Between any two pure states there exists a reversible transformation. If one requires the transformation from the last axiom to be continuous, one separates quantum theory from the classical probabilistic one.

This is an interesting quote from an article about “Quantum Theory and Beyond”, and is found on the arXiv repository. “Continuous transformation” may seem like trivia to most people, but a big question about the universe and reality lies behind it. And that question is this: is reality discreet, digital and mosaic-like, as quantum physics implies (recall that the “quantum” in quantum physics is a set fixed unit of transaction, no lower value is possible)? Or is reality continuous — which requires infinity, given that you need an infinity of numbers to properly describe any variable in the state of a continuous system, and the number of different possible states of that system are also infinite.

So, is there infinity in the world? Does physics require or at least hint at the presence of infinity? Recall that I had previously discussed whether reality is ultimately cubist or continuous, about 11 years ago. If physics does require infinity (e.g., the inflation paradigm in cosmology has certain versions that require “eternal inflation” with an infinite number of universes), that could have some interesting metaphysical and even spiritual implications.

Or, by contrast, is the world just some arrangement of building blocks which you can’t break into, mosaic chips that you cannot see inside, cannot know what goes on within (sort of like a black hole), there cannot be any interact with smaller chips of the basic mosaic piece? Black holes suggest that this might be true (i.e., the theoretically infinite “singularity” within the black hole is completely cloaked from the universe, and might as well be thought to not exist, just as the “inner divisions” of a quanta are ultimately irrelevant). If so, then perhaps the boffins will eventually be the masters of the universe, since there is ultimately a limited number of things to know — perhaps that number is still quite staggering, but in theory anyway, it might ultimately be investigated and somehow understood. If that is true, this would be the end of metaphysics. » continue reading …