**Appendix C: Detailed Graph Data (Edges)** **C.3: Edges Originating from Quantum Mechanics (QM - Standard Interpretation) Nodes:** | Source Node ID | Target Node ID | Type | Rationale | Conf. | Dir. | |:-------------------------- |:-------------------------- |:----- |:-------------------------------------------------------------------------------------------------------------------------------------- |:---- |:--- | | `QM` | `CM` | `F-LIM` (Inverse) | Quantum Mechanics contains Classical Mechanics as its macroscopic or large quantum number limit (Correspondence Principle). | H | D | | `QM` | `SM` | `F-BAS`| Quantum Mechanics provides the foundational principles upon which the Standard Model (as a QFT) is built. | H | D | | `QM` | `Math::HilbertSpace` | `S-FORM`| The standard mathematical formulation of QM uses Hilbert spaces to represent states and operators. | H | D | | `QM` | `Math::ProbabilityTheory` | `F-BAS`| QM fundamentally relies on probability theory via the Born rule to connect formalism to experimental outcomes. | H | D | | `QM` | `Problem::QuantumGravity` | `F-REQ`| Standard QM does not incorporate gravity dynamically, necessitating a unification with GR (Quantum Gravity). | H | D | | `QM` | `Problem::QMeasurement` | `S-COMP`| The measurement problem is an internal conceptual inconsistency or incompleteness within standard QM interpretations. | H | D | | `QM::StateVector` | `QM` | `S-COMP`| The state vector (wavefunction) is the core representation of a system’s state in QM. | H | D | | `QM::StateVector` | `QM::Superposition` | `L-ENT`| The vector nature of states in Hilbert space directly entails the principle of superposition (linear combinations are valid states). | H | D | | `QM::HilbertSpace` | `QM::StateVector` | `F-BAS`| Hilbert space is the mathematical structure within which state vectors are defined. | H | D | | `QM::ObservableOperator` | `QM` | `S-COMP`| Associating observables with operators is a core postulate of QM. | H | D | | `QM::ObservableOperator` | `QM::Quantization` | `L-ENT`| The postulate that measurement results are eigenvalues of operators directly leads to observed quantization. | H | D | | `QM::SchrodingerEq` | `QM` | `S-COMP`| The Schrödinger equation is the core postulate governing time evolution (between measurements). | H | D | | `QM::SchrodingerEq` | `QM::UnitaryEvolution` | `L-ENT`| The mathematical form of the Schrödinger equation ensures that time evolution is unitary. | H | D | | `QM::UnitaryEvolution` | `QM::MeasurementCollapse` | `L-CTR`| Unitary evolution is deterministic and preserves superposition, contradicting the non-unitary, probabilistic nature of collapse. | H | S | | `QM::BornRule` | `QM` | `S-COMP`| The Born rule is the core postulate linking the formalism (state vector) to experimental probabilities. | H | D | | `QM::BornRule` | `QM::IntrinsicIndeterminism`| `F-BAS`| The Born rule provides probabilities, which are interpreted as fundamental indeterminism in standard QM. | H | D | | `QM::MeasurementCollapse` | `QM` | `S-COMP`| The projection postulate (collapse) is a core component of the standard description of measurement. | H | D | | `QM::MeasurementCollapse` | `CM::ObjectiveProperties` | `L-CTR`| Collapse implies properties are defined/created by measurement, contradicting classical objective reality. | H | S | | `QM::MeasurementCollapse` | `Phil::Realism` | `F-CHL`| The nature of collapse challenges simple forms of scientific realism about pre-measurement properties. | M/H | D | | `QM::MeasurementCollapse` | `Problem::QMeasurement` | `L-ENT`| The collapse postulate is central to the measurement problem, conflicting with unitary evolution. | H | D | | `QM::Superposition` | `QM` | `S-COMP`| Superposition is a fundamental principle arising from the linearity of the Hilbert space structure. | H | D | | `QM::Quantization` | `CM` | `L-CTR`| Observed quantization contradicts the classical assumption that physical quantities can take continuous values. | H | S | | `QM::IntrinsicIndeterminism`| `CM::Determinism` | `L-CTR`| Fundamental indeterminism contradicts classical determinism. | H | S | | `QM::IntrinsicIndeterminism`| `Phil::Determinism` | `L-CTR`| Standard QM interpretation contradicts the philosophical thesis of determinism. | H | S | | `QM::IntrinsicIndeterminism`| `Phil::CausalClosure` | `F-CHL`| If quantum events are truly random, it potentially challenges the idea that all physical events have sufficient *physical* causes. | M | D | | `QM::Complementarity` | `CM::ObjectiveProperties` | `F-CHL`| Complementarity challenges the classical assumption that all properties can possess definite values simultaneously. | H | D | | `QM::UncertaintyPrinciple` | `QM` | `S-COMP`| The Uncertainty Principle is a core principle derived from the QM formalism (non-commuting operators). | H | D | | `QM::UncertaintyPrinciple` | `CM::ObjectiveProperties` | `F-CHL`| The Uncertainty Principle places fundamental limits on the simultaneous definability of properties assumed objective in CM. | H | D | | `QM::Entanglement` | `QM` | `S-COMP`| Entanglement is a key phenomenon predicted and described by the QM formalism for multi-part systems. | H | D | | `QM::Entanglement` | `CM::Locality` | `F-CHL`| Entanglement demonstrates non-local correlations that challenge the implicit locality assumptions of classical mechanics. | H | D | | `QM::Entanglement` | `Phil::LocalRealism` | `L-CTR`| Experimental verification of Bell’s theorem violations using entangled states contradicts local realism. | H | S | | `QM::NonLocality` | `GR::Locality` | `L-CTR` / `F-CHL` | QM non-locality conflicts with the local nature of interactions described by classical GR field equations. | H | S/D | | `QM::ClassicalDescriptionReq`| `QM` | `S-COMP`| Bohr’s requirement for classical descriptions is a component of the Copenhagen interpretation. | H | D | | `QM::ClassicalDescriptionReq`| `Problem::QMeasurement` | `C-INF`| This requirement contributes to the measurement problem by creating an ambiguous quantum-classical divide. | M | D | | `QM::MeasurementProblem` | `QM` | `F-CHL`| The measurement problem indicates a fundamental conceptual incompleteness or inconsistency within standard QM interpretations. | H | D |