Photon Momentum
A Quantum Theory of the Scattering of X-rays by Light Elements (1923)
Do photons have momentum? Anyone familiar with rudimentary high school physics knows that the answer to this question is by no means obvious. Momentum is typically brought up to describe collisions between objects with mass—a violent car crash or an expert pool player’s subtle manipulation of billiard balls.
But, photons have no mass. It is precisely this property that allows them to move at the maximum possible speed in our universe: the speed of light. It thus follows that photons shouldn’t be able to take part in collisions with massive objects.
The truth could not be further from the case. A critical insight into this apparent mismatch was provided by American physicist Arthur H. Compton in his paper, A Quantum Theory of the Scattering of X-rays by Light Elements, published in 1923. In it, he establishes the incontrovertible proof of electromagnetic momentum.
Why Does Scattered X-ray Radiation Have a Longer Wavelength?
Before Compton’s work, J. J. Thomson’s classical theory of scattering, known as Thomson scattering, predicted that X-rays scattered off electrons would retain their original wavelength. Experiments, however, showed that the scattered X-rays had a longer wavelength than the incident ones. Classical physics, therefore, could not account for the energy loss necessary to explain this shift.
Compton proposed that X-rays must interact with electrons as discrete quanta of energy and momentum. When an X-ray photon collides with an electron, it transfers some of its energy to the electron, causing the electron to recoil.
The remaining energy is carried away by the scattered photon, which now has a lower frequency (i.e., a longer wavelength). This process, now known as Compton scattering, has become one of the pillars of quantum field theory.