What I never understood is why the electric field doesn’t distort spacetime more than gravity. The force between 2 electrons is like 4*10^42 times stronger than gravity. So a tiny electric field should cause the same spacetime bending as a massive object.
Not really that simple. Is EM curving space time? Yes. But it does it in a very different way. EM is a force which couples to charges, magnetism, transferred by light. Gravity is a completely different beast. Super weak, but couples to everything. Mass? Yeah. Massless particles (light)? Yeah. The interraction strength itself is not an indication on how it affects the curvature of space (well, EM as a gauge theory is a curvature of a mathematical space, but gravity is one of physical space).
As far as I know, none of the observed black holes (like in LIGO) have ever observed something that would be a charged black hole, but there is the theoretical formulation of one called a Reissner Nordström black hole. In that formulation you can see how adding charge and mass acts differently. For one thing, EM charge can be negative and positive, but either sign affects the spacetime the same, in a very simple way: the square of the charge appears in the expression. But mass only appears linear. Just as an example of how they play a very different role when it comes to curvature.
True. The em field is significantly more energetic, meaning that it contributes more to the stress energy tensor than the force of gravity
But recall that the force of gravity is the momentum change “due to” the curvature of spacetime. The fact that the force of gravity can bend spacetime at all is a really weird second-order perturbative effect.
These perturbative effects are typically described with a quantum field theory, but gravity has been thus far notably difficult to quantize.
What I never understood is why the electric field doesn’t distort spacetime more than gravity. The force between 2 electrons is like 4*10^42 times stronger than gravity. So a tiny electric field should cause the same spacetime bending as a massive object.
It does. The energy density of the em field will contribute to the stress-energy tensor that changes the metric of spacetime.
Though the force itself is irrelevant
But force is a measure of the rate at which energy is transferred over a distance.
So if one force is greater than another and the distance is the same, then the energy is greater in the case of the greater force.
Not really that simple. Is EM curving space time? Yes. But it does it in a very different way. EM is a force which couples to charges, magnetism, transferred by light. Gravity is a completely different beast. Super weak, but couples to everything. Mass? Yeah. Massless particles (light)? Yeah. The interraction strength itself is not an indication on how it affects the curvature of space (well, EM as a gauge theory is a curvature of a mathematical space, but gravity is one of physical space).
As far as I know, none of the observed black holes (like in LIGO) have ever observed something that would be a charged black hole, but there is the theoretical formulation of one called a Reissner Nordström black hole. In that formulation you can see how adding charge and mass acts differently. For one thing, EM charge can be negative and positive, but either sign affects the spacetime the same, in a very simple way: the square of the charge appears in the expression. But mass only appears linear. Just as an example of how they play a very different role when it comes to curvature.
True. The em field is significantly more energetic, meaning that it contributes more to the stress energy tensor than the force of gravity
But recall that the force of gravity is the momentum change “due to” the curvature of spacetime. The fact that the force of gravity can bend spacetime at all is a really weird second-order perturbative effect.
These perturbative effects are typically described with a quantum field theory, but gravity has been thus far notably difficult to quantize.
But didn’t you just say that the electric field curves it too?