe so many rules that the universe operates by, but we don't know fundamentally why. Or why they should even exist.

I'm guessing though, that the whole problem of uncertainty about the position of subatomic partials has to do with the fact that matter is not discreet. It's very difficult to wrap your head around the wave properties of matter. I can't wait to take modern physics.