This site is supported by donations to The OEIS Foundation.

Planck units

From OeisWiki
Jump to: navigation, search


This article is under construction.            

Please do not rely on any information it contains.            



This article page is a stub, please help by expanding it.


The Planck units are a system of natural units uniquelely defined from fundamental physical constants and first proposed by the physicist Max Planck.

Basic Planck units

Planck time

The Planck time, denoted , is the unit of time in the system of natural units known as Planck units. It is a basic unit in the system of Planck units. The Planck time can be uniquely defined from three fundamental physical constants: the speed of light in a vacuum, Planck's constant, and the gravitational constant. It is the time required for light to travel, in a vacuum, a distance of 1 Planck length.[1] The unit is named after Max Planck, who was the first to propose it.

The Planck time is defined as

where

is the reduced Planck's constant (sometimes is used instead of in the definition[1]),
is the [universal] gravitational constant, and
is the speed of light in a vacuum.

Planck time (according to NIST)

According to "The NIST Reference on Constants, Units, and Uncertainty"[2][3] (the two digits between parentheses denote the standard error of the estimated value):

≈ 5.39106(32) × 10 -44 s,

where is the SI unit of time, the second.

Planck time (according to OEIS)

According to the OEIS:

A078302 Decimal expansion of Planck time = 5.39124 × 10 -44 second (SI units).

{5, 3, 9, 1, 2, 4, ...}

Planck length

The Planck length, denoted , is the unit of length in the system of natural units known as Planck units. It is a basic unit in the system of Planck units. The Planck length can be uniquely defined from three fundamental physical constants: the speed of light in a vacuum, Planck's constant, and the gravitational constant. It is the distance traveled by light, in a vacuum, in a time interval of 1 Planck time. The unit is named after Max Planck, who was the first to propose it.

The Planck length is defined as

where

is the reduced Planck's constant (sometimes is used instead of in the definition[1]),
is the [universal] gravitational constant, and
is the speed of light in a vacuum.

The Planck length is about 10 −20 times the diameter of a proton, and thus is extremely small.

Planck length (according to NIST)

According to "The NIST Reference on Constants, Units, and Uncertainty"[4][5] (the two digits between parentheses denote the standard error of the estimated value)[6]:

≈ 1.616199(97) × 10 -35 m,

where is the SI unit of length, the metre.

Planck length (according to OEIS)

According to the OEIS: Planck length = × Planck time = 1.616252 × 10 -35 meter (SI units), where is the speed of light in vacuum (A003678).

A078300 Decimal expansion of Planck length = 1.616252 × 10 -35 meter (SI units).

{1, 6, 1, 6, 2, 5, 2, ...}

Planck mass

The Planck mass, denoted , is the unit of mass in the system of natural units known as Planck units. It is a basic unit in the system of Planck units. The Planck mass can be uniquely defined from three fundamental physical constants: the speed of light in a vacuum, Planck's constant, and the gravitational constant.

The Planck length is defined as

where

is the reduced Planck's constant (sometimes is used instead of in the definition[1]),
is the [universal] gravitational constant, and
is the speed of light in a vacuum.

The Planck mass is approximately the mass of the Planck particle, a hypothetical minuscule black hole whose Schwarzschild radius equals the Planck length. Unlike all other Planck base units and most Planck derived units, the Planck mass has a scale more or less conceivable to humans. (It is traditionally said to be about the mass of a flea, but more accurately it is about the mass of a flea egg.) The Planck mass is an idealized mass thought to have special significance for quantum gravity when both general relativity and the fundamentals of quantum mechanics become mutually important.

Planck mass (according to NIST)

According to "The NIST Reference on Constants, Units, and Uncertainty"[7][8] (the two digits between parentheses denote the standard error of the estimated value)[9]:

≈ 1.2209 × 10 19 GeV/c 2 = 2.17651(13) × 10 -8 kg (or 21.7651 μg),

where is the SI unit of mass, the kilogram.

Planck mass (according to OEIS)

According to the OEIS:

A078301 Decimal expansion of Planck mass = 2.17644 × 10 -8 kilogram (SI units).

{2, 1, 7, 6, 4, 4, ...}

Derived Planck units

Planck density

The unit of density in derived Planck units is called the Planck density, denoted by

where

is the reduced Planck's constant (sometimes is used instead of in the definition[1]),
is the Planck mass,
is the Planck length,
is the speed of light in a vacuum,
is the [universal] gravitational constant.

This is a unit which is very large, about equivalent to 10 23 solar masses squeezed into the space of a single atomic nucleus. At one unit of Planck time after the Big Bang, the mass density of the Universe is thought to have been approximately one unit of Planck density.

≈ 5.1 × 10 96 kg/m 3.

Planck energy

The unit of energy in derived Planck units is called the Planck energy, denoted by

where

is the reduced Planck's constant (sometimes is used instead of in the definition[1]),
is the speed of light in a vacuum,
is the [universal] gravitational constant.

An equivalent definition (from the Heisenberg uncertainty principle ) is

where is the Planck time.

Also (from Einstein's mass–energy equivalence)

where is the Planck mass.

≈ 1.956 × 10 9 J ≈ 1.22 × 10 28 eV ≈ 0.5433 MWh.

Planck temperature

The unit of temperature in derived Planck units is called the Planck temperature, denoted by It serves as the defining unit of the Planck temperature scale. In this scale the magnitude of the Planck temperature is equal to 1, while that of absolute zero is 0.

Other temperatures can be converted to Planck temperature units. For example, 0 °C = 273.15 K = 1.9279 × 10 -30

The Planck temperature is defined as

1.416833(85) × 10 32 K,

where is Boltzmann's constant. (The two digits between the parentheses denote the standard error of the last two digits of the estimated value.)

As for most of Planck units, a Planck temperature of 1 (unity) is a fundamental limit of quantum theory, in combination with gravitation, as presently understood. At temperatures greater than or equal current physical theory breaks down because we lack a theory of quantum gravity.[10]

Sequences

A003678 Decimal expansion of the speed of light in vacuum (SI units). (Since 1983 the speed of light has been defined to be exactly 299792458 m/s.)

{2, 9, 9, 7, 9, 2, 4, 5, 8}

A003676 Decimal expansion of Planck constant (joule sec). ( = 6.62606896(33) * 10 -34 Joule second.)

{6, 6, 2, 6, 0, 6, 8, 9, 6, ...}

A070058 Decimal expansion of Newton's gravitational constant. ( = 6.67384(80)*10 -11 m^3/(kg*s^2) (digits in parentheses are estimates).)

{6, 6, 7, 3, 8, 4, ...}

Notes

  1. 1.0 1.1 1.2 1.3 1.4 1.5 “Big Bang models back to Planck time”. Georgia State University. 19 June 2005. 
  2. CODATA Value: Planck Time – The NIST Reference on Constants, Units, and Uncertainty.
  3. NIST's published CODATA constants.
  4. CODATA Value: Planck Length – The NIST Reference on Constants, Units, and Uncertainty.
  5. NIST's published CODATA constants.
  6. John Baez, The Planck Length.
  7. Planck Mass (value in GeV), Planck Mass(value in kg) – The NIST Reference on Constants, Units, and Uncertainty.
  8. NIST's published CODATA constants.
  9. John Baez, The Planck Length.
  10. Nova: Absolute Hot