In particle physics and physical cosmology, Planck units are a system of units of measurement defined exclusively in terms of four universal physical constants: c, G, ħ, and kB. Expressing one of these physical constants in terms of Planck units yields a numerical value of 1. They are a system of natural units, defined using fundamental properties of nature (specifically, properties of free space) rather than properties of a chosen prototype object. Originally proposed in 1899 by German physicist Max Planck, they are relevant in research on unified theories such as quantum gravity. The term Planck scale refers to quantities of space, time, energy and other units that are similar in magnitude to corresponding Planck units. This region may be characterized by particle energies of around 1019 GeV or 109 J, time intervals of around 10−43 s and lengths of around 10−35 m (approximately the energy-equivalent of the Planck mass, the Planck time and the Planck length, respectively). At the Planck scale, the predictions of the Standard Model, quantum field theory and general relativity are not expected to apply, and quantum effects of gravity are expected to dominate. 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 numerical value 1 when expressed in these units are:
c, the speed of light in vacuum, G, the gravitational constant, ħ, the reduced Planck constant, and kB, the Boltzmann constant. Variants of the basic idea of Planck units exist, such as alternate choices of normalization that give other numerical values to one or more of the four constants above.
Introduction Any system of measurement may be assigned a mutually independent set of base quantities and associated base units, from which all other quantities and units may be derived. In the International System of Units, for example, the SI base quantities include length with the associated unit of the metre. In the system of Planck units, a similar set of base quantities and associated units may be selected, in terms of which other quantities and coherent units may be expressed. The Planck unit of length has become known as the Planck length, and the Planck unit of time is known as the Planck time, but this nomenclature has not been established as extending to all quantities. 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. For example, Newton's law of universal gravitation,
F = G m 1 m 2 r 2 = ( F P l P 2 m P 2 ) m 1 m 2 r 2 , {\displaystyle F=G{\frac {m_{1}m_{2}}{r^{2}}}=\left({\frac {F_{\text{P}}l_{\text{P}}^{2}}{m_{\text{P}}^{2}}}\right){\frac {m_{1}m_{2}}{r^{2}}},}
can be expressed as:
… excerpt ends here. Continue reading the full article.
