Planck temperature, denoted by TP, is the unit of temperature in the system of natural units known as Planck units.
The Planck temperature is thought to be the upper limit of temperature.
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 TP.
In SI units, the Planck temperature is about 1.417×1032 kelvin (equivalently, degrees Celsius, since the difference is trivially small at this scale), or 2.55×1032 degrees Fahrenheit or Rankine. [1]
What today is known as the Planck temperature was first introduced in 1899 by Max Planck together with his introduction of what today is known as the Planck length, the Planck mass and Planck time. [2] [3]
The Planck temperature is defined as:
or
where:
The two digits between the parentheses are used to denote the standard error of the last two digits of the estimated value. [4]
As with most of the Planck units, a Planck temperature of 1 (unity) is a fundamental limit of quantum theory, in combination with gravitation, as presently understood. In other words, the wavelength of light emitted by an object can be calculated by its temperature. If an object were to reach the temperature of 1.42×1032 kelvin (TP), the radiation it would emit would have a reduced wavelength of 1.616×10−35 m (Planck length), at which point quantum gravitational effects become relevant. At temperatures greater than or equal to TP, current physical theory breaks down because we lack a theory of quantum gravity. [5]
 | Look up planck temperature in Wiktionary, the free dictionary. |
Wien's displacement law states that the black-body radiation curve for different temperatures will peak at different wavelengths that are inversely proportional to the temperature. The shift of that peak is a direct consequence of the Planck radiation law, which describes the spectral brightness of black-body radiation as a function of wavelength at any given temperature. However, it had been discovered by Wilhelm Wien several years before Max Planck developed that more general equation, and describes the entire shift of the spectrum of black-body radiation toward shorter wavelengths as temperature increases.
The Boltzmann constant, named after its discoverer, Ludwig Boltzmann, is a physical constant that relates the average relative kinetic energy of particles in a gas with the temperature of the gas. It occurs in the definitions of the kelvin and the gas constant, and in Planck's law of black-body radiation and Boltzmann's entropy formula. The Boltzmann constant has the dimension energy divided by temperature, the same as entropy.
In the physical sciences, the wavenumber is the spatial frequency of a wave, measured in cycles per unit distance or radians per unit distance. Whereas temporal frequency can be thought of as the number of waves per unit time, wavenumber is the number of waves per unit distance.
The Fermi energy is a concept in quantum mechanics usually referring to the energy difference between the highest and lowest occupied single-particle states in a quantum system of non-interacting fermions at absolute zero temperature. In a Fermi gas, the lowest occupied state is taken to have zero kinetic energy, whereas in a metal, the lowest occupied state is typically taken to mean the bottom of the conduction band.
In physics, the Planck mass, denoted by mP, is the unit of mass in the system of natural units known as Planck units. Planck mass is the mass such that the reduced Compton wavelength is 2π times the Schwarzschild radius or half the Schwarzschild radius.
In quantum mechanics, the Planck time is the unit of time in the system of natural units known as Planck units. A Planck time unit is the time required for light to travel a distance of 1 Planck length in a vacuum, which is a time interval of approximately 1.911 × 10−43 s or 5.39 × 10−44 s. The unit is named after Max Planck, who was the first to propose it.
The Bohr radius is a physical constant, equal to the most probable distance between the nucleus and the electron in a hydrogen atom in its ground state. It is named after Niels Bohr, due to its role in the Bohr model of an atom. Its value is 5.29177210903(80)×10−11 m.
The Hartree atomic units are a system of natural units of measurement which is especially convenient for atomic physics calculations. They are named after the physicist Douglas Hartree. In this system the numerical values of the following four fundamental physical constants are all unity by definition:
In spectroscopy, the Rydberg constant, symbol for heavy atoms or for hydrogen, named after the Swedish physicist Johannes Rydberg, is a physical constant relating to the electromagnetic spectra of an atom. The constant first arose as an empirical fitting parameter in the Rydberg formula for the hydrogen spectral series, but Niels Bohr later showed that its value could be calculated from more fundamental constants via his Bohr model. As of 2018, and electron spin g-factor are the most accurately measured physical constants.
In physics, Planck energy, denoted by EP, is the unit of energy in the system of natural units known as Planck units.
In physics, the Planck length, denoted ℓP, is a unit of length that is the distance light travels in one unit of Planck time. It is also the reduced Compton wavelength of a particle with Planck mass. It is equal to 5.72938×10−35 m or 1.61623×10−35 m. It is a base unit in the system of Planck units, developed by physicist Max Planck. The Planck length can be defined from three fundamental physical constants: the speed of light in a vacuum, the Planck constant, and the gravitational constant. It is the smallest distance about which current, experimentally corroborated, models of physics can make meaningful statements. At such small distances, the conventional laws of macro-physics no longer apply, and even relativistic physics requires special treatment.
In physics, the Planck electric charge, denoted by , is one of the base units in the system of natural units called Planck units. It is a quantity of electric charge defined in terms of fundamental physical constants.
The old quantum theory is a collection of results from the years 1900–1925 which predate modern quantum mechanics. The theory was never complete or self-consistent, but was rather a set of heuristic corrections to classical mechanics. The theory is now understood as the semi-classical approximation to modern quantum mechanics.
In physics, the thermal de Broglie wavelength is roughly the average de Broglie wavelength of the gas particles in an ideal gas at the specified temperature. We can take the average interparticle spacing in the gas to be approximately (V/N)1/3 where V is the volume and N is the number of particles. When the thermal de Broglie wavelength is much smaller than the interparticle distance, the gas can be considered to be a classical or Maxwell–Boltzmann gas. On the other hand, when the thermal de Broglie wavelength is on the order of or larger than the interparticle distance, quantum effects will dominate and the gas must be treated as a Fermi gas or a Bose gas, depending on the nature of the gas particles. The critical temperature is the transition point between these two regimes, and at this critical temperature, the thermal wavelength will be approximately equal to the interparticle distance. That is, the quantum nature of the gas will be evident for
The Compton wavelength is a quantum mechanical property of a particle. It was introduced by Arthur Compton in his explanation of the scattering of photons by electrons. The Compton wavelength of a particle is equal to the wavelength of a photon whose energy is the same as the mass of that particle.
The Planck angular frequency (or Planck angular speed) is the unit of angular frequency or angular speed, denoted by ωP, in the system of natural units known as Planck units.
Planck momentum is the unit of momentum in the system of natural units known as Planck units. It can be denoted by . Then
The quantum concentrationnQ is the particle concentration of a system where the interparticle distance is equal to the thermal de Broglie wavelength.
The Planck constant, or Planck's constant, denoted , is a physical constant that is the quantum of electromagnetic action, which relates the energy carried by a photon to its frequency. A photon's energy is equal to its frequency multiplied by the Planck constant. The Planck constant is of fundamental importance in quantum mechanics, and in metrology it is the basis for the definition of the kilogram.
In particle physics and physical cosmology, Planck units are a set of units of measurement defined exclusively in terms of five universal physical constants, in such a manner that these five physical constants take on the numerical value of 1 when expressed in terms of these units.
