Energy Momentum Tensor - General Properties

[TSC]

It is often stated and proved in textbooks that the momentum density is also the energy flux.
The explanation is often done using the dust model.
However, it is possible that in a real fluid, there is heat conduction via particle collision. There is energy flux, but since no molecules are ever transported in the IRF, how come there is momentum density?

 

[pervect]

Energy and momentum in special relativity are related by the fact that their combination $(E, \vec{P})$ transforms as a 4-vector, via the Lorentz transform.

This means that what appears as "just energy" in one frame of reference, appears as energy and momentum in another. A transfer of energy in one frame of reference is a transfer of energy and momentum in another frame of reference, moving relative to the first.

This is similar to the way that time and space form a 4-vector, Time and space 'mix together" in just the same way as energy and momentum due, the mathematical formalism that describes this mixing together is the 4-vector formalism.