The Importance of Symmetry in Stress Tensors

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Discussion Overview

The discussion centers on the symmetry of stress tensors, particularly in the context of their physical implications and mathematical properties. Participants explore the reasons for the requirement of symmetry in stress tensors, referencing Cauchy's second law of motion and its consequences in general relativity (GR).

Discussion Character

  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • One participant questions why the stress tensor must be symmetric.
  • Another participant asserts that a nonsymmetric stress tensor indicates an interior source of stress energy, referencing Cauchy's second law of motion.
  • Several participants seek clarification and examples to understand the physical meaning of these concepts.
  • A participant explains the components of the stress-energy tensor, noting that the diagonal components represent momentum flows or pressures, while off-diagonal components represent shear stresses.
  • There is a suggestion that in general relativity, the stress-energy tensor typically represents a perfect fluid, which can be either dust or radiation.
  • One participant expresses confusion and proposes an alternative perspective regarding the symmetry of the tensor.

Areas of Agreement / Disagreement

Participants express varying levels of understanding and agreement regarding the implications of a nonsymmetric stress tensor, with some supporting the idea of an interior source of energy while others seek further clarification and examples. The discussion remains unresolved with multiple competing views on the topic.

Contextual Notes

Participants highlight the need for references and examples to clarify the physical meaning of the concepts discussed, indicating potential gaps in understanding and the complexity of the topic.

LagrangeEuler
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Why stress tensor must be symmetric?
 
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A nonsymmetric stress tensor means that there is an interior source of stress energy (Cauchy's second law of motion).
 
Some reference for this perhaps? What that means physically? -Example!
 
The T00 component of the stress energy tensor is energy density, the T11, T22, T33 (the diagonal components) are momentum flows or pressures. The off diagonals represent shear stresses and as Andy has pointed out a non-symmetric tensor means there is an interior source of energy. In GR this tensor usually represents a perfect fluid which is either dust (zero pressures) or radiation which is a fluid with pressure but no shear stress.
 
I don't understand this. Is there some other way. If [tex]\hat{N}[/tex] is symmetric then [tex]\hat{N}=\hat{N}^*[/tex]. Maybe from this?
 

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