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Directional units

Of the base units of the International System of Units (SI) only two concern movement in a direction: the units of length (metre) and duration (second). The candela measures luminous intensity in a direction without regard for movement. Derived units of movement include speed and velocity (metres per second), force (newton), pressure (pascal), energy (joule), power (watt), acceleration (metres per second squared), momentum (newton second), and action (joule second). Angular measures are directional through the axis of movement: angular velocity (radians per second), angular acceleration (radians per second squared), angular momentum (newton metre second), and torque (newton metre).

All of these units are directed in three dimensions. The units for space (length) and time are the directional base units. The derived units have directions in three-dimensional phase spaces, which follow the directions of space and time. If only one of the components of a derived unit has a direction, then the derived unit has the dimensions of that component. For example, velocity has the direction of length since it uses the time magnitude rather than the time direction.

The second is defined as the duration of 9,192,631,770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium 133 atom. The metre is the distance traveled by light in a vacuum in 1/299,792,458 second.

The light-year is defined by the International Astronomical Union (IAU) as the distance that light travels in a vacuum in one Julian year (365.25 days). Although it is a unit of length, with the speed of light in a vacuum it may be converted to a unit of time. This conversion is commonly used in astronomy so that looking at the stars is considered looking into the distant past — in three dimensions of direction.

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