[Fussball (OP)]

Does a field line (of a proton for example) weigh anything? More generally does the field contribute to the weight of a particle? If we observe a field line under a microscope what do we see? What is a field made of? Is it material or is it mathematical?

[evan_au]

Does a field line (of a proton for example) weigh anything?

A field line is a conceptual way of representing fields graphically.
- I guess it has the weight of the ink you use to draw it.
See: https://en.wikipedia.org/wiki/Field_line

does the field contribute to the weight of a particle?

Yes, the electric field of the electron forms part of the mass of the electron.

The electromagnetic field of the photon makes up the mass/energy of the photon.

There are apparently problems with the hypothetical graviton: When you try to calculate the contribution of the graviton to the gravitational field, you end up with infinities that won't go away (with current mathematical techniques).

If we observe a field line under a microscope what do we see?

Field lines are conceptual, rather than physical, so there is nothing physical to see, unless you use something to outline them.

One example is using iron filings to outline the field lines of a magnet.
See: https://physics.stackexchange.com/questions/349464/why-iron-filings-sprinkled-near-a-bar-magnet-aggregate-into-separated-chunks

[jeffreyH]

What if the graviton does not contribute to the gravitational field? A gravitational wave does not necessarily move an object towards the source of the wave but only temporarily perturbs spacetime. Therefore, it could be argued that gravity does not beget gravity.