electromagnetism - How do virtual photon cloud produce discrete magnetic field lines in bar magnet?

I think magnetic field is the exchange of virtual photon constantly absorbed and emitted by electrons roughly speaking so assume the setup isn't in a complete vacuum and I have a piece of bar magnet and some iron filings to show the magnetic field lines. So is the magnetic field lines due to the interference pattern of virtual photon if not what really going on? Help me visualize magnetic field on the quantum scale!

Answer

Ι think magnetic field is the exchange of virtual photon constantly absorbed and emitted by electrons roughly speaking

Virtual particles are a mathematical construct made visual by the Feynman diagrams. Feynman diagrams are an iconal mathematical method to represent the perturbative expansions for the solution of specific interactions between elementary particles. They are called virtual because they have only the quantum numbers of the exchanged paraticle, not the mass. The four vector representing them is integrated over the limits of the interaction and is off mass shell for the named particle.

In this case, a virtual photon is a line :

representing the quantum numbers of a photon. The adverb "constantly" is in the mathematical space of integration. If one measures at a specific time t, the whole integration has been carried out to produce the measurement

so assume the setup isn't in a complete vacuum and I have a piece of bar magnet and some iron filings to show the magnetic field lines.

Let us take a simpler set up: instead of iron filings take a single atom with a magnetic dipole The dipole will exchange virtual photons with the atoms which are building up the field, and will orient itself at the minimum energy of pointing correctly along a "line". The line is not in space, it is the interaction with the magnet that sets up the orientations which shows the vectorial direction of the magnetic field. I could not find a feynman diagram for this, because when it comes down to mathematics it gets complicated, but roughly, a virtual photon exchanged between the magnet and a dipole with a random orientation, turns it in the correct NS direction by emitting a real photon which takes away the extra energy and balances momentum and angular momentum.

So is the magnetic field lines due to the interference pattern of virtual photon if not what really going on ?

So it is an interaction, as always at the quantum level, not an interference.

Iron filings are composed of numerous dipoles ( don't forget avogadro's number is of order 10^23) and a collective interaction builds up that will orient the iron filings in the minimum energy configuration.