Physics

Classical wave theory treats light as a continuous electromagnetic wave that can transfer energy smoothly to electrons, predicting that higher-energy (shorter-wavelength) photons should transfer more energy and produce larger wavelength shifts. The fact that $\Delta\lambda$ depends only on $\theta$—independent of the initial wavelength—reveals that something discrete and particle-like is happening: each photon carries a definite momentum that depends only on its direction change, not its initial energy. This is the signature of photon-electron collision mechanics, which requires Einstein's photon concept and cannot emerge from classical wave descriptions.

Classical wave theory treats light as a continuous electromagnetic wave that can transfer energy smoothly to electrons, predicting that higher-energy (shorter-wavelength) photons should transfer more energy and produce larger wavelength shifts. The fact that $\Delta\lambda$ depends only on $\theta$—independent of the initial wavelength—reveals that something discrete and particle-like is happening: each photon carries a definite momentum that depends only on its direction change, not its initial energy. This is the signature of photon-electron collision mechanics, which requires Einstein's photon concept and cannot emerge from classical wave descriptions.