Orthodox Quantum Mechanics
Orthodox quantum mechanics has two seemingly contradictory mathematical descriptions:
1. deterministic unitary time evolution (governed by the Schrödinger equation) and
2. stochastic (random) wavefunction collapse.
Most physicists are not concerned with this apparent problem. Physical intuition usually provides the answer, and only in unphysical systems (e.g., Schrödinger's cat, an isolated atom) do paradoxes seem to occur.
Orthodox quantum mechanics can be reformulated in a quantum-probabilistic framework, where quantum filtering (see Bouten et al. for introduction or Belavkin, 1970s ) gives the natural description of the measurement process. This new framework encapsulates the standard postulates of quantum mechanics, and thus all of the science involved in the orthodox postulates.
Read more about this topic: Quantum Probability
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