Planck momentum

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Planck momentum is the unit of momentum in the system of natural units known as Planck units. It has no commonly used symbol of its own, but can be denoted by $m_{{\text{P}}}c$ , where ${m_{{\text{P}}}}$ is the Planck mass and $c$ is the speed of light in a vacuum. Then

$m_{{\text{P}}}c={\frac {\hbar }{l_{{\text{P}}}}}={\sqrt {{\frac {\hbar c^{3}}{G}}}}\approx 6.52485{\text{ kg m/s}},$

where

$\hbar$ is the reduced Planck's constant,

${l_{{\text{P}}}}$ is the Planck length,

$G$ is the gravitational constant.

In SI units Planck momentum is approximately 6.5 kg m/s. It is equal to the Planck mass multiplied by the speed of light, usually associated with the momentum of primordial photons in some prevailing Big Bang models. Unlike most of the other Planck units, Planck momentum occurs on a human scale. By comparison, running with a five-pound object (10⁸×Planck mass) at an average running speed (10^-8×speed of light in a vacuum) would give the object Planck momentum. A 70 kg human moving at an average walking speed of 1.4 m/s (5.0 km/h; 3.1 mph) would have a momentum of about 15 $m_{{\text{P}}}c$ .

Notes and references

v t e Planck's natural units

Base Planck units	Planck time Planck length Planck mass Planck charge Planck temperature

Derived Planck units	Planck energy Planck force Planck power Planck density Planck angular frequency Planck pressure Planck current Planck voltage Planck impedance Planck momentum Planck area Planck volume

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Planck momentum

Notes and references

See also