Why Isn't Gravity a Repulsive Force Based on Energy Arguments?

[Antiphon]

Frankly, I think gravity should be repulsive force on the basis of a simple energy argument which I will now make. I request anyone with insight to find the flaw in my argument. (there has to be one since I think we'd all agree that gravity is an attractive force.)

One way to compute forces is to take a differential of a field energy along some spatial displacement. The force will point in the direction that decreases the energy of the field. Simple example: two electrons near one another. If you integrate the energy of the electrostatic fields through space 1/2*epsilon*E^2 in MKS units, you'll find that there is less energy in the field if the electrons are further apart. Therefore the force they experience is repulsive.

Why is this not the case for gravity? By this reasoning, masses should repel one another.

What am I missing?

 

[Dale]

What is the energy density of the gravitational field?

 

[Antiphon]

What is the energy density of the gravitational field?

Good question. But there has to be one otherwise lifting weights at the gym wouldn't build muscles, right?

 

[johng23]

Using a field argument to claim that a force should be opposite to what is observed seems backwards. Isn't a field essentially a mathematical construct for describing the force that a body would feel at every point in a space?

 

[Antiphon]

Using a field argument to claim that a force should be opposite to what is observed seems backwards. Isn't a field essentially a mathematical construct for describing the force that a body would feel at every point in a space?

Yes.

I found a thread with a good review of the question at https://www.physicsforums.com/showthread.php?t=316784&page=3

I'm comfortable with a negative energy density in the gravitational field as the origin of it.

 

[Dale]

Good question. But there has to be one otherwise lifting weights at the gym wouldn't build muscles, right?

Building muscles requires a force, not necessarily a conservative force that would be associated with an energy density and a conserved energy.