# How can gravitational energy cancel out the rest energy of mass in the universe [duplicate]

I've heard that some physicists think that the net energy of the universe is zero. For this to happen, I would assume that the negative gravitational energy of a body ought to cancel out its rest energy. A back-of-the envelope calculation for the Earth gives me a rest energy around $10^9$ greater than its gravitational energy. I would assume that for other ordinary matter we get a disparity on the same order of magnitude. This means that the rest-energy of ordinary matter far outweighs its gravitational energy. Even if ordinary matter only contributes 4% of the gravitational energy in the universe, a claim I've heard, the rest energy of ordinary matter still far outweighs the total gravitational energy in the universe. So how is it still a plausible hypothesis that the net energy of the universe is zero? Where does the rest of the negative energy come from?

## marked as duplicate by John Rennie, Rob Jeffries, Community♦May 6 '15 at 7:03

I've heard that some physicists think that the net energy of the universe is zero.

Me too. They talk about gravitational energy being negative. But see Einstein talking about gravitataionl field energy here. It's positive.

For this to happen, I would assume that the negative gravitational energy of a body ought to cancel out its rest energy.

That's what they say, but IMHO like John Rennie said, it's wrong. When two bodies falls together, some of their rest-mass energy is converted into kinetic energy. They collide, and the kinetic energy is converted into heat and eventually gets radiated away. Then you'[re left with a mass deficit. But it's a mass deficit, not an energy deficit. Conservation of energy applies. You don't end up with less energy than what you started with.

A back-of-the envelope calculation for the Earth gives me a rest energy around $10^9$ greater than its gravitational energy...

Yes, gravitational field energy isn't much. Nor is the mass deficit.

So how is it still a plausible hypothesis that the net energy of the universe is zero?

IMHO it isn't. IMHO the people who say this sort of thing tend to be popscience cosmologists with a book to plug.

• +1 for the statement the people who say this sort of thing tend to be popscience cosmologists with a book to plug :-) – John Rennie May 6 '15 at 7:28
• @John Rennie : thanks John. I have to say I have watched cosmology programs on the Discovery Channel, and have wanted to throw cushions at the TV. Naming no names of course. ;) – John Duffield May 6 '15 at 16:25