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I do recognize the distinction between vectors (which exist independent of
coordinate frames) and the *components* of vectors (which depend on the
choice of frame).
In the non-relativistic limit energy exists by itself
and is conserved by itself; in general it is part of a vector which is
conserved and which exists independent of frame.
Energy is as real as distance. Indeed, in a gravitational field, a
measurement of height is a measurement of energy. Most people agree that
stones are real. But the law of conservation of energy is stronger than
the law of conservation of stones.