The Planck length changes

Planck units


The Planck units form a system of natural units for the physical quantities.

They are calculated directly as products and quotients of the fundamental natural constants from:

Expressed in Planck units, these natural constants (or certain conventional multiples of these) therefore all have the numerical value 1. In this system of units, many calculations are numerically simpler. The Planck units are named after Max Planck, who noticed in 1899 that with his discovery of the quantum of action, enough fundamental natural constants were now known to define universal units for length, time, mass and temperature.

The importance of the Planck units is, on the one hand, that the Planck units mark minimal limits (e.g. for length and time) up to which we can differentiate between cause and effect. This means that beyond this limit, the previously known physical laws are no longer applicable, e.g. in the theoretical explanation of the processes shortly after the Big Bang (see Planck scale).

On the other hand, as Planck put it, the Planck units “independently of special bodies or substances retain their meaning for all times and for all, including extraterrestrial and extraterrestrial cultures, and [...] can therefore be called“ natural units of measurement ” “, That is, our laws of nature are universally applicable, understandable and communicable in the cosmos down to the Planck units.


Basic sizes

The Planck units result from a simple dimension analysis. They result as mathematical expressions of the dimension of a length, time or mass, which are only products and quotients of suitable powers of , and contain. If one also uses the electrical permittivity of the vacuum and the Boltzmann constant, so can also be a Planck charge and a Planck temperature as further basic parameters. The Planck charge fulfills the condition that the gravitational force between two Planck masses and the electromagnetic force between two Planck charges are equally strong: .

Surname sizedimensionterm Value in SI unitsValue in other units
Planck massDimensionsM. 2,176 · 10−8kg1,311 · 1019u, 1.221 x 1019GeV / c2
Planck lengthlengthL. 1,616 · 10−35m3,054 · 10−25a0
Planck timetimeT 5,391 · 10−44s 
Planck chargechargeI T 1,876 · 10−18C.11.71 e
Planck temperaturetemperatureΘ 1,417 · 1032K 

The symbols mean:

Instead of will sometimes set to one, the unit of mass is the reduced Planck mass:

With the definition of a correspondingly reduced Planck charge In this case, the above-mentioned equality of forces is retained.

Derived quantities

In addition to these five basic quantities, the following derived quantities are also used:

Surname sizedimensionterm Value in SI units
Planck surfacesurfaceL.22,612 · 10−70m2
Planck volumevolumeL.34,222 · 10−105m3
Planck energyenergyML2T−21,956 · 109J
= 1,2209 · 1028eV
= 543.4 kWh
Planck impulsepulseMLT−16.525 kg m / s
Planck forceforceMLT−21,210 · 1044N
Planck performancepowerML2T−33,628 · 1052W.
Planck densitydensityML−35,155 · 1096kg / m3
Planck angular frequencyAngular frequencyT−11,855 · 1043s−1
Planck printprintML−1T−24,633 · 10113Pa
Planck currentElectrical currentQT−13,479 · 1025A.
Planck tensionElectric voltageML2T−2Q−11,043 · 1027V.
Planck impedanceresistanceML2T−1Q−229.98 Ω
Planck accelerationaccelerationLT−25,56 · 1051m · s−2
Planck magnetic fieldMagnetic flux densityMI−1T−24,29361 · 1059T

The Planck unit for the angular momentum results from the product of Planck length and Planck momentum to the value . This is precisely the unit of angular momentum quantization known from quantum mechanics.

The Planck area plays an important role especially in string theories and when considering the entropy of black holes in connection with the holographic principle.


At the end of the 19th century, during his investigations into the theory of black body radiation, for which he received the Nobel Prize in Physics two decades later, Planck discovered the last natural constant required to define the Planck units, the quantum of action that was later named after him. He recognized the possibility of defining a universally valid system of units and mentioned this in a lecture “About irreversible radiation processes”. The following quote gives an impression of the importance Planck accorded these units

"... keep their meaning for all times and for everyone, including extraterrestrial and extraterrestrial cultures, and which can therefore be called 'natural units of measurement' ..."

Although Planck dedicated a chapter (§ 159. Natural Units of Measure) to this system of units in his book “Theory of Thermal Radiation”, published in 1906, and took up this topic again later, it was not used in physics either. The disadvantages that the value of the gravitational constant was not (and still is) known precisely enough for use in a system of measurement, and that practical quantities - expressed in its units - have absurd numerical values, were not matched by any advantage, as in no physical theory at the same time the quantum of action and the constant of gravity appeared.

It was only after initial work on the unification of quantum theory and gravity in the late 1930s that the later field of application of the Planck units emerged. When John Archibald Wheeler and Oskar Klein published in 1955 about the Planck length as the limit of the applicability of general relativity, Planck's proposal was almost forgotten. After the “rediscovery” of Planck's proposals for such a system of measurements, the name was used from 1957 onwards Planck units common.

However, the Planck units commonly used today differ from Planck's original units, since it has been shown in the course of the development of quantum mechanics that is the more practical natural unit than that chosen by Planck .

Today's meaning

One formulates equations that are the natural constants , and contained in Planck units, the constants can be omitted. This simplifies the equations considerably in certain disciplines of theoretical physics, for example in general relativity, in quantum field theories and in the various approaches to quantum gravity.

The Planck units also allow an alternative view of the fundamental forces of nature, the strength of which is described in the International System of Units (SI) by very different coupling constants. When using the Planck units, the situation is as follows: Between two particles that have exactly the Planck mass and the Planck charge, the gravitational force and the electromagnetic force would be exactly the same. The different strength of these forces in our world is the result of the fact that a proton or an electron has a charge of around 0.085 Planck charges, while their masses are 19 or 22 orders of magnitude smaller than the Planck mass. The question: “Why is gravity so weak?” Is therefore equivalent to the question: “Why do the elementary particles have such low masses?”.

Various physicists and cosmologists are concerned with the question of whether we could notice if dimensional physical constants changed slightly, and what the world would look like if there were major changes. Such speculations are, among other things, at the speed of light and the gravitational constant employed, the latter in the expansion theory of the earth since around 1900. The atomic physicist George Gamow says in his popular science book Mr. Tompkins in Wonderlandthat a change from would result in significant changes.

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Date of the last change: Jena, 22.04. 2021