Understanding the Relative vs Absolute Nature of Energy Conservation

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Energy conservation is a fundamental principle that holds true in any reference frame, meaning that the total energy remains constant over time within that frame. However, energy is not invariant across different reference frames, leading to varying values for an object's energy depending on the observer's perspective. In General Relativity, the conserved quantity is referred to as the stress-energy pseudotensor, which is coordinate dependent and can create confusion about global energy conservation. This distinction between "invariant" and "conserved" is crucial for understanding energy dynamics in both Newtonian mechanics and relativity. Ultimately, while energy conservation is upheld locally, its absolute nature can be complex and context-dependent.
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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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