When a proton attracts an electron in the electromagnetic field is the proton "bending" the field?

Question

As the question states when a proton attracts an electron in the electromagnetic field is the proton "bending" the electromagnetic field like the earth bends space time ("creating" gravity)?

Answer 1

If you could look at a map of the electric field lines in the vicinity of two separated charged particles, you would see that the field lines appear to bend. However, you would just be seeing the result of the vector sum of the two fields. The field at any point would just be the sum of the fields due to the two particles separately. So it is not really appropriate to think of the fields of the two particles "bending" each other.

To first order, the same is true of the gravitational field in the vicinity of two masses. However, there is a higher-order term that represents a nonlinearity in the behavior of gravitational fields. The term is very small except in the case of very strong gravitational fields. The nonlinear term can be interpreted as "bending" the gravitational field lines, because it results in a typically very small but nonetheless significant difference between the actual gravitational field at any point and the vector sum of the separate gravitational fields due to the two masses.

A good start is to think carefully about what you mean when you say "bending the field". What do you mean by "field" and "bending" (in terms of how you would measure them)? Normally, the electrostatic field at a point is defined as a vector whose magnitude is the force experienced by a point charge placed at that point, divided by the charge, and whose direction is the direction of the force. In electrostatics, the force is directly proportional to the value of the test charge. In gravity, it's almost proportional to the value of a test mass -- but not quite. When a relationship like that is not directly proportional, it's called "nonlinear".

Actually, in the case of extremely strong electromagnetic fields, there is reason to believe that nonlinearities do appear, due to quantum electrodynamic (QED) effects that arise, referred to as "vacuum polarization".