In classical physics, momentum is defined as the product of mass and velocity (p = mv), implying that only objects with mass can have momentum. However, in the realm of relativistic physics and quantum mechanics, it is understood that particles can have momentum even if they have no mass. This concept is a fundamental aspect of special relativity.
According to Einstein's theory of special relativity, the relationship between energy (E), momentum (p), and mass (m) is described by the equation:
E^2 = (pc)^2 + (mc^2)^2
Here, c represents the speed of light in a vacuum, and p is the momentum of the particle. The equation states that the energy of a particle is composed of two terms: one associated with its rest mass (mc^2), and the other associated with its momentum (pc).
For particles with rest mass (m ≠ 0), the equation simplifies to the famous equation E = mc^2, which indicates that mass can be converted into energy and vice versa. This equation is commonly associated with the equivalence of mass and energy.
However, for particles with zero rest mass (m = 0), such as photons (particles of light), the equation becomes:
E = pc
In this case, since the rest mass is zero, the entire energy of the particle is solely due to its momentum. Photons, being massless particles, have momentum proportional to their frequency or inversely proportional to their wavelength, as described by the equation p = hf/c, where h is Planck's constant and f is the frequency.
This equation demonstrates that particles without rest mass can still possess momentum and energy solely due to their motion and frequency. It highlights the unique properties of massless particles within the framework of special relativity.