A field does not physicslly exist. It's an abstraction. We speak of waves and fields as first class objects, but this is reification. A field is a description of a pattern of relationships in the sequence finite states and possible state transitions. The intellect can grasp continuity but, physically, continuity can only be approximated. Because continuity is a concept. The fact that the intellect can grasp infinite and uncomputable things says something about the intellect, but it does not make infinite/continuous things physical. The invention of digital scarcity showed the requirements of a system implimenting conservation