jambaugh

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Introduction
Superposition.jpg

One should first and foremost understand that superposition has both a mathematical an a physical meaning, or rather it originates as a mathematical property of the system description which will have implications in the physics.  The mathematical concepts are fairly straightforward aspects of linear algebra which will be briefly reviewed first.  To understand the physical implications of the mathematics we need to understand how representations in the mathematics get translated to operationally meaningful statements of the physical phenomena we observe.  So the next step is to consider if where and how mathematical aspects of superposition connect to the logical structure of our empirically verifiable statements about physical systems.  When this is understood then one has a solid foundation to stand upon while contemplating the physical and philosophical meaning of this idea...
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Stephen Tashi

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Classical logic is concretely expressed using the algebra of sets.



Reference https://www.physicsforums.com/insights/understanding-superposition/
As I remember the article Quantum mechanics made transparent. by Richard C. Henry, it makes the argument that probability distributions for classical states can be conveniently represented by vectors that lie on the surface of an n-dimensional sphere (or equivalence classes of rays that pass through such points).

Perhaps there is a way to present the transistion between classical logic and quantum mechanics in a more gradual manner instead of the jump from the logic of sets to the methods of QM. The properties of probability distributions on classical states could be an intermediate step.
 

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