How does the Stress Energy tensor relate to Noether's theorem?

In summary, the stress-energy tensor is a Noether current that arises naturally in special relativity and is related to the conservation of energy and momentum. While there are various derivations for the stress-energy tensor, it is most commonly applied to spacetime as a perfect fluid. For a more detailed explanation, refer to section 1.3.2 of David Tong's QFT notes.
  • #1
Rearden
16
0
Hi,

I was wondering if the stress-energy tensor arose naturally in special relativity in the same way that plain energy and momentum do via Lagrangians. I understand Noether's theorem for particles, but Wikipedia describes the stress-energy tensor as a Noether current; can anyone explain what this is?
Unfortunately, I don't know enough about differential forms to follow the standard definition. The other derivations based on dust etc. all seem a little contrived, deriving vanishing divergence almost as an aftherthought. I'm hoping that this line of inquiry will bring me more satisfaction.

Thanks a lot!
 
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  • #3
That's exactly what I need!
Thanks again
 
  • #4
Sorry to bother again...I now understand the derivation of the Noether current, but which field do I apply it to if I want the standard stress-energy tensor? Is this where "spacetime as a perfect fluid" comes into play?
 

1. What is the Stress Energy tensor?

The Stress Energy tensor is a mathematical object used in Einstein's theory of general relativity to describe the distribution of matter and energy in spacetime. It contains information about the density, pressure, and flow of energy and momentum in a given region of spacetime.

2. How does the Stress Energy tensor relate to Noether's theorem?

Noether's theorem states that for every continuous symmetry in a physical system, there exists a corresponding conserved quantity. The Stress Energy tensor is the conserved quantity for the symmetry of spacetime translation. This means that the Stress Energy tensor represents the conservation of energy and momentum in a system due to the symmetry of spacetime.

3. What is the significance of the Stress Energy tensor in general relativity?

In general relativity, the Stress Energy tensor plays a crucial role in the Einstein field equations, which describe how matter and energy curve spacetime. It also helps to define the geodesic equation, which describes the motion of a particle in a curved spacetime.

4. How is the Stress Energy tensor calculated?

The Stress Energy tensor is calculated using the Einstein equations, which are a set of ten differential equations that relate the curvature of spacetime to the distribution of matter and energy. The equations take into account the density, pressure, and flow of energy and momentum in a given region of spacetime.

5. Can the Stress Energy tensor be used in other theories besides general relativity?

Yes, the Stress Energy tensor can be used in other theories besides general relativity. It is also used in classical field theory and quantum field theory to describe the energy and momentum of a system. It is a fundamental concept in physics and has applications in various fields, including cosmology, astrophysics, and particle physics.

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