Planck units
Expressing one of these physical constants in terms of Planck units yields a numerical value of 1.Originally proposed in 1899 by German physicist Max Planck, they are relevant in research on unified theories such as quantum gravity.One example is represented by the conditions in the first 10−43 seconds of our universe after the Big Bang, approximately 13.8 billion years ago.The four universal constants that, by definition, have a numeric value 1 when expressed in these units are: Variants of the basic idea of Planck units exist, such as alternate choices of normalization that give other numeric values to one or more of the four constants above.All Planck units are derived from the dimensional universal physical constants that define the system, and in a convention in which these units are omitted (i.e. treated as having the dimensionless value 1), these constants are then eliminated from equations of physics in which they appear.Referring to "G = c = 1", Paul S. Wesson wrote that, "Mathematically it is an acceptable trick which saves labour.Planck underlined the universality of the new unit system, writing:[5] ... die Möglichkeit gegeben ist, Einheiten für Länge, Masse, Zeit und Temperatur aufzustellen, welche, unabhängig von speciellen Körpern oder Substanzen, ihre Bedeutung für alle Zeiten und für alle, auch ausserirdische und aussermenschliche Culturen nothwendig behalten und welche daher als »natürliche Maasseinheiten« bezeichnet werden können.... it is possible to set up units for length, mass, time and temperature, which are independent of special bodies or substances, necessarily retaining their meaning for all times and for all civilizations, including extraterrestrial and non-human ones, which can be called "natural units of measure".Planck considered only the units based on the universal constantsFor in natural (Planck) units, the strength of gravity simply is what it is, a primary quantity, while the proton's mass is the tiny number 1/13 quintillion.From the point of view of Planck units, this is comparing apples with oranges, because mass and electric charge are incommensurable quantities.[22][23] During the 1950s, multiple authors including Lev Landau and Oskar Klein argued that quantities on the order of the Planck scale indicated the limits of the validity of quantum field theory.[22][24] In 1959, C. A. Mead showed that distances that measured of the order of one Planck length, or, similarly, times that measured of the order of Planck time, did carry special implications related to Heisenberg's uncertainty principle:[25] An analysis of the effect of gravitation on hypothetical experiments indicates that it is impossible to measure the position of a particle with error less than 𝛥𝑥 ≳ √𝐺 = 1.6 × 10−33 cm, where 𝐺 is the gravitational constant in natural units.[26] The Planck scale is therefore the point at which the effects of quantum gravity can no longer be ignored in other fundamental interactions, where current calculations and approaches begin to break down, and a means to take account of its impact is necessary.[27] On these grounds, it has been speculated that it may be an approximate lower limit at which a black hole could be formed by collapse.It is generally assumed that quantum effects of gravity dominate physical interactions at this time scale.[31] Table 3 lists properties of the observable universe today expressed in Planck units.[32][33] After the measurement of the cosmological constant (Λ) in 1998, estimated at 10−122 in Planck units, it was noted that this is suggestively close to the reciprocal of the age of the universe (T) squared.It is equal to 1.616255(18)×10−35 m[7] (the two digits enclosed by parentheses are the estimated standard error associated with the reported numerical value) or about 10−20 times the diameter of a proton.[35] It can be motivated in various ways, such as considering a particle whose reduced Compton wavelength is comparable to its Schwarzschild radius,[35][36][37] though whether those concepts are in fact simultaneously applicable is open to debate.The Bekenstein–Hawking entropy of a black hole is one-fourth the area of its event horizon in units of Planck length squared.[11]: 370 Since the 1950s, it has been conjectured that quantum fluctuations of the spacetime metric might make the familiar notion of distance inapplicable below the Planck length.Higher-energy collisions, rather than splitting matter into finer pieces, would simply produce bigger black holes.[42][43] In theories with large extra dimensions, the Planck length calculated from the observed value of[46][47] Proposals for theories of doubly special relativity posit that, in addition to the speed of light, an energy scale is also invariant for all inertial observers.[56] Physical quantities that have different dimensions (such as time and length) cannot be equated even if they are numerically equal (e.g., 1 second is not the same as 1 metre).As already stated above, Planck units are derived by "normalizing" the numerical values of certain fundamental constants to 1.The factor 4π is ubiquitous in theoretical physics because in three-dimensional space, the surface area of a sphere of radius r is 4πr2.[11]: 56 Hence a substantial body of physical theory developed since Planck's 1899 paper suggests normalizing not G but 4πG (or 8πG) to 1.In fact, alternative normalizations frequently preserve the factor of 1/4π in the nondimensionalized form of Coulomb's law as well, so that the nondimensionalized Maxwell's equations for electromagnetism and gravitoelectromagnetism both take the same form as those for electromagnetism in SI, which do not have any factors of 4π.In theories emerging after 1899, G nearly always appears in formulae multiplied by 4π or a small integer multiple thereof.Hence, a choice to be made when designing a system of natural units is which, if any, instances of 4π appearing in the equations of physics are to be eliminated via the normalization.
particle physicsphysical cosmologysystem of units of measurementphysical constantsnatural unitsfree spaceprototype objectMax Planckquantum gravityenergieslengthsStandard Modelquantum field theorygeneral relativityquantum effects of gravityfirst 10−43 secondsBig Banguniversal constantsspeed of lightgravitational constantreduced Planck constantBoltzmann constantbase unitsInternational System of UnitsSI base quantitiesNewton's law of universal gravitationdimensionally consistentdimensionless quantitiesPaul S. WessonGeorge Johnstone StoneyStoney unitselectron chargeactionWien approximationblack-body radiationlengthtemperatureCoulomb constantvacuum permittivityfine-structure constantvolumemomentumkg⋅m/senergydensityaccelerationorders of magnitude22 microgramsanthropocentricsecondPlanck lengthFrank Wilczekquintillioncomparing apples with orangeselectric chargeincommensurableproton chargeproton massArthur EddingtonLev LandauOskar KleinJohn Archibald WheelerHeisenberguncertainty principleenergy scaleenergy equivalentquantum effectsgravitynon-renormalizabilityfundamental interactionsquantum mechanicsstring theoryM-theoryloop quantum gravitynoncommutative geometrycausal set theoryChronology of the universeTime-variation of fundamental constantsBig Bang cosmologytime passedunified forceunified with gravitationgrand unification epochinflationary epochobservable universelight-yearssolar massesEddington numbercosmic microwave background radiationCosmological constantHubble constantage of the universestandard errorprotonreduced Compton wavelengthSchwarzschild radiusBekenstein–Hawking entropy of a black holeevent horizonfoam at the Planck scalelarge extra dimensionsvacuumultra-high-energy cosmic rayobserved in 1991doubly special relativitythermal radiationthermal equilibriumHawking evaporationnondimensionalizationenergy–momentum relationDirac equationtheoretical physicssphereinverse-square lawGauss's lawdivergenceflux densitygravitationalelectrostatic fieldshigher-dimensional spheresPoisson's equationgravitoelectromagnetismGauss's law for gravityPoisson equationgravitoelectromagneticgravitational fieldslocally flat spacetime