Originally Posted by
AppMathDoc
To divert away from religion and back to physics, let me suggest that randomness does exist, along with a well-respected line of argument for its existence that should allow for a civil -- and constructive -- discussion of the topic. First, what is "randomness?" We now know that a deterministic process can be unpredictable, so simply saying a process is random if it is not deterministic is not a good approach. Thus, in conjunction with the Quantum Theorists, we should probably restrict our discussion to the possible existence of objective randomness -- e.g., whether or not wave function collapse or spontaneous "separation" of wave functions is fully explained by non-local causality such as entanglement.
In this arena, we can turn to a well-established theorem, which is that for any probability measure, there must exist sets that are non-measurable. I suggest (as have many others --this isn't my idea) that the existence of non-measurable sets implies the necessity of objective randomness in any theory, much along the same lines as the Banach-Tarski paradox. Given any wave function, a probability can be assigned to the event of being outside a sphere, and if that sphere is large enough, the probability assigned to the interior of the sphere is greater than 0.5. Now divide --using measure preserving cuts -- that sphere into 2 identical, disjoint spheres with identical probabilities and notice that the probability of being in their union exceeds 1.
This is impossible, and so we must arrive at one of only a handful of conclusions. First, that some divine hand insures that the only sets that occur in nature are those that we can measure. Second, that set theory -- and thus all of mathematics itself -- is insufficient in the description of the universe. Or third -- and the one I prefer -- that the wave function fluctuates randomly during any process, mathematically or otherwise, and thus by the time any program is carried out the original supposition is no longer valid.