Discussion Overview
The discussion revolves around the relationship between the Cauchy Stress Tensor and the Energy Momentum Tensor in the context of General Relativity (GR). Participants explore the similarities in their SI units, the dimensional implications of time in the Energy Momentum Tensor, and the mathematical transformations between the two tensors.
Discussion Character
- Technical explanation
- Debate/contested
Main Points Raised
- Some participants question why the Cauchy Stress Tensor and the Energy Momentum Tensor share the same SI units, suggesting that the addition of time as a dimension should alter the units of the Energy Momentum Tensor.
- Others assert that the units of stress (force per unit area) and energy density (energy per unit volume) are equivalent, thus explaining the shared units.
- There is a claim that no mathematical operation can transform the Cauchy Stress Tensor into the Energy Momentum Tensor, as they are fundamentally different tensors existing in different dimensional spaces.
- Some participants express skepticism about whether Einstein began with the Cauchy Tensor when developing the field equations of GR, with others stating that he did not.
- A participant notes that in relativistic physics, the Cauchy Stress Tensor corresponds to the space-space components of the Energy Momentum Tensor, while the time-time component represents energy density.
- It is mentioned that solutions to the Einstein equations require simultaneous solutions to the equations of motion for matter, linking the mechanical energy momentum tensor to the consistency of GR solutions.
Areas of Agreement / Disagreement
Participants express differing views on the relationship and transformation between the Cauchy Stress Tensor and the Energy Momentum Tensor, with no consensus reached on whether Einstein utilized the Cauchy Tensor in his work on GR.
Contextual Notes
The discussion includes assumptions about the dimensionality of tensors and their implications for physical interpretations, which remain unresolved. The relationship between mechanical energy momentum tensors and the Einstein equations is also noted but not fully explored.