The name for the point where a probability changes

But the wavefunction evolves according to the time dependent Schrodinger equation.

I do not wholeheartedly agree. My understanding of Quantum mechanics is that the universe is deterministic. The wavefunction evolves according to causality. It is the initial conditions which are indeterministic. Such was the downfall of classical theory, which stated that knowing the initial conditions of a system one could predict its future behavior. One cannot know the initial conditions with absolute certainty. But, the wavefunction evolves in a deterministic fashion.

I agree completely. However, the question was about whether QM was deterministic and based on causality. Some of my understanding comes from scattering experimentation. The Rutherford scattering formula was derived under the assumptions of classical mechanics, which is decidedly (?) deterministic. With the application of Quantum theory, ie. the uncertainty in the position/momentum of the scatterer, the formula turns out to be the same. This, to me implies that the outcome is deterministic although the initial conditions are not. In other words, the wavefuntion evolves deterministically from the fundamental forces (potentials). I admit, I am not an expert. If you have other ideas I would love to hear them.

Could you please explain how the wavefunction evolving in a deterministic fashion would prove Dr. Heisenberg wrong?This message has been edited by Peeper, 01-10-2005 14:28 AM

Please do not think I am trying to belittle you, I am not. First, what is a function?A function from a set of D to a set R is a rule that assigns a single element of R to each element of D..The word single in the definition means that each input in the function’s domain has only one output in the range..Thomas and Finney, Calculus and Analytical Geometry, p.12Therefore, the waveFUNCTION has one, and only one, output for a given input.In order to determine the evolution of the wavefuntion one uses separation of variables in the Schrodinger equation. This allows one to solve for the initial wavefuntion state at time zero. The wavefunction then evolves (deterministically) according to the time dependent Schrodinger equation.This idea is born out experimentally in the use of such things as MRI, where the transitions (probability) among excited states is uniquely determined by the evolution of the wavefunction.Therefore, the wavefunction evolves deterministically (according to the Schrodinger equation). But the wavefunction, in and of itself, is not real. What in the hell does this mean?

Wow, you might want to try a more creditable source than the link you cited. If you want to argue that QM is not a complete theory, be my guest, but be prepared to back it up with experiment.What do you mean that the physical laws of the universe are yet indeterminate?As far as I know, nothing gives us a more exact picture of physical phenomena than QM.How many decimal places would satisfy you?

I am going to assume you don’t really mean this. Just because we can’t explain everything, is no reason to ignore the deterministic nature of those things we do understand. I do understand your quandary though in the definition of what we mean by deterministic. The same type of ambiguity occurs in the definition of causality in regards to the EPR paradox and superluminal influence.It appears, however, that you have a good understanding of what I am trying to say. The uncertainty inherent in quantum mechanics is in no way catastrophic to the (supposed) deterministic nature of the fundamental laws. Until we understand more about the reality of the wavefunction and wavefunction collapse, who can say what determines the nature of reality? Perhaps, as Wounded King suggested, we are merely thinking about this in the wrong way.

OUCH!!!