A geometric quantum mechanics framework for quantum systems and measurement

Developed by Zayn Blore (https://orcid.org/0009-0009-8447-7247),Independent Researcher

Constraint-Surface Dynamics is a research programme developing a geometric formulation of quantum mechanics in which dynamics, measurement, and probability arise from constrained structure rather than axioms or interpretive postulates.

CSD builds on the tradition of geometric quantum mechanics, extending it to address long-standing questions about measurement, outcome structure, and operational probability in a unified and technically grounded way.

What CSD is

CSD treats quantum systems as evolving on constrained geometric surfaces, with measurement corresponding to measurement-induced structure on that surface, rather than an external collapse rule.

In this framework:

• Quantum evolution is deterministic at the level of the underlying geometric state.

• Measurement corresponds to a structured partition induced by physical interaction.

• Probabilities arise from geometric typicality on a preparation measure over constrained regions.

• Decoherence reflects loss of effective isolation to additional degrees of freedom.

What CSD has achieved so far

The CSD programme has already delivered concrete results at the conceptual and mathematical level.

• A consistent geometric account of quantum measurement
  Outcomes are defined operationally as regions induced by measurement interaction, without invoking collapse or branching metaphysics.

• Selects the Born rule from SU(n) invariance and operational consistency
  In the symmetry-compatible finite-dimensional sector, the Born form follows from the unique SU(n)-invariant projective measure together with standard Gleason-class operational consistency requirements (Busch effect-Gleason for the qubit case), rather than being assumed as an axiom.

• Machine-checks Bell violation with deterministic outcomes

  This paper provides an explicit Lean 4 construction in which deterministic, context-indexed outcomes reproduce the complete singlet probability table and the maximal CHSH value 2√2. It verifies that Bell violation, locally factorised measurement dynamics and operational no-signalling coexist, while proving that no compatible global assignment across the four CHSH settings can reproduce the correlations.

• Clear separation of ontology and operational description
  The framework distinguishes the underlying geometric state from the observed structure without introducing hidden variables or signalling pathologies.

• Formal consistency with standard quantum mechanics
  All results are constructed to remain empirically equivalent to standard QM in their domain of applicability.

The programme is documented in twelve published records: four conceptual papers, four technical notes, and three Lean 4 formalisation preprints, all archived on Zenodo with DOIs. Papers A and B are also open for post-publication commentary on Qeios, where they have received five reviews. Across Zenodo and Qeios, the corpus has approximately 6,360 views and 3,400 downloads. Publication figures last checked 17 August 2026.

Research status and review

The work has been publicly disseminated and reviewed through:

• Published papers and preprints

• Independent technical feedback from researchers in quantum foundations and quantum mechanics

• Open critical discussion and revision based on reviewer comments

The programme is intentionally transparent about assumptions, scope, and open questions.

This site complements the papers by focusing on clarity, synthesis, and accessibility, rather than formal derivations alone.

What CSD is working toward

The current goals of the programme are:

• To develop a clean geometric language for measurement and probability

• To connect geometric structure to operational questions in sensing, control, and quantum technologies

• To make the framework usable for education and interdisciplinary dialogue

• To identify where the approach succeeds, and where it may fail

Later work will address extensions to multi-particle systems, field-theoretic limits, and relativistic structure, where appropriate.

What CSD does not do

Clarity about boundaries is essential.

CSD does not:

• Propose new experimental predictions beyond standard quantum mechanics (at present)

• Replace quantum mechanics or its formalism

• Commit to a specific interpretation (Copenhagen, Many-Worlds, etc.)

• Claim to solve all foundational problems

• Offer engineering guarantees or performance claims

Where results are partial or conditional, this is stated explicitly.

Who this is for

CSD is intended for:

• Researchers in quantum foundations and geometric quantum mechanics

• Physicists interested in measurement, probability, and structure

• Educators seeking coherent conceptual frameworks

• Practitioners interested in geometric and operational perspectives

It is not a product pitch and not a finished theory.

Get started

If you are interested in a geometric approach to quantum systems and measurement, you can begin with a short primer introducing the framework, its motivations, and its limits.

Find the CSD Primer here.