Question

Why are position and velocity mutually exclusive (oil and water) in Heisenberg's law of uncertainty? Has this been plumbed philosophically?

Answer 1

It is often said that quantum theory (as a whole) can only be grasped mathematically. Trying to understand it intellectually will lead to flaws in understanding since much of it defies logic. Unfortunately a growing area of pseudoscience comes from people trying to explain or express the philosophical 'significance' of ANY aspect of quantum mechanics in a philosophical or simply a qualitative way. Part of this is a result of the 'thought experiments' led by Schrodinger et al which have enspired non-mathematicians, writers, artists and dreamers to consider 'quantum weirdness' as a way to sell products. The short answer is that there are innumerable low-impact philosophical ideas based around all aspects of contemporary physics, but many are dangerous because they come to conclusions based on flawed logic rather than a deeper mathematical understanding of quantum physics.

Answer 2

Is part of the problem that of not having an associated geometry to go with the deep math, assuming nature suddenly decides not to behave conceptually at the quantum level?

Answer 3

I think the real problem here is people usually take quantum effects and tranfers them to the classical world. This cannot be done easily, quantum theory only works in the quantum world. So, any conclusion you might extract from the uncertainty principle should be applied in the quantum world ONLY. In fact, this principle comes from a mathematical relation between hermitian operators, just as simple as that.