Understanding Planck Units: The Impact of kB in Temperature Definition

In summary, Planck units are defined using the constants G, c, and \hbar, with temperature being the only unit that involves the constant kB. This may seem arbitrary, but it is a consequence of the relationships between gravity and quantum theory. In a vector basis, the addition of units corresponds to multiplication of constants, with only temperature having a "4-dimensional" unit compared to the "less-dimensional" units of length, time, and mass. This could have interesting implications.
  • #1
Sunfire
221
4
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 kB;
But temperature contains all G, c and [itex]\hbar[/itex] and kB;

Perhaps this is okay; just seems "uneven" that kB 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?
 
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  • #2
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).
 
  • #3
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 kB 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.
 

Related to Understanding Planck Units: The Impact of kB in Temperature Definition

1. What are Planck units?

Planck units are a set of universal physical units that are based on fundamental constants of nature, such as the speed of light, the gravitational constant, and the reduced Planck constant. They are named after the German physicist Max Planck, who first proposed them in 1899.

2. Why are Planck units important?

Planck units are important because they provide a way to describe physical quantities at the most fundamental level, without any dependence on arbitrary human systems of measurement. They also have significance in theoretical physics, particularly in the study of quantum gravity and the unification of the four fundamental forces.

3. How are Planck units calculated?

Planck units are calculated using the fundamental constants of nature in a way that creates dimensionless quantities. For example, the Planck length is calculated by dividing the reduced Planck constant by the mass of a particle (m), multiplied by the speed of light (c) squared: lP = ℏ / (m*c2).

4. What is the significance of the Planck length?

The Planck length, which is approximately 1.6 x 10-35 meters, is often considered to be the smallest possible length that has physical meaning. It is the scale at which quantum effects are expected to become significant and the fabric of spacetime is thought to be "foamy," according to some theories of quantum gravity.

5. Are Planck units used in everyday life?

No, Planck units are not typically used in everyday life. They are usually only used in theoretical physics and cosmology, as they are extremely small and not practical for most everyday measurements. However, they are useful for comparing different physical quantities on a universal scale.

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