In special relativity (SR), momentum (p) and energy (E) are related through the famous equation:
E^2 = (pc)^2 + (mc^2)^2
where m represents the rest mass of an object, c is the speed of light, p is the momentum, and E is the total energy (which includes both the object's rest energy and its kinetic energy).
This equation is known as the relativistic energy-momentum relation. It shows that momentum and energy are intrinsically interconnected in a relativistic context. When an object is at rest (v = 0), the equation reduces to the well-known mass-energy equivalence equation: E = mc^2.
The equation indicates that as an object's momentum increases, its energy also increases, and vice versa. The term (mc^2)^2 represents the object's rest energy, which is the energy it possesses even when it is not in motion. The term (pc)^2 represents the object's kinetic energy due to its momentum.
This relationship is fundamental in understanding the behavior of particles at relativistic speeds, as it demonstrates that mass and energy are two facets of the same physical quantity.