# Negative energy is repulsive, but PE is negative, so?

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## Main Question or Discussion Point

I am missing something basic here. In https://en.wikipedia.org/wiki/Negative_energy, it is stated that "a universe in which negative energy dominates will either expand indefinitely or...." But gravitational potential energy is negative, so if I make the substitution, I would get "a universe in which gravitational energy dominates will either expand indefinitely or...", but a universe in which gravity dominates would collapse, no? The only way I see out of this is if the original excerpt means "a universe in which a negative change of energy dominates will either expand indefinitely or...", since changing negative energy would be balanced out by increasing kinetic energy (although, given that the conservation of energy does not necessarily apply for the universe as a whole, so one should better say that each local section of the universe would increase in kinetic energy). But increasing kinetic energy is not enough....after all, if (a section of) the universe is contracting, it could also be doing so at an accelerated pace (until the singularity). Please correct me. Thanks.

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andrewkirk
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The use of negative values for gravitational energy is most common in the Newtonian theory of gravity. The gravitational PE of an object approaches zero from below as it is moved increasingly far away from a massive body.

The notion of negative energy for the universe as a whole comes up in the context of General Relativity - Einstein's theory of gravity rather than Newton's. Under that theory, gravity has two components: an attractive force between massive objects that pulls things closer and a repulsive force that arises from empty space that pushes things apart. Both are gravity, as they come from the same equation, and they compete with each other. When there's a lot of mass-energy close together, the attractive force wins - which is why you and I stay firmly on Earth and the Earth continues to orbit the sun. But where there's a lot of empty space, like between galactic clusters - the repulsive force wins.

The reason your word substitution seems to create a paradox is that you are taking a concept out of Newtonian theory - in which gravity is always attractive - and inserting it without modification into Einsteinian theory, in which gravity can also be repulsive.

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