  It is shown that a system with quantum coherence can be nontrivially affected
by adjacent magnetic or adjacent time-varying electric field regions, with this
proximity (or remote) influence having a gauge origin. This is implicit
(although overlooked) in numerous works on extended systems with inhomogeneous
magnetic fields (with either conventional or Dirac materials) but is generally
plagued with an apparent gauge ambiguity. The origin of this annoying feature
is explained and it is shown how it can be theoretically removed, leading to
macroscopic quantizations (quantized Dirac monopoles, integral quantum Hall
effect, quantized magnetoelectric phenomena in topological insulators). Apart
however from serving as a theoretical probe of macroscopic quantizations, there
are cases (experimental conditions, clarified here) when this "gauge
nonlocality" does not really suffer from any ambiguity: an apparently innocent
gauge transformation corresponds to real change in physics of a companion
system in higher dimensionality, that leads to physical momentum transfers to
our own system. This nonlocality, together with the associated "proximity" or
remote effects are then real and lead to the remarkable possibility of inducing
topological phenomena from outside our system (which always remains field-free
and can even reside in simply-connected space). Specific procedures are then
proposed to experimentally detect such types of nonlocal effects and exploit
them for novel applications. General consequences in solid state physics (such
as the first violation of Bloch theorem in a field-free quantum periodic
system) are pointed out, and formal analogies with certain high energy physics
phenomena (axions, {\theta}-vacua and some types of Gribov ambiguities), as
well as with certain largely unexplored phenomena in mechanics and in
thermodynamics, are noted.
