Understanding the Relative vs Absolute Nature of Energy Conservation

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SUMMARY

The discussion clarifies that energy conservation is a relative concept, applicable within specific reference frames, as established in both Relativity and Newtonian mechanics. While energy is conserved (the sum of kinetic energy and potential energy remains constant over time in a single reference frame), it is not invariant across different frames. In General Relativity, the conserved quantity is referred to as the stress-energy pseudotensor, highlighting the coordinate-dependent nature of energy conservation. This distinction explains why energy may appear not to be globally conserved.

PREREQUISITES
  • Understanding of Newtonian mechanics
  • Familiarity with the principles of General Relativity
  • Knowledge of kinetic energy (KE) and potential energy (PE)
  • Concept of reference frames in physics
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  • Study the implications of the stress-energy pseudotensor in General Relativity
  • Explore the differences between invariant and conserved quantities in physics
  • Learn about energy conservation in different reference frames
  • Review Edmund Bertshinger's notes on General Relativity for deeper insights
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Students of physics, educators teaching energy conservation concepts, and researchers exploring the implications of General Relativity and energy in different reference frames.

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Or is it absolute? I've heard the conservation of energy on a large scale doesn't hold true. How can this be so?
 
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Energy is relative, both in Relativity and in Newtonian mechanics. This means that different reference frames will determine different values for the energy of a given object at a given point in space and time. However, the conservation of energy holds in any reference frame. This means that, in a single reference frame the total energy (KE + PE) will be constant over time.

This is the difference between the concepts of "invariant" and "conserved". Energy is conserved, but not invariant.
 
In General relativity, for technical reasons, the conserved quantity is called the stress-energy pseudotensor, rather than the stress-energy tensor. This is why you may have heard that energy is not globally conserved. As DaleSpam indicated, the stress-energy pseudotensor is globally conserved, but it is coordinate dependent.

Edmund Bertshinger's notes:
http://web.mit.edu/edbert/GR/gr7.pdf
 
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