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

Click For Summary

Discussion Overview

The discussion revolves around the relationship between the stress-energy tensor and Noether's theorem, particularly in the context of special relativity and Lagrangian mechanics. Participants explore the derivation of the stress-energy tensor as a Noether current and seek clarity on its application and underlying concepts.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification

Main Points Raised

  • One participant questions whether the stress-energy tensor arises naturally in special relativity similar to energy and momentum through Lagrangians.
  • The same participant expresses confusion regarding the definition of the stress-energy tensor as a Noether current and seeks an explanation.
  • Another participant suggests a specific resource (David Tong's lecture notes) that may provide clarity on the topic.
  • A later reply indicates that the original poster has gained understanding of the Noether current derivation but seeks guidance on which field to apply it to in order to obtain the standard stress-energy tensor.
  • The original poster wonders if the concept of "spacetime as a perfect fluid" is relevant to this application.

Areas of Agreement / Disagreement

Participants do not appear to reach a consensus, as there are ongoing questions and explorations regarding the application of Noether's theorem to the stress-energy tensor and its derivation.

Contextual Notes

The discussion highlights limitations in understanding the derivation of the stress-energy tensor and its relation to Noether's theorem, particularly regarding the application to specific fields and the role of concepts like "spacetime as a perfect fluid."

Rearden
Messages
16
Reaction score
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!
 
Physics news on Phys.org
That's exactly what I need!
Thanks again
 
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?
 

Similar threads

Undergrad Noether's second theorem: two questions
  • · Replies 7 ·
Replies
7
Views
3K
High School Special Cases of Stress-Energy Tensor in GR
  • · Replies 10 ·
Replies
10
Views
3K
Undergrad Understanding the Stress-Energy Tensor in Special Relativity
  • · Replies 4 ·
Replies
4
Views
2K
Undergrad Pressure term in the energy stress tensor
  • · Replies 9 ·
Replies
9
Views
3K
Graduate Stress-energy tensor of a rotating rod
  • · Replies 21 ·
Replies
21
Views
4K
Graduate Exploring the Stress-Energy Tensor of a Perfect Fluid
  • · Replies 3 ·
Replies
3
Views
2K
Graduate A global energy conservation law in general relativity
  • · Replies 36 ·
2
Replies
36
Views
2K
Undergrad How does the stress-energy tensor act on gravity?
  • · Replies 26 ·
Replies
26
Views
4K
Undergrad Conservation of energy in general relativity
  • · Replies 42 ·
2
Replies
42
Views
7K
Undergrad How big are the non-mass parts of the stress-energy tensor?
  • · Replies 21 ·
Replies
21
Views
3K