Actually I read my previous post and notice that perhaps I was thinking more about the Schrödinger's Cat paradox rather than the Heisenberg principle itself.
However, the Heisenberg principle is related to "knowing" in the sense of "measuring", and its intuitively explanation is that the limit in knowing has to do with the impossibility of measuring things without interacting with them in some way and therefore disturbing them, thus adding some margin of error. If you try to measure one thing only, the disturbance is technology-related only, so you can always hope to decrease the error by improving your technology. If you try to measure two things at once and those two things happen to be
quantistically paired (possibly this is not the correct expression, sorry but I'm not a physicist
) - like velocity & position - then the errors of the two cannot be both decreased without limit due to the nature itself of the particle.
Agreed. If two quantum mechanical operators commute, then their corresponding variables can be known to infinite accuracy simultaneously. Position and momentum operators do not commute, so their corresponding physical variables can't be simultaneously known to infinite accuracy.
Notice that the term "measuring" is often misleading because it makes us think of a human observer, and then wonder if the situation would be different for a particle that was far away from us (or other intelligent life), and no one would want to "measure". The problem remains if generalized in terms of "interacting" with the particle by anything else, another particle or object. When considering a particle-crashing scenario, the second particle could for example "find" the first particle in different places and with different momentums, i.e. multiple values (in a range that is limited, but cannot be shrunk to zero for both the velocity and position).
Agreed. Wavefunction collapse doesn't require there to be a concious observer.
However God would have absolutely no problem in knowing both the position and the velocity of the particle, because he doesn't need to interact with it in any way. He could just know. Only something that belongs to the material universe is required to interact, a God could clearly just watch from beyond the material universe.
Which begs the question of
how he watches. How is information extracted from the universe? This is a form of Maxwell's Demon, which is a thermodynamic paradox, so I think it only gets you into more troubles. Further, simply positing that God can know both variables misses the point: it's not a question of
how the variables can be known, but
whether they can be known. If the position of a particle is known to arbitrary accuracy, then its momentum
can't be known: not because it's impossible to practically measure, but because
it doesn't have momentum.
However......
Back to my previous post... There is a problem in what we think a particle is. It is not a dot, which would have clearly a position. It is not a small ball (or whatever shape), which would have a position of each of its points. It might be something akin to a small "cloud", with no clearly identified surface: in such case, we cannot talk about a "position" clearly, we can say that some points are certainly occupied by it and others certainly not, but there is no points where exactly the cloud starts or end. Often in quantum physics, particles are "wave packets" which are however pretty complex objects to imagine, but once again where do they start and end is pretty much without answer. So if something does not have an answer, God doesn't know it, but He obviously isn't at fault, and in any case He certainly know that the answer is "there is no answer". If we see this as a problem or as fault, it's only because our own logic doesn't get it.
Quantum mechanically, particles are wavefunctions over all of space. Nonetheless, this wavefunction describes where they
can be (and goes some way to explaining why they can't have discrete positions and momenta). You can still measure the particle and say that, at time
t, the particle was somewhere in this blob of space.
Naturally, it doesn't make sense to criticise God's omniscience by pointing out that he cannot know the answer to an impossible question. Rather, the Uncertainty Principle
doesn't say you
can't know a particle's position and momentum. It places limits on what you can know about them, sure, but you can still know things. So the question is: what? What does God know?
Does he know the position of all particles to 1nm accuracy? 0.1nm? What of momentum? Does he sacrifice knowledge of position for knowledge of momentum, or vice versa?
Consider two weights that are linked; you pull one down, the other goes up. Ideally, both are at the floor, but that's impossible. So, how high do you set them? Omniscience is akin to claiming that both weights are on the floor, but, quantum mechanically, this is impossible.
