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¶
7 citations across 7 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.
Supported in partVerified against the publisher's abstract
Heisenberg's abstract establishes that canonically conjugate quantities cannot be simultaneously sharp — the physics instance of the claim, not its three cross-domain analogies.
“und es wird gezeigt, daß kanonisch konjugierte Größen simultan nur mit einer charakteristischen Ungenauigkeit bestimmt werden können (§ 1)”
- 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.
Supported in partVerified against the publisher's abstract
Heisenberg's abstract states canonically conjugate quantities are simultaneously determinable only with a characteristic imprecision — the joint under-determination half only.
“daß kanonisch konjugierte Größen simultan nur mit einer charakteristischen Ungenauigkeit bestimmt werden können (§ 1)”
- (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.
Supported in partVerified against the publisher's abstract
The abstract states conjugate quantities can be determined simultaneously only with characteristic imprecision; it says nothing of measurement disturbing its target, nor of bidirectional coupling.
“es wird gezeigt, daß kanonisch konjugierte Größen simultan nur mit einer charakteristischen Ungenauigkeit bestimmt werden können”
- 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.
Supported in partVerified against the publisher's abstract
The 1927 paper's own abstract grounds measurement imprecision as a fundamental feature of quantum mechanics, but says nothing about the gamma-ray microscope analysis or about this being the first formalization.
“es wird gezeigt, daß kanonisch konjugierte Größen simultan nur mit einer charakteristischen Ungenauigkeit bestimmt werden können (§ 1). Diese Ungenauigkeit ist der eigentliche Grund für das Auftreten statistischer Zusammenhänge in der Quantenmechanik.”
- 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.
- Observer Effect
- 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¶
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? Read against the text for 4 of 7 citations: 4 supported in part. Each verdict is shown under its citation below, with what in the work backs the sentence.
Support is checked per citation rather than per work — the same source can be cited soundly in one article and wrongly in another. Per-citation recording began recently, so a citation with no recorded check is a gap in the record rather than evidence it went unchecked.
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