E=mc^2 and gravitational potential energy

In summary: So, in summary, when a boulder is lifted into the air, its mass increases slightly due to the increase in potential energy. This potential energy is a combination of the mass of the boulder and the interaction between the boulder and the Earth, resulting in a greater overall mass for the system. This increase in mass can be described as bonding energy. Despite the infinite regress suggested, the increase in mass ultimately converges due to the finite amount of energy needed to separate the bound particles. This extra mass is contained within the increased potential energy, as described by E=mc2. Gravity is self-gravitating and also contributes to this increase in mass.
  • #1
Archosaur
331
1
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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  • #2
Archosaur said:
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.
 
  • #3
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).
 
  • #4
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.
 
  • #5
Doc Al said:
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?
 
  • #6
That's the magic of E=mc2. The inertia is in the energy itself.
 

Related to E=mc^2 and gravitational potential energy

1. What is the equation E=mc^2 and what does it mean?

The equation E=mc^2 is one of the most famous equations in physics, and it stands for energy equals mass times the speed of light squared. This equation represents the relationship between mass and energy, and it shows that mass and energy are interchangeable.

2. How does E=mc^2 relate to gravitational potential energy?

E=mc^2 is a fundamental equation in physics that applies to all forms of energy, including gravitational potential energy. This equation shows that mass and energy are equivalent, so any form of energy, including gravitational potential energy, can be converted into an equivalent amount of mass.

3. What is gravitational potential energy and how is it calculated?

Gravitational potential energy is the energy an object possesses due to its position in a gravitational field. This energy is calculated by multiplying the mass of the object by the acceleration due to gravity and the height of the object above a reference point. The equation for gravitational potential energy is PE = mgh, where m is the mass, g is the acceleration due to gravity, and h is the height.

4. How does mass affect gravitational potential energy?

The more mass an object has, the more gravitational potential energy it has. This is because the equation for gravitational potential energy, PE = mgh, includes mass as a variable. So, the greater the mass of an object, the greater its potential to do work due to its position in a gravitational field.

5. Can gravitational potential energy be negative?

Yes, gravitational potential energy can be negative. This occurs when an object is below the reference point for calculating gravitational potential energy. In this case, the potential energy is negative because work would need to be done to move the object to the reference point, and the object would gain energy in the process.

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