In classical physics, momentum is defined as the product of an object's mass and its velocity. However, in the realm of relativity and quantum mechanics, the concept of momentum expands beyond classical notions and can be associated with objects that have no mass.
In relativistic physics, the momentum of a particle is given by the relativistic momentum equation:
p = γm v
Here, p represents momentum, m is the particle's rest mass (or invariant mass), v is its velocity, and γ (gamma) is the Lorentz factor:
γ = 1 / √(1 - v^2/c^2)
c is the speed of light in a vacuum.
This equation applies not only to massive particles but also to massless particles, such as photons (particles of light) or gluons (mediators of the strong force). For these massless particles, their momentum arises solely from their energy and the relativistic relationship between energy and momentum.
Regarding Einstein's equation, E = mc^2, it is the energy-mass equivalence equation derived within the framework of special relativity. This equation states that the energy (E) of an object is equal to its mass (m) multiplied by the speed of light squared (c^2). However, it is important to note that this equation specifically applies to particles with rest mass. For massless particles, like photons, their energy is given by E = pc, where p is their momentum.
So, while particles with no mass can have momentum, Einstein's equation, E = mc^2, is not applicable to them. Instead, the energy-momentum relationship E = pc accurately describes their behavior.