Explain why the law of conservation of energy must also include changes in mass.

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Energy is a description of how masses interect.  We make arbitrary divisions in physical reality for ease of study. When we focus on one aspect it is easy to forget that nothing exists in isolation.  The law of conservation of energy is a description of the observation that energy is neither created  nor destroyed, so since it is changing, it will be conserved and apparent losses or gains are in fact changes in the masses involved.

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