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But for our purposes finite-dimensional spaces will suffice for discussing the major conceptual difficulties of quantum theory and how the histories approach resolves them.
Some, at least, of the interpretive difficulties of quantum mechanics would have to be resolved before a meaningful assessment of chaos in quantum mechanics could be achieved.
Invoking decoherence by itself outside the framework provided by the histories approach does not solve the conceptual difficulties of quantum theory; see, e.g., Adler (2003).
For about fifteen years following its publication, the EPR paradox was discussed at the level of a thought experiment whenever the conceptual difficulties of quantum theory became an issue.
As it is absent from classical physics and from most quantum textbooks, the concept is unfamiliar, and one has to work through various examples in order to gain an intuitive as well as a formal understanding of how it deals with the various paradoxes and other conceptual difficulties of quantum theory.
Relational interpretations of quantum mechanics propose a solution to the interpretational difficulties of quantum theory based on the idea of weakening the notions of the state of a system, event, and the idea that a system, at a certain time, may just have a certain property.
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Indeed, for many physicists the measurement problem is not merely one conceptual difficulty of quantum mechanics; it is the conceptual difficulty.
Once again, the difficulty of quantum theory is that there is an apparent contradiction between the fact that the quantity q of the system assumes an observed value in the measurement, while the composite S+O system still has to be considered in a superposition state, if we want to properly predict the outcome of measurements on the S+O system.
If science were prepared to settle for less than unification, the difficulty of reconciling quantum mechanics and general relativity wouldn't be the biggest problem in physics.
This "second observer" situation captures the core conceptual difficulty of the interpretation of quantum mechanics: reconciling the possibility of quantum superposition with the fact that the observed world is characterized by uniquely determined events q, q′, q″, ….
The difficulty in the interpretation of quantum mechanics derives from the fact that the theory was first constructed for describing microscopic systems (atoms, electrons, photons) and the way these interact with macroscopic apparatuses built to measure their properties.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com