The Theory of Quantum Monads

This page is the canonical system overview: it presents the formal order of the theory through four categories and four modules.

The theory is formulated as an ontologically oriented structure model: it models state entities and their couplings as relational state configurations, without conflating descriptive levels.

A concise overview of practical applications and use-oriented perspectives of the theory is provided at Quantum Monads: Applications in Physics, AI and Society .

Concept, formal structure, and elaboration: Jürgen Theo Tenckhoff (since 2024).

Abstract depiction of an entangled state field as a structural space
published via IPNS

Structural principle and formal reading

The Theory of Quantum Monads is not a worldview narrative, but a formal ordering model. Its structure therefore does not follow historical disciplines, but a minimal categorical logic that distinguishes what something is (Substance), how it is coupled (Relation), which state qualities are measurable (Accidence), and under which norms dynamics are evaluated (Modus).

This choice is deliberate. It allows physics, cognition, social order and ethics to be described within a shared formal language, without mixing explanatory levels or elevating any single discipline to a “master explanation”.

Formal reading instead of metaphor

Central to the theory is a consistent Hilbert-space and operator semantics: states, couplings, projections and dynamics are described within a mathematically controlled framework. This is the safeguard against arbitrary metaphor. Concepts such as “field”, “energy” or “coherence” are formally bound (as state variables, operator effects or metrics) — not freely interpretable buzzwords.

Information is understood as structural relationality, not as a Shannon-type quantity. Energy is not thermodynamic, but denotes the qualitative contribution of a state to overall coherence.

What does this mean for the disciplines?

  • Physics: no naïve identification. Structural concepts (state space, operator formalism, entanglement) are adopted as form, not as claims of new physics.
  • Metaphysics: a structured, in-principle testable metaphysics — not belief, but a model of coherence conditions and field effects.
  • Philosophy: Leibniz’ Monadology is taken seriously as a conceptual name- and structure-giver, but reformulated formally: monads as relational state entities.
  • Sociology: coupling, resonance, recursion and stabilisation become modelable as state dynamics of meaning systems — without psychologisation and without reduction.
  • Computer science / AI: agents can be described as state machines with coupling and feedback; IEQ and XDM provide metrics and a normative framework for human–AI systems.

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Four categories as the ordering principle of the theory

The theory of Quantum Monads is developed within a Brentano-inspired categorical logic: Substance, Relation, Accidence, Modus.

These categories structure the Quantum Monadics — the formal theoretical and modelling framework — and are concretised through the following modules: XQM , VQM , IEQ and XDM .

  • Substance → structural foundation ⇒ XQM (eXtended Quantum Monadics – state spaces & entities)
  • Relation → coupling ⇒ VQM (Vectorial Quantum Monadics – coupling & dynamics)
  • Accidence → metrics ⇒ IEQ (Interaction Energy Quotient – coherence & interaction quality)
  • Modus → normativity ⇒ XDM (eXtended Decision Monadics – evaluation & responsibility)

Substance XQM – eXtended Quantum Monadics

Foundational structural theory of Quantum Monadics: state spaces and formal conditions under which quantum monads, coherence and stability can be determined.

XQM

Relation VQM – Vectorial Quantum Monadics

Theory of directed couplings and entanglement structures through which relational orders emerge, stabilise, or transition into new states.

VQM

Accidence IEQ – Interaction Energy Quotient

Measurement and comparison of coherence contributions: connectivity, temporal reliability, and interaction stability.

IEQ

Modus XDM – eXtended Decision Monadics

Normative evaluation of actions and systems according to their field effects: coherence-enhancing or disintegrative.

XDM

Order: Substance (XQM)Relation (VQM)Accidence (IEQ)Modus (XDM).

Note: Quantum Monads denote the ontological entities of the theory. Quantum Monadics refers to the formal theoretical and modelling framework. X denotes cross-dimensional / overarching. QM refers to Quantum Monads (not quantum mechanics).

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Positioning and conceptual delimitation

The Theory of Quantum Monads denotes a theoretical framework developed systematically since 2024, integrating structural concepts from quantum physics, information theory, and social and cultural theory. At its core is the modelling of reality as a network of relationally coupled state entities, whose coherence emerges through coupling, entanglement, and dynamics.

The term draws on the Monadology of Gottfried Wilhelm Leibniz as a historical name- and structure-giver, but does not adopt it in a substance-metaphysical sense. Whereas Leibniz conceived monads as coordinated by a pre-established harmony without real interaction, monads are here conceived as relational state entities whose order is not presupposed but understood as an emergent result of dynamic coupling.

In more recent intellectual history, several approaches relate monadological motifs to quantum physics or process-oriented ontologies. The physicist Shimon Malin, in Nature Loves to Hide (German: Dr. Bertlmann’s Socks), interprets quantum states as potential realities and draws philosophical analogies to monadic figures of thought. In a similar spirit, the process philosophy of Alfred North Whitehead connects physical events to processual units of becoming.

These works represent important conceptual convergences, but they do not develop an explicit state-and-dynamics theory for social, cognitive, or artificial interaction systems. There, the monad concept remains primarily philosophical or interpretive.

The Theory of Quantum Monads is deliberately constructed to require a formal and structural reading. Core concepts are defined explicitly, their relations follow clear correspondence rules, and theoretical extensions are subject to verifiable criteria of applicability and consistency.

Metaphysical motifs may be addressed within this framework, but they remain bound to the model and do not become guiding narratives. The internal order of the theory thus follows from the formal structure of the state, relation, and dynamics models themselves.

Other works that employ monadological terms in quantum-related contexts pursue different aims. Quantum Monadology by Teruaki Nakagomi (1992) formulates a mathematical-ontological world model, without developing a systematic theory of social, cognitive, or artificial interactions.

Contributions in theoretical computer science, such as Quantum Monad on Relational Structures by Samson Abramsky and collaborators, use the monad concept as a categorical tool to describe quantum information processing, without claiming a comprehensive state-, actor-, or society-related framework.

More recent work in mathematical physics, among others by Hisham Sati and Urs Schreiber, develops highly abstract monadological structures within modern quantum theory and category theory. These approaches are primarily motivated by foundational physics and are not directed at non-physical interaction systems.

The Theory of Quantum Monads developed by Jürgen Theo Tenckhoff differs fundamentally from these lines. It articulates a coherent interdisciplinary theory architecture integrating state modelling, relation theory, operational measurement models (IEQ), dynamics (XDM), and normative applicability. Quantum-mechanical structures are used not metaphorically but structurally, without transferring physical ontology to non-physical systems.

In this sense, Quantum Monads here denotes neither a loose analogy nor a single formal technique, but a closed theoretical framework with clearly defined terminology, a coherent publication line, and unambiguous authorship.

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From Leibniz to quantum structure: bridges to social theory

From Monadology as a historical structure-giver to today’s operator and coupling semantics, these forerunners trace the lineages in which Quantum Monads develop their formal bridge between quantum structure and social theory.

The thinkers linked below mark key intellectual lineages—spanning the Monadological origin, foundational debates in quantum theory, and modern approaches to social order and normativity.

About this system: This website is part of the Quantenmonads Knowledge System — a six-domain research architecture interlinking canonical theory, structured exposition, applied essays, navigation, author context, and curated reception. Role of this domain: Canonical and formal presentation of the Quantenmonads theory.

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