Light, despite being massless, does indeed have momentum. This phenomenon is a consequence of both relativity theory and quantum mechanics.
In relativity theory, massless particles, such as photons (particles of light), are still found to possess energy and momentum. The famous equation E=mc² is a simplified version of the energy-momentum relation, where "m" represents the mass and "c" is the speed of light. For massless particles, the equation becomes E=pc, where "p" denotes momentum and "c" remains the speed of light. This equation demonstrates that massless particles can possess momentum in proportion to their energy.
Quantum mechanics, specifically the wave-particle duality, further elucidates the momentum of light. According to quantum mechanics, particles can exhibit both wave-like and particle-like behavior. Light, despite being composed of massless photons, displays particle-like characteristics. Photons possess discrete packets of energy called "quanta" or "photons," and these quanta exhibit momentum.
The Heisenberg uncertainty principle also plays a role. It states that there is a fundamental limit to the precision with which certain pairs of physical properties, such as position and momentum, can be simultaneously known. For a photon, its momentum can only be determined within a certain range due to the inherent uncertainties associated with its position and energy.
In summary, while light has no rest mass, it does possess momentum due to the relativistic energy-momentum relation and the particle-like behavior of photons in quantum mechanics. The uncertainty principle imposes limitations on the precise determination of a photon's momentum, just as it does for other particles.