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There is a problem in comparing billiard balls and particles in an analogy. Billiard balls and particles do not follow the same laws. They differ on their predictable states. The universe on the microscale is largely unpredictable, and largely predictable on the macroscale. Hence, particles, and billiard balls.
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Quoting principles of Quantum Theory does not invalidate my analogy. For the second time, it was an analogy intending to relate the measuring of particles in a manner which is more accesible. I gave an example of discovering the existance of a billiard ball which cannot be directly seen, but must be observed via its interactions with another known billiard ball. I never said, nor was it ever implied, that particles behave as these balls, nor that I was in fact measuring particles following the same manner. It was an analogy, nothing more, though it seems still unclear.
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Well we could never infer such a particle that doesn't interact. Proving something that is invisible acts invisible doesn't prove anything else. It doesn't prove the existence of ghosts.
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It can always be said that such particles and ghosts exist. My point is that if such fictitious constructs exist, and they in no way interact with our universe, then for all intents and purposes they are irrelevant. It was this reasoning which I attempted to use to say that God, if he exists in the sense that he may interact with humanity, must be subject to the same laws which affect humanity.