Equation 112 · The Atlas That Refuses to Close
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Symbol sigma_z
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subscript
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The one place any of this touches an actual measured number is optical, not electronic, and it arrives through the weak-value chart rather than through any operator eigenvalue. Light crossing an interface between media of different refractive index acquires a transverse, polarization-dependent displacement, the spin Hall effect of light, far smaller than the beam’s own wavelength under ordinary detection. Hosten and Kwiat used exactly the weak-value amplification structure above, preselecting the photons’ polarization and postselecting on a nearly orthogonal state, to enhance the effective displacement by close to four orders of magnitude and resolve a shift at the angstrom scale [ 12 ] .…
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The one place any of this touches an actual measured number is optical, not electronic, and it arrives through the weak-value chart rather than through any operator eigenvalue. Light crossing an interface between media of different refractive index acquires a transverse, polarization-dependent displacement, the spin Hall effect of light, far smaller than the beam’s own wavelength under ordinary detection. Hosten and Kwiat used exactly the weak-value amplification structure above, preselecting the photons’ polarization and postselecting on a nearly orthogonal state, to enhance the effective displacement by close to four orders of magnitude and resolve a shift at the angstrom scale [ 12 ] . What was measured is a pointer’s mean shift, exactly the Aharonov-Albert-Vaidman quantity, not a photon’s position eigenvalue; the amplification is a direct laboratory instance of a weak value being made large by pushing the postselection toward orthogonality, the identical mechanism behind the imaginary value computed above.
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