Question on Planck units

Sunfire

Hello,

Planck units are defined here
http://en.wikipedia.org/wiki/Planck_units

Length, mass and time are defined via G, c and [itex]\hbar[/itex] and do not involve k_B;
But temperature contains all G, c and [itex]\hbar[/itex] and k_B;

Perhaps this is okay; just seems "uneven" that k_B appears with a zero power in the definitions of length, mass and time but with nonzero power in the definition of temperature.

It seems a bit "ad hoc"... Would anyone have a comment on these definition choices?

mfb

Mass, space and time are connected both via gravity and via quantum theory. This is not true for temperature. It is just (directly) related to energy.

It is not a choice. If you set all those constants to 1, you have no choice how to get planck units (apart from constant prefactors).

Sunfire

The reason I am asking is I read this thread (thread) on Planck units.

It says that c, G and [itex]\hbar[/itex] form a "vector basis" (1,0,0) (0,1,0) and (0,0,1) where adding vectors corresponds to multiplication of units.

It is interesting that adding k_B happens only for temperature, as if temperature has a "4-dimensional" unit, while L, T, M are less-dimensional. Wondering what the implications of this could be.