Natural units

Natural units are measurement systems that set selected physical constants to one, absorbing them into the units used for physical quantities. They simplify equations by expressing relationships without explicit conversion factors.

Dimensional analysis: A method for checking physical equations and scaling relations by tracking the dimensions of quantities. It explains how natural-unit equations retain dimensional consistency after constants disappear.
Unit of measurement: A defined magnitude used as a standard for measuring a physical quantity. Natural units are measurement units chosen through fixed physical constants.
Planck units: A natural-unit system in which c, G, ħ, and the Boltzmann constant are set to one. This specific convention includes gravity and temperature alongside relativity and quantum mechanics.
Quantum field theory: A framework combining quantum mechanics with special relativity to describe fields and their particle excitations. Its equations are usually written with c and ħ set to one.
Planck constant: The fundamental constant that relates a particle’s energy to its frequency and sets the scale of quantum effects. Setting it to one removes explicit quantum-action factors from equations.
Boltzmann constant: The constant relating temperature to energy in statistical mechanics, denoted by kB. Setting kB=1 expresses temperature directly in energy units.
Particle-physics natural units: A convention commonly setting c=ħ=1 while retaining electromagnetic and gravitational constants explicitly. It is the usual narrower choice when discussing relativistic quantum particles.
Special relativity: Einstein’s theory of space and time for inertial frames, with the speed of light invariant for all observers. Natural units make relativistic relations treat time and distance on equal footing.
Speed of light: The speed at which light travels in vacuum, a universal constant denoted by c. Taking c=1 equates time and distance units and simplifies relativistic equations.
Elementary charge: The magnitude of the electric charge of a proton or electron, denoted by e. Some particle-physics conventions also set e or a related electromagnetic constant to one.

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