Is the Law of Conservation of Energy Valid in a Non-Local Context?

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The law of conservation of energy is universally accepted in Newtonian mechanics and special relativity, where energy is conserved both locally and globally. However, in general relativity, energy conservation is complex; it is conserved locally but not globally due to the absence of a fixed global concept of simultaneity. This lack of simultaneity complicates the assertion that total energy remains constant over time. Consequently, the validity of the law of conservation of energy in a non-local context is not straightforward. Overall, while local conservation holds, global conservation presents significant challenges in the framework of general relativity.
Kyle Nemeth
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Is it accepted that the law of conservation of energy can be considered in a non-local context? If this is not accepted, then why not?
 
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Kyle Nemeth said:
Is it accepted that the law of conservation of energy can be considered in a non-local context? If this is not accepted, then why not?
In the context of Newtonian mechanics, energy is strictly and globally conserved.
In the context of special relativity, energy is strictly and globally conserved.

In the context of general relativity, energy is conserved locally but global energy conservation is not simple. One way of seeing this is to realize that there is no fixed global concept of simultaneity. So there is no fixed meaning to an assertion that total energy "now" is the same as total energy "a moment ago".
 
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