Atoms to molecules to macromolecules, the process of modeling these interactions gets increasingly more complex. Biological systems behave

like a macroscopic quantum system [112] therefore quantum mechanics is used to describe them. Modern quantum theory in biology has introduced the non-local property of interconnectedness, where the emphasis is no longer on isolated objects, but on relations, exchanges and interdepen­dences on processes, fields and wholes [136].

The ability to detect, interpret and meaningfully interact with the en­dogenous bioelectromagnetic systems of living organisms could lead to dramatic advancements in modern biological sciences and engineering applications. However, in the case of biophotonic, distant interaction, and multipolar EMF experiments, where there is a destructive interfer­ence of EM signals, it becomes exceedingly difficult to directly measure phase conjugated or completely compensated EM fields in superposition. The decomposition of an electromagnetic field into scalar potential func­tions [137,138] is a traditional mathematical apparatus to describe EMFs at the complete destructive field interference. A conventional wisdom in engineering is that potentials have only mathematical, not physical signifi­cance. For instance, classical electrodynamic theory regards the complete cancellation of two fields as an absence of any field or effect. However, be­sides the case of quantum theory, where it is well known that the potentials are physical constructs, there are a number of physical phenomena — both classical and quantum mechanical, which possess physical significance as global-to-local operators or gauge fields, in precisely constrained topolo­gies, such as the Aharonov-Bohm and Altshuler-Aronov-Spivak effects, the topological phase effects of Berry, Aharonov, Anandan, Pancharatnam, Chiao and Wu, the Josephson effect, the quantum Hall effect, the De Haas — Van Alphen effect, and the Sagnac effect [139]. In particular, the Aha — ronov-Bohm effect theoretically emphasized the importance of potentials rather than the force fields [140,141]. It was later experimentally demon­strated that interfering electromagnetic potentials could produce real ef­fects on the phase via the magnetic vector potential (A-field) of charged particle systems even though the magnitude of the force field was zero around the charged particles [142]. Due to the relative phase factor of two interfering charges, the scalar field can transfer information, even though there is no transport of electromagnetic energy [143]. Furthermore, it ap­pears that information is encoded as frequencies of alternating magnetic vector potential, and should be possible to control chemical reactions in

vitro and in vivo through the interaction of magnetic vector potential with chemical potential [100].

The mathematics to describe the decomposition of an electromagnetic field or wave into two scalar potential functions was advanced by Whit­taker at the turn of the century [137,138], which later became the basis for superpotential theory [144,145]. Maxwell’s linear theory is of U(1) sym­metry form, with Abelian commutation relations, but it can be extended to include physically meaningful A-field effects by its reformulation in SU(2) and higher symmetry forms. The commutation relations of the con­ventional classical Maxwell theory are Abelian. When extended to SU(2) or higher symmetry forms, Maxwell’s theory possesses non-Abelian com­mutation relations, and addresses global, i. e., nonlocal in space, as well as local phenomena with the potentials used as local-to-global operators [139]. Success has been achieved in developing theoretical models for to­pological criteria for multiple coupled oscillators and higher group sym­metry manifolds based on both classical and quantum electromagnetism to explain several phenomena in microbiology, nanoscience and metamateri­als [146-150].

The application of these extended, higher topological mathematical models and quantum theories into biophysics and biophotonics may help elucidate the embedded or internal dynamics of the scalar potential func­tions that comprise the electromagnetic fields that destructively interfere between coupled biological systems or cultures. Despite the overwhelm­ing complexity of modeling interdependent coherent electromagnetic in­teractions in complex biological systems, there exist both theoretical and empirical evidence that establishes spatial and temporal topology of fun­damental geometric superposition, and interdependent relationships, such as multipolar influences, can uniquely affect biological systems.