Bohr’s idea of complementarity emphasizes the context-dependence of physical statements. For the Theory of Quantum Monads this points to observer-relative projections within a shared field. His insistence on the observer’s setup shows that reality cannot be described independently of perspective.
Bohr (Nobel Prize 1922) headed the Copenhagen Institute and shaped the early debates on quantum mechanics. His principle of complementarity says: wave and particle are context-dependent, mutually completing descriptions – and the actual description is decided by the measurement situation (observer, apparatus).
We extend complementarity to social and informational couplings: in the monadic field several valid descriptions coexist and only together form an adequate view. In the Hilbert space we model context choice as projection; VQM describes the relations, IEQ evaluates coherence / stability.
Bohr argued on the epistemological level; we provide the operatorial version with state spaces, functionals and simulations (context switch as operator sequence).
Bohr’s complementarity says that multiple, yet context-bound descriptions can be valid without contradiction. In the monadic field we formalise context change as projection operators on the state space: different measurement / interpretation frames are different projections of the same field. This logic applies to physics, communication and AI alike.
We measure the quality of a context change with IEQ: does the projection increase coherence (integrating contributions) or does it create dephasing (fragmentation)? In this way, complementarity becomes a controllable property of processes: we plan sequences of projections that together yield maximum coherence and interpretability – a bridge from Bohr’s philosophy to coupling practice in VQM.
Practical guide: (1) name context goals, (2) choose projection operators, (3) plan sequences, (4) measure IEQ effects, (5) ablate weak projections, (6) anchor the policy in XDM.
Bohr’s complementarity continues to act in philosophy, sociology and cognitive science: multiple readings coexist in a context-dependent way. In the monadic field we capture this through state spaces / operators whose projections act context-sensitively.
For AI, communication and ethics: decisions are situated. Context-dependence is not a flaw but a constitutive principle of coherent systems – compatible with XQM, VQM, IEQ and XDM.
Selected works by Niels Bohr
The observer-as-part-of-the-system feeds into our IEQ logic: coherence is always relational and context-bound.
Uncertainty & observer.
Non-locality & correlation.
Operators & projection.
Implicate order & holism.
Multiple descriptions are valid and mutually completing. Formally: different projections in the Hilbert space, activated according to context.
As part of the system: measurement / observation is a projection whose effects we evaluate via IEQ.
The operatorial implementation: XQM (formalisation), VQM (relation / topology), IEQ (measurement) and XDM (ethics) make complementarity computable.