Looking for a stress analogue in E&M

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    E&m Stress
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Discussion Overview

The discussion revolves around the search for an analogue of stress in electromagnetism (E&M) that parallels the concept of stress in General Relativity (GR). Participants explore the theoretical implications and relationships between the stress-energy tensor in GR and potential counterparts in E&M, focusing on the nature of sources influencing fields in both frameworks.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant inquires about the existence of an analogue to stress in E&M, noting the similarities between GR and E&M in terms of source influences.
  • Another participant identifies the Maxwell stress tensor as a relevant concept but acknowledges that it is indeed a form of stress, which complicates the search for a true analogue.
  • A further response clarifies that there is no analogue of stress acting as a source in electromagnetism, highlighting the differences in tensor structures between GR and E&M.
  • One participant suggests that a tensor could be conceptualized as a "Current flux tensor" or "\dot{I} density tensor," indicating a need for further exploration of this idea.
  • A resource is provided that may contain relevant discussions on the topic, specifically referencing a monograph by Albert Tarantola.

Areas of Agreement / Disagreement

Participants express differing views on the existence and nature of an analogue to stress in E&M. While some acknowledge the Maxwell stress tensor, others argue that it does not fulfill the role of an analogue as sought in the discussion. The conversation remains unresolved regarding the existence of a true analogue.

Contextual Notes

The discussion highlights limitations in the understanding of how stress concepts translate between GR and E&M, particularly regarding the source structures and tensor types involved. There are unresolved questions about the implications of these differences.

jfy4
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Hello,

I was wondering if anyone has heard of or seen any work done into looking for what would be the analogue of stress in General Rel. for E&M. I am not talking about actual stress but the analogue to it. In the flat space metric with perturbations, linearized gravity begins to have close resemblance with E&M, save for the stress tensor. the densities and the currents are both analogues, however it doesn't look like E&M has a source for influence on the fields from what would be analogues for stress. Any comments on this?
 
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The thing you're looking for is called the Maxwell stress tensor. More generally, the full stress-energy tensor for an electromagnetic field [itex]F_{ab}[/itex] is
[tex] T_{ab} = \frac{1}{4\pi} ( F_{a}{}^{c} F_{bc} - \frac{1}{4} g_{ab} F_{cd} F^{cd} )[/tex]
Purely spatial components of this do not necessarily vanish.
 
Stingray said:
The thing you're looking for is called the Maxwell stress tensor. More generally, the full stress-energy tensor for an electromagnetic field [itex]F_{ab}[/itex] is
[tex] T_{ab} = \frac{1}{4\pi} ( F_{a}{}^{c} F_{bc} - \frac{1}{4} g_{ab} F_{cd} F^{cd} )[/tex]
Purely spatial components of this do not necessarily vanish.

Unfortunately I was trying to avoid this confusion, but the Maxwell stress tensor is stress. I am looking for the analogue if there is one. I can see the similarities between GR and E&M from there sources for influence. Mainly energy density vs charge density, and energy flux/momentum density vs current density, but then there is [tex]T^{ij}[/tex] which is the stress tensor in GR and which there appears to be no analogue in E&M. To me it seems like it would be a tensor of sort named "Current flux tensor" or "[tex]\dot{I}[/tex] density tensor" with the dot being the time derivative.

has anyone seen work related to this or have any suggestions or comments?
 
Ah, ok. I misunderstood you.

There is no analog of stress that acts as a source in electromagnetism. Gravity is described by a symmetric rank 2 tensor (the metric), and electromagnetism by a rank 1 tensor (the vector potential). The former requires a more complicated source structure than the latter.
 

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