The central role played by Planck quantities in modern theories of matter and the formation of the universe (string theory and cosmology) is well summarized in a set of glossary descriptions which can be found at the NED site (NASA/IPAC Extragalactic Database) in a section called Level 5. Since there may be delays getting to the site (nedwww.ipac.caltech.edu/Level5) I will simply quote excerpts here.
Here's the header telling who compiled the information under whose auspices:
<<Level 5 — A Knowledgebase for Extragalactic Astronomy and Cosmology
Principal Investigator Dr. Barry F. Madore
Caltech and Carnegie Pasadena, California, USA
Under the sponsorship of NASA's Applied Information Systems Research Program
(AISRP)>>
Part of the Level 5 compendium (which includes articles and essays on related topics as well) is a glossary of terms used in astronomy and cosmology. Another item of interest is an article on Planck quantities adapted from P. Coles, 1999, The Routledge Critical Dictionary of the New Cosmology.
Here are some excerpts from the Level 5 glossary. For information as to the sources, which are indicated in square brackets, consult the website itself.
<< Planck energy An energy of 1.22 × 1019 GeV (billion electron volts), at which the strength of the gravitational interactions of fundamental particles becomes comparable to that of the other interactions. It is believed that the quantum effects of gravity become important at approximately this energy. [G97]
Planck energy About 1,000 kilowatt hours. The energy necessary to probe to distances as small as the Planck length. The typical energy of a vibrating string in string theory. [G99]
Planck epoch/Planck time The first instant following the beginning of the expansion of the universe, when the cosmic matter density was still so high that gravitational force acted as strongly as the other fundamental forces on the sub-atomic scale. [F88]
Planck era The first 10-43 seconds of the Universe's existence. Physics can currently say very little about this time. Quantum gravity is needed before quantum cosmology can be fully realised. Planck length (a) The dimension at which space is predicted to become ``foamlike'' and at which Einstein's theory is supposed to break down. [(G /h-bar c3)1/2=1.6 × 10-33 cm] [H76] (b) The size limit at which normal notions of space-time are supposed to break down. [P88]
Planck length About 10-33 centimeters. The scale below which quantum fluctuations in the fabric of spacetime would become enormous. The size of a typical string in string theory. [G99]
Planck mass About ten billion billion times the mass of a proton; about one-hundredth of a thousandth of a gram; about the mass of a small grain of dust. The typical mass equivalent of a vibrating string in string theory. [G99]
Planck tension About 1039 tons. The tension on a typical string in string theory. [G99]
Planck time About 10-43 seconds. Time at which the size of the universe was roughly the Planck length; more precisely, time it takes light to travel the Planck length. [G99]
Planck time An instant in the Big Bang, prior to which Einstein's theory of gravitation breaks down and a quantized theory of gravity is needed. It can be expressed as (G /h-bar c5)1/2 where G is Newton's constant of gravitation, is Planck's constant, and c is the speed of light, and it equals 10-43 second. [Silk90]
Planck units Fundamental units of length, time, mass, energy, etc. involving Planck's quantum constant, h-bar, Newton's gravitational constant, G, and the speed of light, c. As they incorporate both the quantum and gravitational constants, the Planck units play a key role in theories of quantum gravity. [CD99]
Planck's constant Denoted by the symbol h-bar, Planck's constant is a fundamental parameter in quantum mechanics. It determines the size of the discrete units of energy, mass, spin, etc. into which the microscopic world is partitioned. Its value is 1.05 × 10-27 grams - cm/sec. [G99]>>
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