A Fringe-Shift Measurement of the Photon Circulation Radius: A Test of the Helical Identity mcrγ = ħ

We propose an interferometric test of a definite kinematic postulate: a photon of energy E carries the kinetic mass m = E/c² and moves on a helical path, advancing uniformly at speed c along an axis while circulating uniformly about it. In this picture the empirical relations E = mc² and E = hν together imply the identity mcrγ = ħ, with circulation radius rγ = ħ/(mc) = λ/2π. The identity is circular, however, unless rγ can be measured without reference to the wavelength. We show how such a measurement can be made. If the circulation couples to material boundaries, the two edges of a slit of width a should imprint a differential phase δφ = C·2πrγ/a on the transmitted light, where C is an order-unity constant that the edge dynamics must supply. The aperture thereby acquires a linear phase ramp, and the far-field pattern moves sideways as a whole, without distortion, by a fraction C·rγ/a of its own scale. The sign of the shift follows the sense of the circulation, and hence the helicity of the photon: the pattern moves one way under σ⁺ illumination and the opposite way under σ⁻, while linearly polarized light, an equal mixture of the two, shows no net shift and provides a built-in null. The helicity-dependent shift should grow linearly with wavelength at fixed geometry and fall off as 1/a at fixed wavelength, with every fringe spacing unchanged. No phase of standard optics behaves this way: geometric phases are achromatic, dynamical phases scale as 1/λ, and a mirror-symmetric passive structure under symmetric illumination cannot displace its own diffraction pattern at all. Heterodyne phase metrology at 10⁻³–10⁻⁴ rad tests the identity at the 0.2–1% level at three visible wavelengths. A null result at this sensitivity rules out the postulate at order-unity coupling; a shift that fails to reverse with helicity, violates either scaling, or disagrees between classical and heralded single-photon light falsifies the postulate as stated.