# Planck's constant

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Planck's constant (h) defines the relationship of energy (of a photon) to frequency. It is 6.626176 x 10-34 joule-seconds (approx); [cgs] 6.626176 x 10-27 erg-seconds (approx).

The relationship is defined by: ${\displaystyle E=h\nu .\,}$ ie the energy of a photon is equal to its frequency times Planck's constant.

Its actual existence, formulated by Max Planck was a founding pillar of Quantum mechanics.

## Slash aitch

A related value called the reduced Planck constant, also known as slash aitch or h-bar from its symbol (${\displaystyle {\hbar }}$), is equal to ${\displaystyle {\frac {h}{2\pi }}}$. While playing around with the equations involved in quantum mechanics, scientists found that the Planck constant kept appearing when divided by ${\displaystyle 2{\pi }}$ and introduced a new symbol to make their lives a little easier.

For example, in addition to a photon's frequency ν (cycles per second), physicists often do calculations involving its angular frequency ω (radians per second), which by definition is 2π times the frequency. Thus, the relationship between the energy of a photon and its angular frequency is ${\displaystyle E=\hbar \omega .}$

## Planck units

The system of Planck units was designed to make the lives of quantum physicists easier still. In the Planck unit system, five basic constants of the universe -- the speed of light (c), the reduced Planck constant (ħ), Newton's gravitational constant (G), the Coulomb constant (ke), and the Boltzmann constant (kB) -- are all set equal to 1. The base units of length, time, mass, electric charge, etc., are then derived from these constants. For example, the Planck charge qP is defined as:

${\displaystyle q_{\text{P}}={\sqrt {\frac {\hbar c}{k_{\text{e}}}}}}$

... which works out to approximately 11.706 times the charge on a proton.

Some of the Planck units, such as the Planck mass[1] and the Planck charge, seem not to have any fundamental meaning themselves and could very well end up being completely arbitrary; but others have special significance within the quantum world. Note also how most of them are way beyond daily experience and are relevant just for physicists who study that field.[2]

The Planck length is, theoretically, the shortest distance that can possibly be measured.[3] It is approx 1.6 x 10-35 m, about 1020 times smaller than the nucleus of an atom.

The Planck time is the time taken to travel the Planck length at the speed of light. It is approx 10-43 seconds. It is also the earliest time for which a valid description of the universe can ever be made.[4]

The Planck density is one planck mass per cubic Planck length. It is much, much denser than all but the tiniest black holes. One unit of Planck time after the Big Bang, the mass density of the universe is thought to have been one Planck density.

The Planck temperature unit is about 1.4 x 1032 Kelvin. It's about 9 x 1024 times hotter than the core of the sun, and is theoretically the highest temperature at which matter could exist at all. One unit of Planck time after the Big Bang, the temperature of the universe is thought to have been one Planck temperature.