How do I get from the Energy-Momentum equation of a particle to its Stress-Energy equation?(adsbygoogle = window.adsbygoogle || []).push({});

By way of introducing the energy-momentum equation:

For a single particle, in units where c=1, a relationship between mass, energy and momentum appear as a direct result of the 4-velocity:

[tex]m^2 = E^2 - p^2[/tex]

We can define a 4-vector,

[tex]m^\mu = (E^0, p^i) \ ,[/tex]

(Greek indices ranges from 0 to 3, Latin indices ranges from 1 to 3 indexing spatial coordinates, and 0 is the temporal coordinate.)

Mass is defined as the magnitude of the 4-vector,

[tex]m^2 = m^\mu m_\mu \ .[/tex]

If the world line of the particle in question passes through some 4-volume, equally distrubuted in the volume, dtdxdydz we should have a stress-energy energy equation for this volume. Or am I wrong?

...I guess it's better to ask about an infinitessimal mass, dm, or about a finite 4-volume delta t delta x delta y delta z. Either way, it would be wonderful to know how to approach this problem.

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Energy-Momentum Equation of a Particle

**Physics Forums | Science Articles, Homework Help, Discussion**