The mass of a particle whose Compton wavelength is equal to the Planck length. It is given by mP = √(ħc/G), where ħ is the rationalized Planck constant, c is the speed of light, and G is the gravitational constant. The description of an elementary particle of this mass, or particles interacting with energies per particle equivalent to it (through E = mc2), requires a quantum theory of gravity. Since the Planck mass is of order 10−8 kg (equivalent energy 1019 GeV), and, for example, the proton mass is of order 10−27 kg and the highest energies attainable in present-day particle accelerators are of order 103 GeV, quantum-gravitational effects do not arise in laboratory particle physics. However, energies equivalent to the Planck mass did occur in the early universe according to big-bang theory, and a quantum theory of gravity is important for discussing conditions there (see Planck time).