In Physical, the units of Planck are a Système of units of measurement, in reference to max Planck, system which is a preliminary definition of natural Unités . The system is only defined using the Constantes fundamental physics which follow, and is “natural” with the direction where the values of these constants become 1 when they are expressed in this system. (In the System CGS, it is the constant of the force of Coulomb of the Loi of Coulomb which is standardized to 1, rather than the Permittivité of the vacuum. This is similar to the standardization of the gravitational Constante of the law of Newton like the east the original project of Planck to define the units of Planck).

Constantes fundamental:

__TOC The units of Planck are often considered to joke by the physicists like the " Units of God ". They eliminate arbitrary the anthropocentric from the system of units: certain physicists think that an extraterrestrial intelligence could use such a system.

The natural units can help the physicists with recadrer certain questions. Frank Wilczek undoubtedly explains it better (June 2001, Physics Today):

" … We see that the question is not " Why gravity is so weak? " but rather " Why the mass of the proton is so small? " Indeed, in natural units (of Planck), the force of gravity is simply what it is, a fundamental size, whereas the mass of the proton is the tiny number of 1 divided by 13 billion milliards."

The force of gravity is simply what it is and the electromagnetic force is simply what it is. The electromagnetic force acts on a quantity (the electric charge) different from the gravity (which acts on the mass), and thus one cannot compare it directly with gravity. To consider gravity as a extremely weak force is, from the point of view of the natural units, like comparing apples and oranges. If it is true that the repulsive electrostatic force between two protons (only in the vacuum) is very largely larger than gravitational attraction between the two same protons, it is because the load of the protons is with little thing close a natural unit of load, whereas the mass of the protons is much lower than the natural unit of mass.

These units have the advantage of simplifying many equations in Physique, by removing conversion factors. For this reason, they are very popular in research in quantum Gravité. For example, equation of Einstein $E=m.c^\; \{2\; celebrates\; it\}$ becomes only $E=m$, i.e. a body of mass 5000 units of Masse of Planck will have an intrinsic energy of 5000 units of energy of Planck .

However, the units are too small or too large to be of an everyday usage, as long as they are not adjusted with great powers of 10. They also suffer from uncertainties of measurement of some of the constants on which they are based, primarily the gravitational Constante G .

Principal the equation of physics with the units of Planck

|----- |align=" center" | universal Law of the gravitation of Newton | |----- | align=" center" | Equation of Schrödinger | |----- | align=" center" | Energy of a photon or a particle of pulsation ω | |----- | The famous formula Mass-Energy of Einstein | |----- | Equation of the gravitational field of Einstein (General relativity) | |----- | Definition of the temperature by the energy of a particle per degree of freedom | |----- | Law of Coulomb | |----- | colspan=" 2" | Maxwell's equations |- |align=" center" |* | |- |align=" center" |* | |- |align=" center" |* | |- |align=" center" |* | |}

(NB: The factors 4π would have been eliminated if ε₀ had been standardized in the place of the constant of the force of Coulomb 1 (4πε₀.)

Units of Planck: basic units

The three constants of physics are thus expressed simply by using the basic units of Planck:

$c\; =\; \backslash \; frac\; \{l\_P\}\; \{t\_P\}\; \backslash$

$\backslash \; hbar\; =\; \backslash \; frac\; \{m\_P\; l^2\_P\}\; \{t\_P\}\; \backslash$

$G\; =\; \backslash \; frac\; \{l^3\_P\}\; \{m\_P\; t^2\_P\}\; \backslash$

$\backslash \; epsilon\_0\; =\; \backslash \; frac\; \{q^2\_P\; t^2\_P\}\; \{4\; \backslash \; pi\; m\_P\; l^3\_P\}\; \backslash$

$k\; =\; \backslash \; frac\; \{m\_P\; l^2\_P\}\; \{t^2\_P\; T\_P\}\; \backslash$

Units of Planck: derived units

Discussion

For a Planck's constant scale (in lasted, Length, Density or Temperature), it is necessary to consider at the same time the effects of the quantum Mécanique and those of the General relativity. But that requires a theory of the quantum gravity, which does not exist yet.

The majority of the units of Planck are either too small, or too large to be usable in practice, unless transporting powers of 10 in calculations. They also suffer from uncertainties as far as certain constants on which it are based, in particular the Constante of gravitation G which has an uncertainty of 1 out of 7000.

The load of Planck definite nor was not proposed at the origin by Planck. It is a unit of load which was defined same manner as the other units of Planck and which is used by the physicists in certain publications. The Elementary charge is thus defined by the load of Planck in this manner:

$e\; =\; \backslash \; sqrt\; \{\backslash \; alpha\}\; \backslash \; q\_P\; =\; 0.085424543\; \backslash \; q\_P\; \backslash$

where $\{\backslash \; alpha\}\; \backslash$ is the constant of the fine structure

$\backslash \; alpha\; =\; \backslash \; left\; (\backslash \; frac\; \{E\}\; \{q\_P\}\; \backslash \; right)\; ^2\; =\; \backslash \; frac\; \{e^2\}\; \{\backslash \; hbar\; C\; 4\; \backslash \; pi\; \backslash \; epsilon\_0\}\; =\; \backslash \; frac\; \{1\}\; \{137.03599911\}$

The value of the constant without dimension of fine structure is defined by the quantity of load, measured in natural units (load of Planck), that electrons, protons, and other particles charged have indeed. Because the electromagnetic Force between two particles is proportional to the product of the loads of the two particles (which are each one, in units of Planck, proportional to $\backslash \; sqrt\; \{\backslash \; alpha\}\; \backslash$), the intensity of the electromagnetic force compared to the other forces is proportional to $\{\backslash \; alpha\}\; \backslash$.

The impedance of Planck is equal to the impedance characteristic of the vacuum divided by 4π: one thus has, in term of units of Planck, $\{Z\_0\; =\; 4\; \backslash \; pi\; Z\_P\}\; \backslash$. The coefficient 4π comes owing to the fact that it is the coefficient $1\; (4\; \backslash \; pi\; \backslash \; epsilon\_0)\; \backslash$ of the Loi of Coulomb which is standardized to 1, and not the permittivity of the vacuum $\backslash \; epsilon\_0\; \backslash$. It is thus an arbitrary definition, which is not perhaps optimal with a view to define possible system of physical unit the most natural as the system of Planck aims at it.

Units of Planck and the invariance of scale of nature

According to Duff in How one time-variation off fundamental constant and Duff, Okun and Veneziano in constant Trialogue one the number off fundamental ( The operationally indistinguishable world off Mr. Tompkins ), if all the physical quantities (mass and other properties of the particles) were expressed in units of Planck, these quantities would be numbers without dimension (a mass divided by the mass of Planck, a length divided by the length of Planck, etc). The only quantities which we finally measure in the experiments in physics or by our perception of reality are numbers without dimension. Indeed, when one measures usually a length with a rule or a meter-ribbon, one counts in fact the marks made according to a standard; in other words one measures the length relative to this reference length. The same applies to the experiments in physics, where all the physical quantities are measured relative with other dimensioned physical sizes. We could note changes so certain quantities without dimension like $\backslash \; alpha\; \backslash$ or the report/ratio of the masses proton/electron was modified (atomic strucure would change), but if all the physical quantities without dimension remained constant, we could not say if a dimensioned quantity, like speed of light, C , changed. And, indeed, the concept of Tompkins becomes unimportant in our existence if a dimensioned quantity as ''' C ''' changes, even enormously.

If speed of light C were suddenly divided by two and were changed into C /2, but by keeping unchanged all the adimensionnées constants, then the Length of Planck would be increased of a report/ratio of √8 from the point of view of certain external observers not touched by the change. But as the size of the atoms (roughly the Ray of Bohr) is related to the length of Planck by a constant without dimension:

$a\_0\; =\; =\; l\_P$

then the atoms would be larger (in each dimension) by √8, each one of us would be larger of √8, and thus our rules to be measured would be larger (and thicker, and broader) of a √8 report/ratio, and we would not know anything of this change.

The tick-tock of our watches would be slower of a √32 report/ratio (from the point of view of the external observer nonconcerned by the changes), because the time of Planck would have increased √32, but we would not see the difference. This hypothetical external observer could note that the light moves with half its old speed (just as all speeds), it would always traverse 299792458 our new meters by one of our new seconds. We let us not see any difference.

This contradicted conceptually George Gamow in Mr Tompkins which supposes that if a universal constant as C changed, we would notice the difference easily. We must now ask him: How would we measure the difference if our references of measurement changed same manner?

The discovery of the natural units of Planck

max Planck made for the premère time the list of its natural units (and gave of them values remarkably close to those which we use today) in May 1899 in a paper presented to the Academy of Science of Prussia:
“Irreversible Über Strahlungsvorgänge”. Sitzungsberichte der Preußischen Akademie der Wissenschaften , vol. 5, p. 479 (1899)

At the time when it presented its units, the quantum Mécanique had not been discovered yet. He had not discovered yet the theory of the Rayonnement of the black body (published for the first time in December 1900) in which the Planck's constant $\{H\}\; \backslash$ made his first appearance and for which Planck obtained the Nobel Prize later. The important parts of the paper of 1899 comprised some confusions on the way in which it succeeded in finding the units of time, length, mass, temperature, etc, which we define today by using the constant of Dirac $\backslash \; hbar\; \backslash$ and to justify them by considerations of quantum physics before that $\backslash \; hbar\; \backslash$ and the quantum physics are not known. Here a quotation of the paper of 1899 which gives an idea on the way in which Planck considered its whole of units:

… ihre Bedeutung für ale Zeiten und für ale, auch außerirdische und außermenschliche Kulturen notwendig behalten und welche daher als” natürliche Maßeinheiten “bezeichnet werden können…

… It keep necessarily their significance for all times and all civilizations, same extraterrestrial and nonhuman, and can thus be indicated “  units naturelles  ”…

See too

• dimensional Analysis
• Constant physics

External bonds

• original Article of Planck

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