Transformations of Relativistic Temperature: Planck-Einstein, Ott, Landsberg, and Doppler Formulas

Initializing live version
Download to Desktop

Requires a Wolfram Notebook System

Interact on desktop, mobile and cloud with the free Wolfram Player or other Wolfram Language products.

This Demonstration illustrates spacetime velocity vectors representing internal energy currents and their equilibration for a system of two relativistic thermodynamic bodies in 1+1 dimensions. The velocities of the two bodies are and in units with . The corresponding spacelike internal energy current vectors are and . The equilibration vectors are the sums for . In thermal equilibrium their directions become parallel.

Contributed by: P. Ván and T. S. Bíró (March 2011)
Open content licensed under CC BY-NC-SA



This Demonstration proposes a clarification of contradictory theoretical approaches to relativistic thermodynamics. According to our suggestion, a new concept of internal energy leads to thermodynamic equilibrium conditions that incorporate the existing propositions. You can manipulate spacetime vectors related to the intensive parameter representing energy-momentum equilibration.

In equilibrium, two moving and interacting thermodynamic bodies obey . In the coordinate system of the first body this condition can be expressed by the spacetime velocity vectors of body centers and energy currents as and , respectively. The snapshots show famous particular cases for the relative speed .

Snapshot 1: the Planck–Einstein equilibrium, when the energy current is carried by the moving body, ; in this case the moving body appears cooler

Snapshot 2: the Blanusa-Ott equilibrium, when the energy current stays with the observing body, ; in this case the moving body appears hotter

Snapshot 3: the Landsberg equilibrium, when the energy current velocities compensate each other inside the two bodies, ; in this case the temperatures of the two moving bodies are equal

Snapshots 4 and 5: the Doppler blue shift and red shift () equilibria, when the energy transfer is due to radiation, , ; in these cases the temperatures of the two moving bodies are related by a Doppler shift

For more information see T. S. Biró, P. Ván, "About the Temperature of Moving Bodies".

Feedback (field required)
Email (field required) Name
Occupation Organization
Note: Your message & contact information may be shared with the author of any specific Demonstration for which you give feedback.