- #1

- 4,254

- 2

How do I get from the Energy-Momentum equation of a particle to its Stress-Energy equation?

By way of introducing the energy-momentum equation:

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.

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]

[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.

Last edited: