I do not know much about quantum physics. However, I do know it believes the world is discrete ( has quanta). This seems to contradicts the fact that we can create an object of length root 2 since you can not choose a quanta for an object of root 2 such that the total length sums to root 2. Does quantum physics agree with the fact that root 2 is constructable?
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A common misunderstanding of quantum mechanics is the belief that EVERYTHING in the world is quantized, but this is simply not true. For example the position of a free particle is not quantized but may take on any value.
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