# Gravity adding energy in an isolated system?

1. Jun 4, 2013

### 04qWIGk3

Disclaimer: I am not a physicist and this was just some random question that popped into my head.

According to the law of conservation of energy, energy cannot be destroyed or created. So the energy in our current universe is the same as it was right after the big bang right?

But cant gravity add more energy in a universe thru potential/kinetic energy?

Another way of looking at this: imaging an isolated universe with two grains of sand. Each grain of sand has 100% same amount of atoms, neither of them has any movement speed in any way. Yet each is separated by a distance that it would take gravity a millennium to move them to the point where they eventually orbit each other. If you were to then examine this universe a millennium after its creation, it would appear that it would now have more energy than when it was created.

2. Jun 4, 2013

### Staff: Mentor

No. The total energy would be the same, you'd just be exchanging potential energy for kinetic.

But they have gravitational potential energy.

The gravitational PE they had initially would have been changed to kinetic energy.

3. Jun 4, 2013

### VantagePoint72

The total energy of the universe is not conserved because the metric isn't static (and the dynamic effects due to the geometry of the metric are what we collectively call 'gravity'). With space expanding, there is new vacuum energy (or whatever the cosmological constant is) being created, and the total energy of the universe is increasing with (comoving) time.

Last edited: Jun 4, 2013
4. Jun 4, 2013

### Staff: Mentor

Good point, but I suspect that's a bit too much for this thread. (But good to be accurate, nonetheless.) I was just responding to his toy "universe" and the idea that two particles approaching one another somehow create energy.

5. Jun 4, 2013

### VantagePoint72

Fair enough, though part of the question was, "So the energy in our current universe is the same as it was right after the big bang right?" The answer for the hypothetical toy universe would be 'yes', as you described, but it's 'no' for our universe. Just not for the reasons he/she suggested.

6. Jun 10, 2013

### Khashishi

In the Newtonian picture, the potential energy is
$U=-GMm/R$
M and m are two masses. When the masses get closer together, the potential energy decreases and the kinetic energy increases by exactly the same amount. The center of mass and momentum also stay the same; you can use that fact to figure how the kinetic energy is portioned out.

In general relativity, I don't think people know how to calculate gravitational potential energy, but I may be wrong.

7. Jun 10, 2013

### WannabeNewton

Actually, if we're going to be pedantic, there is no meaningful notion of total energy for a non-asymptotically flat space-time. Komar energy exists for any stationary asymptotically flat space-time (not necessarily static) and Bondi energy / ADM energy-momentum exist for non-stationary asymptotically flat space-times but you still need to have asymptotic flatness. The FRW metric is not asymptotically flat in general so the very notion of total energy is an ill-fated one.

8. Jun 10, 2013

### WannabeNewton

There is a general relativistic analogue of the Newtonian potential for stationary space-times.