Planck momentum

This plot of kinetic energy versus momentum has a place for most moving objects encountered in everyday life. It shows objects with the same kinetic energy (horizontally related) that carry different amounts of momentum, as well as how the speed of a low-mass object compares (by vertical extrapolation) to the speed after perfectly inelastic collision with a large object at rest. Highly sloped lines (rise/run=2) mark contours of constant mass, while lines of unit slope mark contours of constant speed. The plot further illustrates where lightspeed, Planck's constant, and kT figure in. (Note: the line labeled universe only tracks a mass estimate for the visible universe.)

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 $m_{{\text{P}}}c$ . A baseball, which has mass $m=$ 0.145 kg, travelling at 45 m/s (160 km/h; 100 mph) would have a Planck momentum.

Notes and references

Planck's natural units

Planck's constant Planck 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 Planck acceleration

This article is issued from Wikipedia - version of the 7/25/2015. The text is available under the Creative Commons Attribution/Share Alike but additional terms may apply for the media files.

Planck momentum

Notes and references

See also