In classical physics, momentum is defined as the product of mass and velocity. However, in the framework of special relativity, Einstein extended the concept of momentum to include particles that have no mass, such as photons (particles of light).
In special relativity, the momentum of a particle is given by the equation:
p = m * v / √(1 - v^2/c^2)
In this equation, p represents momentum, m is the rest mass of the particle (which is zero for massless particles like photons), v is the velocity of the particle, c is the speed of light in a vacuum, and the denominator term √(1 - v^2/c^2) is called the Lorentz factor.
For a massless particle like a photon, the equation simplifies to:
p = E / c
In this equation, p represents the momentum of the photon, E is its energy, and c is the speed of light.
Now, let's consider Einstein's famous equation, E = mc^2. This equation relates energy (E) to mass (m) and the speed of light (c). It describes the equivalence of mass and energy. However, for massless particles like photons, where the rest mass (m) is zero, the equation becomes:
E = pc
This equation relates the energy (E) of a massless particle to its momentum (p) and the speed of light (c). It shows that for a photon or any other massless particle, its energy is solely determined by its momentum, and the two are directly proportional.
So, while massless particles do not have rest mass, they can still possess momentum due to their energy, and their momentum is directly related to their energy by the equation p = E/c.