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Planck units are a system of units of measurement based on the gravitational constant, Planck's h-bar constant, and the speed of light in vacuum. These units have the advantage of eliminating most of the fundamental physical constants; measured in them, all three constants on which they are based have the value unity. However, they are too small for use for practical purposes, unless prefixed with large powers of ten. They also suffer from uncertainties in the measurement of some of the constants on which they are based.

The SI units are increasingly defined in terms of fundamental constants also, but unlike the Planck units their definition includes arbitrary numbers which are not powers of ten, which are present only for historical reasons.

The above is a partial description. The full set of Planck units includes the Planck temperature (used by cosmologists in describing conditions in the early universe) and the elementary charge. So the complete set is based on five (not three) fundamental physical constants: G, c, h-bar, k, and e. Here k stands for the Boltzmann temperature coefficient. The Planck units are defined by stipulating that all five constants have value one.

The NIST (National Institute of Standards and Technology) website is a convenient source of data on the commonly-recognized constants, including Planck units.

There is a description of human-scale versions of the Planck units at the Misplaced Pages article on practical Planck units.

Planck first listed his set of units (and gave values for them remarkably close to those used today) in May of 1899 in a paper presented to the Prussian Academy of Sciences. Max Planck: 'Über irreversible Strahlungsvorgänge'. Sitzungsberichte der Preußischen Akademie der Wissenschaften, vol. 5, p. 479 (1899). At the time he presented the units, quantum mechanics had not been invented. He himself had not yet discovered the theory of blackbody radiation (first published December 1900) in which the constant h made its first appearance and for which Planck was later awarded the Nobel prize. The relevant parts of Planck's 1899 paper leave some confusion as to how he managed to come up with the units of time, length, mass, temperature etc. which today we define using h-bar and motivate by references to quantum physics before things like h-bar and quantum physics were known. Here's a quote from the 1899 paper that gives an idea of how Planck thought about the set of units.

...These necessarily retain their meaning for all times and for all civilizations, even extraterrestrial and non-human ones, and can therefore be designated as 'natural units'...

...ihre Bedeutung für alle Zeiten und für alle, auch ausserirdische und ausser menschliche Culturen nothwendig behalten und welche daher als 'natürliche Maasseinheiten' bezeichnet werden können...

Planck units are not 'alternative physics' and, in particular, the Planck force (about 10 tons) which is simply the unit force going along with the other Planck units is not, 'alternative physics'. On the contrary, given the units' growing importance in string theory and cosmology, they are mainstream.