The momentum of light in dielectric media has been a century-long controversy that continues to attract significant interest. In a linear dielectric medium with refractive index $n$, the momentum is predicted to be smaller by a factor of $n$ according to Abraham and larger by the same factor according to Minkowski. By studying the coupled dynamics of electromagnetic waves and dipoles in a dielectric medium, we show that the change in momentum of the dipole, expressed by the Lorentz force, corresponds to the Abraham momentum and is given by the expectation value of the spin-projected momentum vector. On the other hand, the Minkowski momentum is obtained as the magnitude of the spin-projected momentum vector from the energy-momentum dispersion relation derived by diagonalizing the coupled Hamiltonian and determines the direction of refraction in accordance with Snell's law. Our model also predicts a zitterbewegung-like oscillation due to helicity mixing between left- and right-handed wave components, mediated by dipole oscillation. These internal wave dynamics may be observable via wave-packet motion or polarization-sensitive measurements.

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• Abraham-Minkowski debate
• Polaritons
• Quantum harmonic oscillator
• Quantum optics
• Dielectrics
• Photons
• Angular momentum
• Spin
• Drude model
• Maxwell's equations