How did Heisenberg’s microscope thought experiment explain measurement uncertainty?

Werner Heisenberg’s microscope thought experiment illustrates the fundamental trade-off between measuring a particle's position and its momentum, a core concept of the Heisenberg uncertainty principle.

To determine an electron's position, one must observe it using light. Due to the wave nature of light, diffraction causes the image to blur, creating an uncertainty in position approximately equal to the light's wavelength. To increase precision, one must use light with a shorter wavelength, such as gamma rays.

However, this creates a conflict: according to the Compton effect, the high-energy photon used for observation collides with the electron, causing it to recoil in a random direction. Because a photon's momentum is inversely proportional to its wavelength, using shorter wavelengths to pinpoint position imparts a greater, more uncertain momentum to the electron. Consequently, increasing the precision of a position measurement inevitably decreases the precision of the momentum measurement, demonstrating that these two observables cannot be simultaneously known with absolute accuracy.1