Über quantentheoretische Umdeutung kinematischer und mechanischer Beziehungen.¶
Heisenberg, W. (1925). Über quantentheoretische Umdeutung kinematischer und mechanischer Beziehungen. Zeitschrift für Physik, 33(1), 879-893.
Cited by¶
4 citations across 4 artifacts.
Each citation links to the sentence it supports in the citing article.
Primes¶
- Commutativity
- conflict-free replicated data types (CRDTs — sets, counters, last-write-wins registers rely on commutative merge operations to achieve eventual consistency without coordination); commutative database operations (can be applied in any order, reducing conflict); concurrent programming (commutative updates need weaker synchronization); functional programming's fold operations (commutative aggregations parallelize with
foldMap). Physics: Commuting observables in quantum mechanics (two observables \(A\) and \(B\) are simultaneously measurable iff \([A, B] = AB - BA = 0\)), as Heisenberg (1925) first revealed in the matrix-mechanics formulationThis sourceMatrix-mechanics paper introducing the non-commuting multiplication rule for observables — supports the claim that Heisenberg first revealed the role of [A,B] = AB − BA ≠ 0 (incompatible / not simultaneously measurable).
- conflict-free replicated data types (CRDTs — sets, counters, last-write-wins registers rely on commutative merge operations to achieve eventual consistency without coordination); commutative database operations (can be applied in any order, reducing conflict); concurrent programming (commutative updates need weaker synchronization); functional programming's fold operations (commutative aggregations parallelize with
- Correspondence Principle
- Thus the correspondence principle predicts a smooth transition from quantum (exponentially small but nonzero tunneling) to classical (strictly zero tunneling) as ℏ shrinks; this agreement validates the WKB method as a faithful bridge between the two regimes.
This sourceThe matrix-mechanics 'Umdeutung' paper. Cited inline (no FACT marker) on the claim that WKB 'validates as a faithful bridge' between quantum and classical regimes, and in T6 on heuristic theory-building.
- Thus the correspondence principle predicts a smooth transition from quantum (exponentially small but nonzero tunneling) to classical (strictly zero tunneling) as ℏ shrinks; this agreement validates the WKB method as a faithful bridge between the two regimes.
- Discrete vs. Continuous (Quantization)
- Foundations span quantum mechanics (Planck 1900, Einstein 1905, Bohr 1913, de Broglie 1924, Schrödinger 1926, Heisenberg 1925
This sourceThe 'Umdeutung' paper that launched matrix mechanics, recasting kinematic/mechanical quantities as non-commuting arrays built from observable transition amplitudes. Cited as a foundational quantum-mechanics source.
- Foundations span quantum mechanics (Planck 1900, Einstein 1905, Bohr 1913, de Broglie 1924, Schrödinger 1926, Heisenberg 1925
- Superposition
This sourceMatrix mechanics formulation showing superposition emerges when expanding in energy eigenbasis.
Verification¶
Does it exist? Confirmed. This work's DOI resolves to a registered record, which fixes its identity. That is all it fixes.
Does it back the claim? Not recorded. Neither this nor any other of the 4 citations of this work carries a recorded support check.
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