How flexible is the principle of causality?

[Alex K]

@Alex I thought quantum mechanics was deterministic? After all, like other areas of physics it's rooted in differential equations over time. I thought that the apparent indeterminism was due to the fact that in order to measure the system, we have to interact with and force it to a particular result by doing so, hence the uncertainty?

Hey,
You're certainly correct that the time evolution of a system isolated from the observer is simply described by the Schrödinger equation, and thus completely deterministic. I think where you may have a misunderstanding is in your assumption that in the measurement process, the result is uniquely determined by the quantum state of the observer and the system. It is not.

There is a "deterministic" formulation of QM, but it doesn't really give you what you would like to have in terms of determinism: Bohmian mechanics. You start with a statistical ensemble of point masses riding on the wave function, and the randomness comes from the fact that you don't know the initial distribution of these guys. It is then in principle deterministic, but the outcome is not determined by the quantum state, but by auxiliary knowledge about this funny ensemble of point masses. It would still be non-deterministic for all practical purposes since there is no known way to measure this distribution, and it may be impossible in principle. I find this formulation very artificial and it is not nicely suited to exted to field theory, and I only mention it for completeness because it is a "deterministic" formulation of QM.

In the relative state interpretation ("many worlds"), you get a split into a superposition of two system final states entangled with two observer final states. It is deterministic in the global sense that the Schrödinger equation governs everything all the time without exception, including the observer, and all possibilities are always realized in parallel. In the Copenhagen interpretation you make a probability statement at that point and discard the part of the superposition which is apparently not realized for the observer ("wave function collapse"), and in this truly random choice it is where you lose the determinism.

Even if you don't "believe" in the relative state picture as what is really going on in the world, it is useful in order to gain an intuition about what measurements do: they produce correlations (entanglement) between you and the measured system, and depending on what quantity you attempt measure, this entanglement is such that the combined observer-system state ends up as a superposition of individual states in which this quantity you have measured is without uncertainty, but then both superimposed. This interaction of observer and system which produces this entanglement is what you probably mean by forcing the system into a certain state. However, it is not the detailed process of this interaction which tells you in which state you end up, you always end up in both, and which one you actually measure is truly random. How to properly define the probability of outcomes here is one of the main theoretical problems of "many worlds" quantum mechanics. Copenhagen doesn't exactly do better in this respect, it simply supplies a prescription to calculate the probabilities.