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Could there be a universe in which energy divided by distance is conserved?

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In our universe energy is conserved. In a parallel universe could energy divided by distance be a conserved quantity instead of energy itself? So in this universe if two objects were to move away from each other at a constant rate the total energy of the system would increase at a constant rate. What kinds of effects would having energy divided by distance as a conserved quantity have on this universe?

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This post was sourced from https://worldbuilding.stackexchange.com/q/41562. It is licensed under CC BY-SA 3.0.

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