Quantum Monads Theory – System Overview (XQM · VQM · IEQ

First Principles

Monads are information- and energy-bearing units in Hilbert space; order arises through coupling and entanglement. The central principle is based on the Quantum-Monads Field Axiom.

The Theory of Quantum Monads models monads as state-bearing entities in high-dimensional Hilbert spaces (XQM). Their relations are not enforced by a synchronising operator but structured by entanglement, constraints, and the topology of a coupling graph (VQM). Measurements correspond to communicative or decisional acts and are understood as POVMs on the joint space; they condition states rather than “collapse” them. The IEQ quantifies coherence versus decoherence in social interactions, while the XDM weights normative evaluations and admissible dynamics. “Pre-established harmony” appears here as an emergent compatibility of the entanglement topology.

POVM – measurements explained

POVM measurements model communicative and decisional acts more generally than sharp projective measurements. Instead of enforcing hard yes/no projections, they allow fuzzy, noisy, or context-dependent observations — which is exactly what we need for social systems.

Formally, a POVM is a set of positive operators {E_k} on the joint space 𝓗 with ∑_k E_k = I. For a state ρ:

Outcome probability: p(k) = Tr(E_k ρ)
State update (Lüders instrument): ρ' = √E_k · ρ · √E_k / p(k)

Why POVMs rather than only projections? Projective measurements are special cases with sharp, orthogonal projectors. POVMs cover multi-stage, probabilistic, and fuzzy acts — e.g., “which narrative fits better?” rather than “is A exactly true?”

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Projective as a special case: If all E_k are projectors (orthogonal, idempotent), you recover the usual “sharp” measurements.
Operational view: Any realistic measurement chain (pre-selection, noise, decision) can be modeled as a POVM.
In our framework: “Measurements” are published acts (statements, posts, decisions) that condition states — precisely what the Lüders update captures.

Scientific ambition

The Theory of Quantum Monads explicitly presents itself as a testable, potentially falsifiable metaphysics. It proposes structures – for example coherence patterns in social fields, in cognitive dynamics, or in human–AI interaction – that are in principle observable, comparable, and refutable.

It does not claim that “everything is physics”. Instead, it offers a formal model of how physical, mental, social, and ethical orders can be coupled without confusing them. We describe this as an entangled quantum monads field.

In that sense, it is not a closed doctrine but a research programme: it can be confirmed – or disproven.

Quantum Monad

A Quantum Monad is a coherent unit of information and energy in a separable Hilbert space. It has an internal state (a “perspective”) and does not appear as an isolated thing, but as a node of relations. Its identity is created through entanglement with other monads.

From these couplings emerge observable structures: physical behaviour, neural patterns, social systems.

Entangled Quantum Monads Field

The entangled quantum monads field refers to the totality of coupled monads and their stable coherence states. It is not only about physical order, but also about attachment, trust, sense-making and joint agency in social settings.

The field therefore acts physically, mentally, socially, and culturally. It keeps world, mind and society coherent.

IEQ – Interaction Energy Quotient

IEQ measures the quality of coupling between two actors – for example between a human and an AI system.

It evaluates attention energy, response coherence, temporal reliability and semantic alignment in a relation. A high IEQ corresponds to a stable, ethically durable entanglement.

IEQ thus becomes a basis for AI ethics in human–machine relations.

The four core modules of the theory

The Theory of Quantum Monads is expressed in four modules: XQM (ontological and mathematical ground structure), VQM (relation and coupling), IEQ (coherence measurement in interaction, especially human–AI), and XDM (ethical evaluation of stability, dignity and responsibility).

These four modules form one coherent research programme. They connect physical, mental, social and normative levels without tearing them apart.

Four categories as ordering principle

We structure the theory using a Brentano-inspired categorical logic: Substance, Relation, Accidence, Modus. These map to XQM, VQM, IEQ, and XDM.

Substance → roof theory ⇒ XQM (cross-dimensional Quantum Monads)
Relation → coupling / resonance ⇒ VQM (linking Quantum Monads)
Accidence → measurable quality ⇒ IEQ (Interaction Energy Quotient)
Modus → ethics / normativity ⇒ XDM (cross-dimensional Deontic Modelling)

Note: X denotes “cross-dimensional / overarching”. QM here means “Quantum Monads” (not “quantum mechanics”).

SubstanceXQM – Basis of being

Monads are smallest coherent carriers of information and energy in a separable Hilbert space. XQM provides their ontological and mathematical basis.

XQM

RelationVQM – Coupling & resonance

Relations emerge through coupling and entanglement. VQM describes how resonance structures, networks and stable orders arise from that.

VQM

AccidenceIEQ – Measuring & simulating

IEQ makes qualitative states quantifiable: How much does a given entanglement contribute to a system’s overall coherence?

IEQ

ModusXDM – Ethics in the field

XDM evaluates actions by their field effect: Good if they support coherence; destructive if they fragment the field – especially in the design of artificial intelligence within social systems.

XDM

The four modules form a closed loop: Substance (XQM) → Relation (VQM) → Accidence (IEQ) → Modus (XDM) – an ordering of being, linkage, quality, and ethics.

XQM – The roof theory (Substance)

XQM is the foundation of the entire Theory of Quantum Monads. It describes how information and energy are organised as monads in a separable Hilbert space – elementary units that carry perception, effect and resonance.

Each monad has an internal state (its “perspective”) and is linked to other monads through entanglement. Out of these links arises what we call reality: from physical particles to neural activity all the way to social systems.

XQM thus provides the ontological base for: Relation (VQM), Measurement and Simulation (IEQ), and Normative evaluation (XDM). It fuses physics, sociology, philosophy and computer science into a consistent model of emergent order.

Practically, XQM reframes reality as a networked field of interacting monads – a mathematical language of coherence.

Go to XQM

On this basis, the three modules VQM, IEQ and XDM unfold the field toward relation, measurement and ethics — from physical behaviour to cultural responsibility.

VQM – Relation

VQM models the dynamic couplings between monads: entanglement, resonance and feedback generate patterns that stabilise across scales – from physical systems to social networks.

Formally, VQM works with coupling operators (e.g. adjacency / kernel matrices) that make stability, synchronisation and phase shifts visible. This explains when order appears, collapses or reorganises.

Go to VQM

IEQ – Accidence

IEQ is the theory’s measurement and simulation instrument. It turns qualitative states into coherence contributions – including temporal evolution, order/entropy, and valence.

Based on observable states (data, signals, interactions), IEQ yields auditable metrics and enables what-if simulations: Which intervention raises coherence? Which structure injects noise or drift?

Go to IEQ

XDM – Modus (Ethics)

XDM turns the field model into normative guidance: actions, technologies and institutions are evaluated by whether they support coherence or cause destructive fragmentation.

This yields principles like minimising decoherence externalities, coherence under constraints, and caution with high-amplification feedback loops – especially in deploying artificial intelligence within social systems.

Go to XDM

Applied theory

The Theory of Quantum Monads is not a speculative thought experiment. It is an operational model for understanding, ethics and preservation. Its structures can be applied to real systems – from ecological equilibria to cultural and technological conflict zones.

🌿 Protecting diversity – by preserving coherence in natural field structures: biodiversity, climate and planetary self-organisation as resonance phenomena.
🤝 Reconciling belief systems – by showing that religious traditions respond to the same deep structure of the monadic field, only expressed in different cultural languages.
🧠 AI ethics – coherence metrics and moral guardrails for adaptive systems, so that technological evolution does not collapse social coherence.
🌍 Societal application – toward a “coherence economy” that optimises stability and mutual intelligibility, not just profit.

The aim is a scientifically testable metaphysics: a theory that is not only thinkable, but falsifiable, and thus entitled to join empirical research.

The Theory of Quantum Monads spans millennia: it draws from the oldest philosophical questions and reaches into a future where coherence is not just a physical property, but an ethical and cultural principle. It offers a common reference frame – for nature, mind, society and technology – that binds past, present and future into one coherent field.

This does not ignore the forerunners – on the contrary. We deliberately draw on them to move their insights into a new, interdisciplinary solution space. Out of their ideas, we build the bridge between quantum physics and quantum sociology.

Quantum physics meets quantum sociology

We connect Bell’s non-locality and Schrödinger’s dynamics with Brentano’s intentionality, Habermas’ communicative ethics and Luhmann’s systems theory. The following forerunners define our roots – and open doors toward application.

Bell Bohm Luhmann Bohr Heisenberg Schrödinger von Neumann Einstein Gödel Leibniz Parsons Brentano Kant Habermas Jaspers Spengler

Philosophy

Leibniz revisited: monads as elementary perspectives on the world, made precise through state spaces and operators.

Sociology

Systems theory (Luhmann): entanglement as coupling between meaning systems; order emerges through recursive selection.

Physics

Structural proximity to quantum mechanics: superposition, projection, decomposition. Not naïve equivalence – structural analogy.

Metaphysics

From pre-established harmony to dynamic coherence: coordinated monadic activity as a constitutive principle.

Mathematics

Linear algebra, spectral decomposition, coherence/entropy metrics; operator algebras for coupling dynamics.

Computer Science

Algorithms, distributed systems, and information structures as the formal frame for emergent order; AI agents as monads with coupled internal states.

Decentralised science with IPFS/IPNS

The InterPlanetary File System (IPFS) identifies digital artefacts – such as documents, images or research data – not by location, but by content. It uses cryptographic hashes (CIDs) and distributes them across a global peer-to-peer network. The complementary InterPlanetary Name System (IPNS) points to the current version of that content.

This decentralised architecture makes scientific publications reproducible, robust against outages, and transparently versioned. It protects texts and datasets against silent manipulation or takedown, and preserves all versions in the network.

A deeper introduction to IPFS / IPNS can be found in “Die eigene Web3-Site im InterPlanetary File System” on tenckhoff.de.

Publication path

Curate assets & texts locally.
ipfs add -r --cid-version=1 → pin / replicate.
ipns publish to point to the current CID.

Profiles

Scientific work on the Theory of Quantum Monads is published across multiple international platforms. These profiles link open publications, citations and research networks to ensure long-term traceability.

ORCID – unique researcher ID
Google Scholar – citations & visibility
ResearchGate – research network
Academia.edu – exchange & discussion

All profiles →

Interdisciplinary approach

The Theory of Quantum Monads is the result of an interdisciplinary career in theoretical electrical engineering, mathematics, sociology, philosophy and computer science.

The goal is not a closed belief system, but a connecting bridge: it makes patterns and resonances visible that can be tested through models, simulations and open publications.

It invites us to cross disciplinary borders and rethink links between natural science, technology and culture – with direct relevance for artificial intelligence, society and future technologies.