Quantum
information is discussed as the universal substance of the world. It
is interpreted as that generalization of classical information, which
includes both finite and transfinite ordinal numbers. On the other
hand, any wave function and thus any state of any quantum system is
just one value of quantum information. Information and its
generalization as quantum information are considered as quantities of
elementary choices. Their units are correspondingly a bit and a
qubit. The course of time is what generates choices by itself, thus
quantum information and any item in the world in final analysis. The
course of time generates necessarily choices so: The future is
absolutely unorderable in principle while the past is always
well-ordered and thus unchangeable. The present as the mediation
between them needs the well-ordered theorem equivalent to the axiom
of choice. The latter guarantees the choice even among the elements
of an infinite set, which is the case of quantum information. The
concrete and abstract objects share information as their common base,
which is quantum as to the formers and classical as to the latters.
The general quantities of matter in physics, mass and energy can be
considered as particular cases of quantum information. The link
between choice and abstraction in set theory allows of “Hume’s
principle” to be interpreted in terms of quantum mechanics as
equivalence of “many” and “much” underlying quantum
information. Quantum information as the universal substance of the
world calls for the unity of physics and mathematics rather than that
of the concrete and abstract objects and thus for a form of quantum
neo-Pythagoreanism in final analysis.
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