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# Planck time

In quantum mechanics, the Planck time (tP) is the unit of time in the system of natural units known as Planck units. The Planck time is the shortest possible duration. A Planck time unit is the time required for light to travel a distance of 1 Planck length in a vacuum, which is a time interval of approximately 1.911 × 10−43 s (Lorentz–Heaviside version) or 5.39 × 10−44 s (Gaussian version). The unit is named after Max Planck, who was the first to propose it.

The Planck time is defined as:[1]

${\displaystyle t_{\mathrm {P} }\equiv {\sqrt {\frac {4\pi \hbar G}{c^{5}}}}}$ (Lorentz–Heaviside version)
${\displaystyle t_{\mathrm {P} }\equiv {\sqrt {\frac {\hbar G}{c^{5}}}}}$ (Gaussian version)

where:

ħ = ​h2π is the reduced Planck constant (sometimes h is used instead of ħ in the definition[2])
G = gravitational constant
c = speed of light in vacuum

Using the known values of the constants, the approximate equivalent value in terms of the SI unit, the second, is

${\displaystyle 1\ t_{\mathrm {P} }\approx 5.391\,247(60)\times 10^{-44}\ \mathrm {s} ,}$

where the two digits between parentheses denote the standard error of the approximated value.[1]

## History

The Planck time (also known as Planck second) was first suggested by Max Planck[3] in 1899. He suggested that there existed some fundamental natural units for length, mass, time, force, energy and power. Planck derived these using dimensional analysis only using what he considered the most fundamental universal constants: the speed of light, the Newton gravitational constant and the Planck constant.

## Physical significance

The Planck time is the unique combination of the gravitational constant G, the special-relativistic constant c, and the quantum constant ħ, to produce a constant with dimension of time. Because the Planck time comes from dimensional analysis, which ignores constant factors, there is no reason to believe that exactly one unit of Planck time has any special physical significance. Rather, the Planck time represents a rough time scale at which quantum gravitational effects are likely to become important. This essentially means that while smaller units of time can exist, they are so small their effect on our existence is negligible. The nature of those effects, and the exact time scale at which they would occur, would need to be derived from an actual theory of quantum gravity.

The reciprocal of the Planck time, which is Planck frequency, can be interpreted as an upper bound on the frequency of a wave. This follows from the interpretation of the Planck length as a minimal length, and hence a lower bound on the wavelength.

All scientific experiments and human experiences occur over time scales that are many orders of magnitude longer than the Planck time,[4] making any events happening at the Planck scale undetectable with current scientific knowledge. As of November 2016, the smallest time interval uncertainty in direct measurements was on the order of 850 zeptoseconds (8.50 × 10−19 seconds).[5]

## References

1. ^ a b CODATA Value: Planck Time – The NIST Reference on Constants, Units, and Uncertainty.
2. ^ "Big Bang models back to Planck time". Georgia State University. 19 June 2005.
3. ^ M. Planck. Naturlische Masseinheiten. Der Koniglich Preussischen Akademie Der Wissenschaften, p. 479, 1899
4. ^ "First Second of the Big Bang". How The Universe Works 3. 2014. Discovery Science.
5. ^ MacDonald, Fiona (14 November 2016). "Scientists have measured the smallest fragment of time ever". Science Alert. Retrieved 14 November 2016.
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