Energy–momentum relation
The relativistic equation E² = p²c² + m²c⁴ relates a particle’s energy, momentum, and rest mass. It applies to massive and massless particles.
Energy: A conserved physical quantity associated with the capacity to cause change or perform work. In the relation, energy combines rest energy with the contribution associated with motion.
Special relativity: A theory of space and time in inertial frames, built on the constancy of light speed and the equivalence of such frames. Its spacetime symmetries make the energy–momentum relation frame-independent in form.
Pair production: The creation of a particle–antiparticle pair from energy, usually in the presence of another body or field. The relation sets the minimum energy needed to create particles with specified masses.
Newtonian kinetic energy: The classical kinetic energy of a body, given by one-half its mass times speed squared. It approximates relativistic kinetic energy when speeds are much smaller than light speed.
Momentum: A vector quantity equal to mass times velocity in classical mechanics, generalized relativistically for high-speed motion. Its relativistic value determines how much energy exceeds the particle’s rest energy.
Invariant mass: The mass of a system defined independently of its reference frame, also called rest mass. The mass in the equation remains unchanged between inertial observers.
Particle decay: The spontaneous transformation of an unstable particle into lighter particles. Energy–momentum conservation uses the relation to constrain possible decay products.
Massless particle: A particle with zero invariant mass, such as a photon, that travels at light speed in vacuum. For zero mass, the relation becomes E = pc rather than the massive-particle form.
Rest energy: The energy a body possesses by virtue of its rest mass, equal to mc². Setting momentum to zero reduces the relation to this energy.
Lorentz transformation: A transformation relating measurements of space and time between inertial frames in special relativity. It changes energy and momentum while preserving the relation’s mass term.