= Foundations of quantum mechanics
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= Quantum foundations
{synonym}
The <foundations of quantum mechanics> study the physical meaning and consistency of <quantum states>, <quantum measurement>, <unitary time evolution> and correlations between systems. The aim is to connect precise mathematical rules with claims about preparation, observation and physical reality.
The <measurement problem> can be seen in a simple model. An initial <quantum superposition> interacting unitarily with a record gives
$$
(a|0\rangle+b|1\rangle)|E\rangle
\longmapsto
a|0\rangle|E_0\rangle+b|1\rangle|E_1\rangle.
$$
If the record states are orthogonal, the system's <reduced density matrix> is diagonal with weights $|a|^2,|b|^2$. This explains suppression of observable interference, while the relation between the joint state and an individual recorded outcome remains a foundational question. <Quantum decoherence>, the <many-worlds interpretation> and <de Broglie-Bohm theory> address different parts of this problem.
<John Stewart Bell> made a separate question experimentally sharp. In his singlet-pair model, local hidden-variable response functions cannot reproduce all the quantum <spin> correlations. A <Bell test> compares measured correlations across analyzer settings with the appropriate <Bell inequality>. <On the Einstein Podolsky Rosen paradox by John Stewart Bell>[Sections II–IV, spin-singlet setup, local response functions and contradiction]{ref} Interpreting such a test requires attention to <measurement independence> and sampling assumptions. <Quantum nonlocality> concerns these joint <probabilities> and is compatible with <quantum no-signalling>.
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