Understanding Planck Units: The Impact of kB in Temperature Definition

  • Context: Graduate 
  • Thread starter Thread starter Sunfire
  • Start date Start date
  • Tags Tags
    Planck Units
Click For Summary
SUMMARY

Planck units are defined using fundamental constants: gravitational constant (G), speed of light (c), reduced Planck constant (\hbar), and Boltzmann constant (kB). While G, c, and \hbar are involved in defining length, mass, and time without kB, temperature uniquely incorporates kB, indicating a different dimensionality. This distinction raises questions about the underlying connections between temperature and energy, contrasting with the interrelations of mass, space, and time through gravity and quantum theory. The discussion highlights the implications of temperature's unique dimensional status in the context of Planck units.

PREREQUISITES
  • Understanding of Planck units and their definitions
  • Familiarity with fundamental constants: G, c, \hbar, and kB
  • Basic knowledge of dimensional analysis in physics
  • Concepts of energy and its relationship to temperature
NEXT STEPS
  • Research the implications of dimensional analysis in physics
  • Explore the role of Boltzmann constant (kB) in thermodynamics
  • Study the interrelations between gravity, quantum theory, and temperature
  • Investigate the concept of "vector basis" in the context of physical constants
USEFUL FOR

Physicists, students of theoretical physics, and anyone interested in the foundational concepts of temperature and its relationship to energy and fundamental constants.

Sunfire
Messages
221
Reaction score
4
Hello,

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

Length, mass and time are defined via G, c and \hbar and do not involve kB;
But temperature contains all G, c and \hbar 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?
 
Physics news on Phys.org
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).
 
The reason I am asking is I read this thread (thread) on Planck units.

It says that c, G and \hbar 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.
 

Similar threads

Undergrad The new definition of kg and the mass-energy equivalence
  • · Replies 4 ·
Replies
4
Views
5K
Graduate Shahar Hod's bound on the fine-structure constant
  • · Replies 10 ·
Replies
10
Views
4K
Graduate How Is Temperature Defined in Kelvin Using Fundamental Units?
  • · Replies 5 ·
Replies
5
Views
2K
Undergrad Does the Friedmann vacuum equation have a linear solution?
  • · Replies 1 ·
Replies
1
Views
2K
Graduate The Draper point and why can't we see human radiation
  • · Replies 14 ·
Replies
14
Views
2K
Graduate Why is the Planck Mass Surprisingly Large Compared to Other Units?
  • · Replies 25 ·
Replies
25
Views
15K
Graduate Will NIST Update Their Constants for Einstein and Planck Units?
  • · Replies 3 ·
Replies
3
Views
2K
Graduate Gravitational Quadrupole Formula: Polarization Tensor
  • · Replies 4 ·
Replies
4
Views
2K
Undergrad Comoving mass density leads to linear cosmology?
  • · Replies 3 ·
Replies
3
Views
2K
Undergrad Differentiated Sakharov Equation for Vacuum Fluctuations
  • · Replies 1 ·
Replies
1
Views
1K