Are the fields in their empty state a single indivisible and static entity? I would also like to know if the gravitational field also has a vacuum state and if the other fields are permanently linked to it. Regards
Fields are "fundamental entities" whether there are particles or not: Particles are just excitations of fields. In their vacuum state quantum fields fluctuates according to Heisenberg uncertainty principle for time and energy. So the vacuum state of the gravitational field would be like seafoam (like Jean-Pierre Luminet's analogy). By definition of quantum fields in curved space-time, all the fields are "linked" to the gravitational field. But for the vacuum states, one has to be careful because the number of particles depends on the referential. So vacuum for an observer may not be the vacuum for another one.