These are two questions.
Question 1: “How do quantum fields work?”
In the same way as the Cosmos/Order, the Cosmos computes and the fields compute, our cells compute. All order/pattern depends upon calculation/computation.
Cosmos/Order/Reason/Ratio. Ratio (Latin) means calculation. Rationem ducere means computare, to calculate. Our cells compute, calculate, we depend upon that calculation, we depend upon that computation. The cosmic order (the patterns, the entities/identities) depends upon a fundamental computation, without calculation, without computation there is no pattern, there is no Cosmos.
How do quantum fields compute?! That is the secret of the Matrix! How does the Matrix compute?! For instance, we know that our cells compute, but how do they compute?! Do we know how each individuated system/nature (ousia) computes?! Atomic, subatomic with respective quantum and subquantum support?! Do we know how the Matrix works in order to sustain the Cosmos?! We do not know!
We may reach down to the level of the quantum behavior in its phenomenological aspects, that which we can see with our tools. From the statistical effects, we can build representations and equations, but these will be fundamentally imitations (imitātiōnēs) of emergent patterns and dynamics, interpreted in accordance with our very sisyphic cognitive matrix of individuated systems with a specific dimensional survival interface, very conditioned by the way in which we organized ourselves socially, economically, politically, culturally and civilizationally, in hierarchized communities and networks of interests and agendas. There is no generalized unconditioned science.
Even some preprint services exercise ferocious censorship on science that goes against the interests of some “scientific” agendas, that is very visible in regards to the protection of Einstein’s “space-time”, it is not just about the “space-time”, which is just a postulate without empirical corroboration, it is about models, theories, paradigms that are failing and, thus, more advanced thinking that might help explain much more is deliberately blocked, and human/Sapiens science and technology is delayed.
For instance, the term “metaphysics” is blocked within the context of some “science political” agendas, the same goes for the term “nonlocality”. Science and (quantum) technology need to operationalize nonlocal dynamics, but an outdated establishment excludes any robust definition of nonlocality. Nonlocality is threatening for many “science political” agendas. However, our cells compute from the nonlocality of the patterns, even the cells of those that exclude and fear the concept of nonlocality.
The dynamics at the level of the quantum fields is always, necessarily, nonlocal. The cosmic Matrix did its work very well. It is all very precise, and no, the so-called “Laws of Physics” are not fundamental, fundamental are the dispositional rules computed by the Matrix for the sustainability of the dimensionally produced order. The heretic statement applies: Computer Science, as disciplinary area, is more fundamental than Physics, sorry, since I like Physics very much, but it is very foolish if one does not understand this.
Question 2: “How is it related to energy and gravity?”
Gravity is a metaphysical force. The force that supports the fields and everything, in its (gravity’s) different modes of working, for instance, the electromagnetism, strongly necessary to the (cogno)reflexivity of the fields and of everything.
Energy?! Intensity of the quantum and subquantum rhythms and vibrations necessary to the production of patterns/order/symmetries. String theory may be interesting in many aspects, namely in this.