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In particle physics and physical cosmology, Planck-scale refers to lengths in the order of the Planck length and volumes in the order of the Planck volume.

Theoretical physics assigns fundamental significance to corresponding Planck units first proposed by physicist Max Planck. They are far smaller than atomic size. Direct observation of Planck-scale dimensions and events is beyond current experimental techniques.

Planck units are units of measurement defined in terms of five universal physical constants so that each constant has the value 1 when expressed in Planck units.

History
In 1856 mathematician Bernhard Riemann noted that granular, rather than continuous, space would ease the fundamental requirements for geometry because this would abviate the need for an arbitrary metric.

Planck units have significance for theoretical physics since they simplify several recurring algebraic expressions of physical law by nondimensionalization. They are relevant in research on unified theories such as quantum gravity. The Planck scale expresses the region in which the predictions of the Standard Model of quantum field theory and of general relativity are no longer reconcilable, and quantum effects of gravity are expected to dominate. This region may be characterized by energies around $1.22 GeV$ (the Planck energy), time intervals around $5.39 s$ (the Planck time) and lengths around $1.62 m$ (the Planck length).

The five universal constants that Planck units, by definition, normalize to 1 are:
 * the speed of light in a vacuum, c,
 * the gravitational constant, G,
 * the reduced Planck constant, ħ,
 * the Coulomb constant, $1⁄4\piε_{0}$
 * the Boltzmann constant, kB

Each of these constants can be associated with a fundamental physical theory or concept: c with special relativity, G with general relativity, ħ with quantum mechanics, ε0 with electromagnetism, and kB with the notion of temperature (statistical mechanics and thermodynamics).

Today the value of the speed of light c in SI units is not subject to measurement error, because the SI base unit of length, the metre, is now defined as the length of the path travelled by light in vacuum during a time interval of $1⁄299 792 458$ of a second. Hence the value of c is now exact by definition, and contributes no uncertainty to the SI equivalents of the Planck units. The same is true of the value of the vacuum permittivity ε0, due to the definition of ampere which sets the vacuum permeability μ0 to 4$\pi$ × 10−7 H/m and the fact that μ0ε0 = $1⁄c^{2}$. The numerical value of the reduced Planck constant ħ has been determined experimentally to 12 parts per billion, while that of G has been determined experimentally to no better than 1 part in $21,300$ (or $47,000$ parts per billion). G appears in the definition of almost every Planck unit in Tables 2 and 3. Hence the uncertainty in the values of the Table 2 and 3 SI equivalents of the Planck units derives almost entirely from uncertainty in the value of G. (The propagation of the error in G is a function of the exponent of G in the algebraic expression for a unit. Since that exponent is ±$1⁄2$ for every base unit other than Planck charge, the relative uncertainty of each base unit is about one half that of G. This is indeed the case; according to CODATA, the experimental values of the SI equivalents of the base Planck units are known to about 1 part in $43,500$, or $23,000$ parts per billion.)

However, most Planck units are many orders of magnitude too large or too small to be of practical use, so that Planck units as a system are really only relevant to theoretical physics. In fact, 1 Planck unit is often the largest or smallest value of a physical quantity that makes sense according to our current understanding. For example:
 * A speed of 1 Planck length per Planck time is the speed of light in a vacuum, the maximum possible physical speed in special relativity; 1 nano-(Planck length per Planck time) is about 1.079 km/h.
 * Our understanding of the Big Bang begins with the Planck epoch, when the universe was 1 Planck time old and 1 Planck length in diameter, and had a Planck temperature of 1. At that moment, quantum theory as presently understood becomes applicable. Understanding the universe when it was less than 1 Planck time old requires a theory of quantum gravity that would incorporate quantum effects into general relativity. Such a theory does not yet exist.

Significance
Planck units are free of anthropocentric arbitrariness. Some physicists argue that communication with extraterrestrial intelligence would have to employ such a system of units in order to be understood. Unlike the metre and second, which exist as base units in the SI system for historical reasons, the Planck length and Planck time are conceptually linked at a fundamental physical level.

Cosmology
In Big Bang cosmology, the Planck epoch or Planck era is the earliest stage of the Big Bang, before the time passed was equal to the Planck time, tP, or approximately 10−43 seconds. There is no currently available physical theory to describe such short times, and it is not clear in what sense the concept of time is meaningful for values smaller than the Planck time. It is generally assumed that quantum effects of gravity dominate physical interactions at this time scale. At this scale, the unified force of the Standard Model is assumed to be unified with gravitation. Inconceivably hot and dense, the state of the Planck epoch was succeeded by the Grand unification epoch, where gravitation is separated from the unified force of the Standard Model, in turn followed by the Inflationary epoch, which ended after about 10−32 seconds (or about 1010 tP).

History
Natural units began in 1881, when George Johnstone Stoney, noting that electric charge is quantized, derived units of length, time, and mass, now named Stoney units in his honor, by normalizing G, c, and the electron charge, e, to 1. In 1898, Max Planck discovered that action is quantized, and published the result in a paper presented to the Prussian Academy of Sciences in May 1899. At the end of the paper, Planck introduced, as a consequence of his discovery, the base units later named in his honor. The Planck units are based on the quantum of action, now usually known as Planck's constant. Planck called the constant b in his paper, though h is now common. Planck underlined the universality of the new unit system, writing:

Planck considered only the units based on the universal constants G, ħ, c, and kB to arrive at natural units for length, time, mass, and temperature. Planck did not adopt any electromagnetic units. However, since the non-rationalized gravitational constant, G, is set to 1, a natural extension of Planck units to a unit of electric charge is to also set the Coulomb constant, $1⁄4\piε_{0}$, to 1 as well. Another convention is to use the elementary charge as the basic unit of electric charge in Planck system. Such system is convenient for black hole physics. The two conventions for unit charge differ by a factor of the square root of the fine-structure constant. Planck's paper also gave numerical values for the base units that were close to modern values.

If the speed of light c, were somehow suddenly cut in half and changed to $1⁄2$c (but with the axiom that all dimensionless physical quantities remain the same), then the Planck length would increase by a factor of 2√2 from the point of view of some unaffected observer on the outside. Measured by "mortal" observers in terms of Planck units, the new speed of light would remain as 1 new Planck length per 1 new Planck time – which is no different from the old measurement. But, since by axiom, the size of atoms (approximately the Bohr radius) are related to the Planck length by an unchanging dimensionless constant of proportionality:


 * $$a_0 = \frac{4 \pi \epsilon_0 \hbar^2}{m_e e^2} = \frac{m_\text{P}}{m_e \alpha} l_\text{P}. $$