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Heisenberg's microscope is a thought experiment, not a report of a performed measurement. In Werner Heisenberg's Nobel lecture, The development of quantum mechanics, delivered on 11 December 1933, the imagined Electron is illuminated with very short-wavelength light and observed through a high-resolution microscope. A scattered photon entering the observer's eye would, through Compton scattering, eject the Electron from its original path. The passage challenges a classical trajectory picture; its microscope is hypothetical. The lecture date is 1933 even though the award is the Nobel Prize in Physics in 1932.^[ref]

The following idealized geometry makes the tradeoff visible. Let the collected light have wavelength $\lambda$ and let the microscope objective accept outgoing directions within a half-angle $\alpha$ about the vertical axis. Take $x$ transverse to that axis and hold the incoming photon momentum fixed. A diffraction-limited estimate of transverse resolution has scale $\delta x\sim \lambda /\sin \alpha$. The unobserved outgoing direction admits transverse photon momentum components between approximately $-(h/\lambda )\sin \alpha$ and $+(h/\lambda )\sin \alpha$, neglecting the angular variation of the scattered wavelength. By conservation of momentum, uncertainty in that component leaves uncertainty in the transverse recoil of the Electron:Here $h=2\pi \hslash$ is the Planck constant; the two $\delta$ symbols denote heuristic resolution and recoil scales, not the standard deviations in the Heisenberg uncertainty relation. Increasing the acceptance angle improves the estimated resolution while broadening the allowed recoil range. Numerical factors depend on the resolution criterion and angular distribution; this scaling argument cannot supply the sharp constant $\hslash /2$.

The thought experiment makes the interaction needed to obtain an image memorable. The preparation uncertainty theorem has broader use: it applies to the prepared quantum state even when the two observables are measured on separate copies. No claim that Werner Heisenberg built this gamma ray apparatus is needed to understand either argument.

Preparation uncertainty describes the outcome spread intrinsic to a specified quantum state preparation. Operationally, prepare many copies of the same quantum state, measure position on one group and momentum on another, and estimate the two variances. Ideal measurements still have the spreads predicted by the Born rule. No earlier position measurement need occur in the momentum group. The Heisenberg uncertainty relation constrains these two distributions belonging to the same preparation.

Measurement backaction concerns how a particular measurement in quantum mechanics changes a quantum state. Instrument resolution concerns how its reported outcomes relate to the intended observable. Those questions require a model of the instrument and its interaction with the system. Substituting an instrument error and an induced change for $\Delta x$ and $\Delta p$ in the Heisenberg uncertainty relation does not follow from its proof. The practical value of preparation uncertainty is that it bounds achievable input spreads before any such instrument model is chosen.