Law-abiding miracles

Newton believed that, if left to the action of gravitational forces alone, the Solar System must be unstable, and only the continuous action of God, counteracting the small perturbations here and there, keeps the system together and wonderfully regular:

The six primary planets are revolved about the sun in circles concentric with the sun, and with motions directed towards the same parts, and almost in the same plane. Ten moons are revolved about the earth, Jupiter and Saturn, in circles concentric with them, with the same direction of motion, and nearly in the planes of the orbits of those planets; but it is not to be conceived that mere mechanical causes could give birth to so many regular motions[...] This most beautiful system of the sun, planets, and comets could only proceed from the counsel and dominion of an intelligent and powerful Being.

This curious picture of God as a careful supervisor of heavenly motions would only be compatible with the same physical laws that Newton crafted if God Himself would possess a physical body with mass and energy (and large quantities of them, for that matter): classical (and relativistic) mechanics is deterministic and does not allow for any degree of freedom that a deity could take advantage of to direct the evolution of a physical system one way or another. In this sense, the action of God as a stabilizer of the Solar System is a sustained miracle, a physical phenomenon incompatible with the laws of physics. This very definition of miracle is logically contradictory to begin with, at least given the premise of a deterministic universe.

On the other hand, if we consider non-deterministic physical theories, there is room for a concept that we could aptly name "law-abiding miracle": for instance, quantum mechanics tunneling allows for the occurence of phenomena that we generally deem impossible, such as wall crossing and other ghostly effects, albeit the probability of their occurrence at a macroscopic level is exceedingly small. So small in fact that it is not reasonable to expect that a macroscopic tunneling event takes place during the entire lifetime of the Universe, let alone in the presence of humans. But unlikely is not impossible: a quantum god can in principle miraculously interfere with the business of the physical world without violating the rules that govern it.

There is, nonetheless, some degree of circularity with this notion of law-abiding miracles within a probabilistic physical theory. If the frequency of such miracles is too high (as it would be the case with the scenario envisioned by Newton of a solar system being constantly tweaked to keep it stable), such divine interventions would show up in the statistical calculations made by physicists when experimentally testing the theory, rendering results highly inconsistent with the theoretical predictions; and this can in the end falsify the theory. The insistence of a deity to meddle in the normal course of events would block humans from acquiring knowledge of the laws of Nature.