Decoherence and the Collapse, 2.2 | Quantum decoherence 7.2.2
superposition ~ indistinguishability
superposition state ~ logically indistinguishable states (forming one SINGLE quantum state)
logically indistinguishable ~ indistinguishable by definition ~ indistinguishable due to “the experiment setup is without detector” part of the definition
By the Leibniz’s Law (Identity of indiscernibles), logically indistinguishable cases are actually the same one SINGLE case, represented by one SINGLE quantum state.
Classically, there are no such logically indistinguishable cases because classically, all particles are distinguishable. So the probability distribution in the newly invented non-classical state should be completely different from any probability distributions provided by classical physics. Such cases of a new kind are called quantum states.
A quantum state’s probability distribution can be calculated from its wave function.
“Why that single quantum state is represented by a superposition of eigenstates and why its wave function is governed by the Schrödinger equation” is ANOTHER set of questions, whose correct answers may or may not be found in the Wikipedia article Theoretical and experimental justification for the Schrödinger equation.
Superpositions always exist. Logically indistinguishable cases are always there. You just trade some logically indistinguishable cases with some other logically indistinguishable cases.
The “superpositions” are superpositions in definition, in language, in logic, in calculation, and in mathematics, but not in physical reality, not in physical spacetime.
— Me@2021-01-24 09:29:13 PM
2021.01.24 Sunday (c) All rights reserved by ACHK