Operators describe the spatial and temporal properties of elementary particles. As particles spread out across space and time, there is a proportional dilution of kinetic energy.

Spatial operators describe the dilution of a particle’s energy across its wavelength. In unit dimensions, operators quantify the ratio of a particle’s wavelength and inertial mass to the Planck length and Planck mass.

Temporal operators describe the dilution of a particle’s energy across time. In unit dimensions, operators quantify the rate of displacement and oscillation period in relation to the Planck time.

Operators have the following properties:

- An extensive operator is the ratio of length, mass, or time to its maximum potential in the same unit dimension. An intensive operator has the combined ratios of maximum potential in two unit dimensions.
- Operators are always dimensionless because the ratios are in the same unit dimension(s).
- Operators are defined on a scale of 0 to 1, where one represents the maximum potential and zero represents the limit of minimum potential.
- Operators are designated by the symbol β with a subscript for the operator type.

## Mechanical operators

Mechanical operators describe the mechanical properties of elementary particles and systems. The following illustration shows the relationships between four of the mechanical operators in terms of wavelength and mass.

**Velocity** operator

𝛽_{𝑣}

**Spin** operator

𝛽_{𝑠}

## Gravitational and electromagnetic operators

Gravitational operators quantify the effects of massive bodies on the gravitational field. The operators are ratios of mass and distance to the Planck mass and Planck length.

The electromagnetic interaction is naturally quantified in dimensions of length, mass, and time. Performing calculations in fundamental unit dimensions requires a unit conversion from traditional electromagnetic units into MKS units. Distance and charge operators give the properties of the electromagnetic field, where the maximum charge potential is equal to the Planck time.

**Mass density** operator

𝛽_{𝜌}

**Distance** operator

𝛽_{𝑟}

**Charge** operator

𝛽_{𝑞}