Light, despite having no mass, does indeed have momentum. This is a consequence of wave-particle duality, a fundamental principle in quantum mechanics. According to quantum mechanics, particles such as photons (particles of light) can exhibit both particle-like and wave-like behavior.
In the context of light, it is described as an electromagnetic wave. Electromagnetic waves carry energy and momentum. The momentum of a photon is given by its wavelength (λ) and the Planck constant (h):
p = h / λ
Where p is the momentum, h is the Planck constant (approximately 6.626 x 10^-34 joule-seconds), and λ is the wavelength of the photon.
Although the relativistic mass of a photon is zero (since it has no rest mass), it still carries energy and momentum. This is consistent with both relativity theory and the Heisenberg uncertainty principle.
In relativity theory, massless particles like photons can have energy and momentum without violating the principles of special relativity. The energy of a photon is related to its frequency (f) by the equation:
E = hf
Where E is the energy of the photon and h is the Planck constant.
Regarding the Heisenberg uncertainty principle, 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 known simultaneously. This principle is not directly related to the mass or lack thereof of light. It applies to all quantum particles, including massless particles like photons.
In summary, light exhibits momentum due to its wave-particle duality. Although light has no rest mass, it carries energy and momentum through its wave-like nature, which is consistent with the principles of relativity theory and the Heisenberg uncertainty principle.