## Quantum mechanics and unitarity (part 1 of 4)

I will start a sequence of posts showing why quantum
mechanics demands only unitary time evolution despite the collapse postulate and how to solve the problem. For
reference, this is based on http://arxiv.org/abs/1305.3594

The quantum mechanics reconstruction project presented in http://arxiv.org/abs/1303.3935 shows
that in the algebraic approach, the Leibniz identity plays a central and early
role. But what is the Leibniz identity? It is the chain derivation rule: D(fg)
= D(f) g + f D(g).

All standard calculus follows from this rule. For example using
recursion one proves D(X^n) = n X^(n-1) and form this and the Taylor
series, the derivation rules for all usual functions follow.

In the algebraic formalism of quantum mechanics, the Leibniz
identity corresponds in the state space to unitarity. Any breaking of unitarity
means that Leibnitz identity is violated as well. This is the case for example in
the epistemological interpretation of the wavefunction where the collapse
postulate is understood as simply information update. However (and here is the
big problem), breaking the Leibniz identity destroys the entire quantum
mechanics formalism. In other words,

**any non-unitary time evolution is fatal for quantum mechanics.**
So how can we understand the collapse postulate? Is quantum
mechanics inconsistent? Should quantum mechanics be augmented by classical
physics to describe the system and the measurement apparatus? From http://arxiv.org/abs/1303.3935 we
know that there cannot be any consistent classical-quantum description of
nature. Also the formalism which highlighted the problem shows the way out of
the conundrum. Part 2 of the series will present preliminary mathematical
structures which will be used to show how quantum mechanics can be fully
unitary

*even during measurement*.
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