Relativistic energy

Intermediate

Total energy includes rest energy.

Key relationE = γmc²

E = γmc² includes rest energy. Total energy grows without bound as v → c.

Worked example

An electron at 0.99c has E = 3.6 MeV (rest energy 0.511 MeV).

Common mistake

Differences matter for kinetic energy.

In more detail

The total relativistic energy is E = γmc². It includes rest energy mc² and kinetic energy, and it grows without bound as speed approaches c.

Accelerators are designed to deliver large relativistic energies.
Nuclear power is based on converting mass into energy.
Particle physicists use relativistic energy to find how much energy a particle needs to reach a chosen speed.

What is the rest energy?

mc², the energy of a particle at rest.

Is energy conserved?

Yes, total relativistic energy is conserved in isolated systems.

Why does the total energy include rest energy?

Relativity says mass is a form of energy, so even a particle at rest carries energy equal to its mass times c squared.