Über den anschaulichen Inhalt der quantentheoretischen Kinematik und Mechanik.¶
Heisenberg, W. (1927). Über den anschaulichen Inhalt der quantentheoretischen Kinematik und Mechanik. Zeitschrift für Physik, 43(3), 3-4.
Cited by¶
6 citations across 6 artifacts.
Each citation links to the sentence it supports in the citing article.
Primes¶
- Conjugate-Observable Complementarity
- Second, there is a conjugate pair of observables, two quantities that stand in an inverse-resolution relationship rather than being independent: position and momentum, time-localization and frequency-localization, fit-to-training-data and generalization, central coordination and local discretion.
This sourceIntroduces the uncertainty principle: conjugate observables (position and momentum) cannot be jointly sharp.
- Second, there is a conjugate pair of observables, two quantities that stand in an inverse-resolution relationship rather than being independent: position and momentum, time-localization and frequency-localization, fit-to-training-data and generalization, central coordination and local discretion.
- Conjugate Variables
- (2) the two descriptions are mutually determining but jointly under-determined: fixing one sharpens while the other broadens, and vice versa
This sourceThe original uncertainty-principle paper; its abstract explicitly states that canonically conjugate quantities (kanonisch konjugierte Größen) can be simultaneously determined only with a characteristic uncertainty — directly supports the joint-under-determination claim and the σ_x σ_p ≳ ℏ relation. DOI verified.
- (2) the two descriptions are mutually determining but jointly under-determined: fixing one sharpens while the other broadens, and vice versa
- Measurement
- The microscope that disturbs what it images, the Hawthorne effect, the act of watching a metric change what the metric is — all are variants of the same structural fact that the instrument-target coupling is bidirectional.
This sourceFirst statement of the uncertainty principle; establishes that measurement disturbs its target, the canonical case of bidirectional instrument–target coupling.
- The microscope that disturbs what it images, the Hawthorne effect, the act of watching a metric change what the metric is — all are variants of the same structural fact that the instrument-target coupling is bidirectional.
- Measurement and Disturbance
- The structural challenge of obtaining information about a system while minimizing—or accounting for—the perturbation introduced by the measurement process itself, a problem first formalized by Heisenberg (1927) in his analysis of the gamma-ray microscope.
This sourceEstablishes the uncertainty principle; shows that measurement of one observable necessarily perturbs the conjugate observable with minimum uncertainty Δx·Δp ≥ ℏ/2; frames measurement as fundamental perturbation, not merely experimental artifact.
- The structural challenge of obtaining information about a system while minimizing—or accounting for—the perturbation introduced by the measurement process itself, a problem first formalized by Heisenberg (1927) in his analysis of the gamma-ray microscope.
- Perturbation
- Physics Perturbation theory in quantum mechanics (Rayleigh- Schrödinger expansion);
This sourceEstablishes the uncertainty principle; shows that measurement of one observable necessarily perturbs the conjugate observable with minimum uncertainty Δx·Δp ≥ ℏ/2; frames measurement as fundamental perturbation, not merely experimental artifact.
- Physics Perturbation theory in quantum mechanics (Rayleigh- Schrödinger expansion);
Domain-specific¶
Verification¶
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