# What really is an electric/magnetic field?

Have you ever wondered how we can see this field or how it's formed its shape in space? I know we can feel that there's one by its effect which is the force. But what does it look like?

We all know that gravitational field was explained by Einstein in terms of warps and curves in the fabric of the space time caused by a mass itself. I want to know if maybe there's a way somehow we can explain the electric and the magnetic field like that.

• Field lines are an excellent way to visualize the shape and distribution of electric and magnetic fields. Sep 21 '19 at 19:53
• Have you heard of Maxwell's equations? Sep 21 '19 at 20:19

There is a geometric picture of the electromagnetic field in terms of "warps and curves," as you put it. This picture is in precise analogy to that general relativity, although it involves different mathematical objects with different physical interpretations.

In general relativity, the "warps and curves" in spacetime are described mathematically by what is called the curvature tensor of spacetime. With the curvature tensor, we can determine the gravitational force on particles. Einstein's equations tell us that the curvature tensor is related to the distribution of matter and energy in spacetime.

In electromagnetism, we can relate electric and magnetic forces to a curvature tensor in a similar way. However, the curvature tensor in the case of electromagnetism is a fundamentally different object both mathematically and physically. It does not describe the curvature of spacetime. Instead, it describes the curvature of a kind of "internal" space that is attached to the points of spacetime. (Mathematically, this "internal" space is a called a fiber bundle. Physically, the study of such spaces is called gauge theory.)

Just like Einstein's equations relate the curvature of spacetime to the presence of energy and matter, Maxwell's equations relate the electromagnetic curvature to the presence of electromagnetic charges and currents.

You cannot explain electric and magnetic fields as curved spacetime. Gravity is different.

Gravity affects everything - electrons, protons, neutrons, and so on. Even light from a distant start is bent by the sun's gravity as it passes close to the surface.

Gravity is a distortion of times and distances. Clocks run a little slower near the Sun. The distance to the center of the Sun is a little farther than you would expect from measuring the circumference. Anything in the region near Sun is affected by these distortions. An object like the Earth follows what seems to be a straight line, but is actually a curve. The result is an attraction toward the Sun.

An electric field from an proton in the nucleus of an atom will attract an electron. It will repel a proton. A neutron or light will not feel a force at all. You can't explain an electric field as a distortion of space and time that makes things follow a curved path if some things do and others don't.