# If a graviton has momentum, does it interact with other gravitons?

General Relativity is a non-linear theory, meaning that if you have the gravitational field for a body B1 sitting in isolation and the gravitational field for body B2 sitting in isolation, the gravitational field for both bodies is not the sum of the gravitational fields for body B1 and B2 sitting in isolation.

Linear theories have this property, for instance electromagnetism has the property the if you take the electric fields produced by two bodies in isolation, the electric field for both bodies is the sum of the electric fields. This can by seen because Gauss' equation for electromagnetism is

and if break apart and solve

then

This means in practice that the electric field doesn't interact with itself (which it basically doesn't). Notice that if Gauss's equation was modified to

then the above method of finding a solution wouldn't work. If you solve

Then you can quickly verify that

doesn't solve the equation. This is because the electric field interacts with itself and how much electric field you produce for a charge depends on how much electric field is there.

Gravity (and the weak force and the strong force) is very similar to this. The slogan is "Gravity Gravitates" which is because there is energy in the gravitational field and energy must gravitate.

The self-interaction of gravity makes a General Relativity more complicated to solve, though the real problem with quantizing General Relativity is because it is a spin 2 particle. Even this isn't the real problem. The real problem arises because of event horizons and singularities which are very difficult to deal with.

Linear theories have this property, for instance electromagnetism has the property the if you take the electric fields produced by two bodies in isolation, the electric field for both bodies is the sum of the electric fields. This can by seen because Gauss' equation for electromagnetism is

and if break apart and solve

then

This means in practice that the electric field doesn't interact with itself (which it basically doesn't). Notice that if Gauss's equation was modified to

then the above method of finding a solution wouldn't work. If you solve

Then you can quickly verify that

doesn't solve the equation. This is because the electric field interacts with itself and how much electric field you produce for a charge depends on how much electric field is there.

Gravity (and the weak force and the strong force) is very similar to this. The slogan is "Gravity Gravitates" which is because there is energy in the gravitational field and energy must gravitate.

The self-interaction of gravity makes a General Relativity more complicated to solve, though the real problem with quantizing General Relativity is because it is a spin 2 particle. Even this isn't the real problem. The real problem arises because of event horizons and singularities which are very difficult to deal with.

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