# E=mc^2 and gravitational potential energy

So, I've heard that if you lift a boulder into the air, it's mass increases slightly as per e=mc^2.
Well, my question is, does gravity act on this new mass? If so then shouldn't it have slightly more gravitational potential energy, and thus slightly more mass etc. ad nauseum?

Would the infinite series I've suggested converge?

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Doc Al
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So, I've heard that if you lift a boulder into the air, it's mass increases slightly as per e=mc^2.
Where did you hear that? The increase in potential energy, which is what I assume you are talking about, doesn't belong to the boulder by itself.

When two objects are attracted to one another, one must do work to separate them. That work increases the energy level of the system and via E = mc2 the mass of the system. The mass of the particles is one thing and the mass of the system is another. The fact is that the mass of the system is a combination of the mass of the parts and the interaction between them.

Also, the infinite regress does converge because it only take a finite amount of energy to separate the bound particles from one another (this is the binding energy of the system).

The question is slightly messed up, but yes, the proper mass of the sum of two separate mass is greater than the total mass of both put together. This is usually described as bonding energy.

I can't make out exactly how you are conceptualizing this, and the fact that you ask if it converges tells me your not that clear about it either. But yes, gravity is self gravitating (nonlinear) in some sense, and it does converge.

Where did you hear that? The increase in potential energy, which is what I assume you are talking about, doesn't belong to the boulder by itself.
Gah... of course :/
Forgetting that the Earth is a thing is an embarrassing mistake.

But then... where is this extra mass? Doesn't mass have to "be" somewhere?

That's the magic of E=mc2. The inertia is in the energy itself.