Photons, despite being massless, can transfer momentum due to their energy and the principles of relativistic physics. The relationship between energy, momentum, and mass is defined by the equation E² = (pc)² + (mc²)², where for photons, the mass (m) is zero. This means that photons possess momentum, represented as p = E/c, allowing them to affect other particles, such as electrons, during interactions like Compton scattering. The discussion emphasizes that in relativistic contexts, momentum can exist independently of mass. Understanding this concept is crucial for grasping the behavior of light and its interactions in physics.