EP and active/passive mass

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SUMMARY

The discussion centers on the relationship between the equivalence principle (EP) and the conservation of stress-energy in theories where geometry and matter are non-minimally coupled. It asserts that in General Relativity (GR), violating the EP through minimal coupling leads to non-conservation of stress-energy-momentum, establishing a link between the EP and the conservation laws that do not exist in Newtonian physics. The inquiry seeks clarification on the stress-energy tensor derived from such actions.

PREREQUISITES
  • Understanding of General Relativity (GR) principles
  • Familiarity with stress-energy tensor concepts
  • Knowledge of non-minimal coupling in field theories
  • Basic grasp of Newtonian physics and its limitations
NEXT STEPS
  • Research the derivation of the stress-energy tensor in non-minimally coupled theories
  • Explore the implications of the equivalence principle in General Relativity
  • Study the differences between active and passive mass in gravitational theories
  • Investigate conservation laws in various gravitational frameworks
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The discussion is beneficial for theoretical physicists, researchers in gravitational theories, and students studying the foundations of General Relativity and its implications on mass and energy conservation.

atyy
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If we start from an action in which geometry and matter are non-minimally coupled, can the resulting theory have a covariantly conserved stress-energy tensor (if so, what is the stress-energy tensor in terms of the action?)

In Newtonian physics the EP (equivalence of inertial/passive mass) and the third law (equivalence of passive/active mass, momentum conservation) are not linked. I'd naively guess that violating the EP (minimal coupling) will cause non-conservation of stress-energy-momentum so that these are linked in GR, if not in Newtonian gravity.
 
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