The American physicist David Bohm, and his Israeli graduate student Yakir Aharonov, predicted in 1955 that a magnetic field affects the quantum properties of an electron in a way that is forbidden by classical physics. The Aharonov-Bohm effect was observed in 1960 and hints at the wealth of surprises still lurking in quantum mechanics.

Y. Aharonov and D. Bohm, Significance of Electromagnetic Potentials in the Quantum Theory," Physical Review, Second Series, 115(3), Aug. 1, 1959, p. 485-491. Quoting, p. 485:

"…contrary to the conclusions of classical mechanics, there exist effects of potentials on charged particles, even in the region where all the fields (and therefore the forces on the particles) vanish."

Indeed, since the field is usually defined as the force per unit charge, then the field as defined does not exist until after the causative "field as a separate entity" interacts with a charged mass.  Hence the field as defined is an effect, never the cause.

Further, being an effect and an observable as defined, it does not exist in spacetime as such, since no observable does.  A priori, any observable is the output (effect) of a ?/?t operation upon LLLT, yielding an LLL "frozen snapshot" at an instant in time, which snapshot itself does not exist in time but was only a 3-space fragment of what was existing in the ongoing interaction at that point in time.  The field-free 4-potential, together with its structure and its dynamics, provides the causes existing in spacetime prior to their interaction with intermediaries to produce effects.