Planck's constant

{{Physics}}{{Sources needed}}
'''Planck's constant''''' (h)'' defines the relationship of [[energy]] (of a [[photon]]) to frequency. It is 6.626176 x 10<sup>-34</sup> joule-seconds (approx); [cgs] 6.626176 x 10<sup>-27</sup> erg-seconds (approx).

The relationship is defined by: <math>E = h\nu.\,</math> 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 (<math>{\hbar}</math>), is equal to <math>\frac{h}{2 \pi}</math>. While playing around with the equations involved in quantum mechanics, scientists found that the Planck constant kept appearing when divided by <math>2{\pi}</math> and introduced a new symbol to make their lives a little easier.

For example, in addition to a photon's frequency ''&nu;'' (cycles per second), physicists often do calculations involving its ''angular'' frequency ''&omega;'' (radians per second), which by definition is 2''&pi;'' times the frequency. Thus, the relationship between the energy of a photon and its angular frequency is <math>E = \hbar\omega.</math>

==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 (&#295;), Newton's gravitational constant (G), the Coulomb constant (k<sub>e</sub>), and the Boltzmann constant (k<sub>B</sub>) -- 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 q<sub>P</sub> is defined as:

:<math>q_\text{P} = \sqrt{ \frac{\hbar c}{k_\text{e}}}</math>
... which works out to approximately 11.706 times the charge on a proton.

Some of the Planck units, such as the Planck mass<ref>About 21.8 micrograms. Since c = 1 in the Planck unit system, the Planck mass is also the Planck unit of energy, which works out to around 2 x 10<sup>9</sup> Joules, roughly the energy released by detonating half a ton of TNT.</ref> 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.<ref>Exceptions besides the already mentioned Planck mass and charge include Planck impedance - just around 30 ohm</ref>

'''The Planck length''' is, theoretically, the shortest distance that can possibly be measured.<ref>According to [[Heisenberg's uncertainty principle]], if you measure the position of a particle to an accuracy of one Planck length, the uncertainty in its momentum will be 3 kilogram-meters per second.</ref> It is approx 1.6 x 10<sup>-35</sup> m, about 10<sup>20</sup> 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<sup>-43</sup> seconds. It is also the ''earliest'' time for which a valid description of the [[universe]] can '''ever''' be made.<ref>This is believed to be true ''no matter what advances are made'' as time and space did not exist before this time. Then, science has been fooled before.</ref>

'''The Planck density''' is one planck mass per cubic Planck length. It is much, much denser than all but the tiniest [[black hole]]s. 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 10<sup>32</sup> Kelvin. It's about 9 x 10<sup>24</sup> 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.

==External Links==
*[http://www.rogermwilcox.com/Planck_ruler.html The Planck length ruler!]

==References==
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[[Category:Physics]]
[[Category:Time]]

Categories: Physics, Time