Invariant Time

Emergent Motion

If we accept that there is a transition point between regimes, we can derive that from quantum geometry, classical motion has to emerge as a probabilistic resolution across a temporal threshold.

Below this scale, directional motion does not exist in a coherent form; instead, particles remain in a regime of non resolved path uncertainty, consistent with quantum mechanical behavior.

If reality is a mathematical structure, then its fundamental processes, are simply properties of that structure.

Our research program starts from the one following function:

Finding a single, elegant mathematical rule that applies across different domains is not a surprising coincidence, it's the expected signature of an underlying mathematical reality.

Discuss the topic further with our AI research assistant, today!

Mathematical formula: F(delta t) = 1 - e^{ -delta t / T_0 }

Research Publications

  • Theory of Emergent Motion

    ToEM, our foundational paper, reinterprets the Feynman path integral as a summation over finite paths, offering an alternative to continuous decoherence or observer induced collapse. The framework provides a transition zone from quantum to classical regimes.

    Read on Zenodo

  • Event Driven First Passage Model

    Bulding on ToEM the EDFPM, provides a comprehensive and falsifiable model, while explaining how motion and structure arise from multi scale cascades of first passage events in invariant proper time, and provides clear laboratory directions and predictions.

    Read on Zenodo

  • Bridge Model Between EDFPM and FPISBS

    How the Ordinal Research Institute latest research on Finite Path Integrals on Stochastic Branched Structures model and the EDFPM connect and how the former provides a geometric and entropic basis for why collapse occurs, while the latter offers a statistical and operational description of how and when it manifests.

    Read on Zenodo

  • Entropic Geometry and First Passage Dynamics

    Discussion on the recent, first ever experimental measurement of Quantum First Passage Time Distributions, providing empirical validation for core phenomenons, marking an important step in the study of quantum foundations.

    Read on Zenodo

  • From Ansatz to Testable Prediction

    Technical sheet on how to derive the entropy driven collapse rate for the Event Driven First Passage Model from the Finite Path Integrals over Stochastic Branched Structures and how to provide a physically motivated link between the geometric entropy of uncollapsed branches.

    Read on Zenodo

  • Finite path integrals on stochastic branched structures

    Research from the Ordinal Research Institute. FPISBS is looking at entropic geometry through the lens of knot physics, and presents a statistical model of spacetime trajectories based on a finite collection of paths organized into a branched manifold.

    Read on Knot Physics

  • Modelling Quantum Transitions Through Stochastic Mechanisms

    The aim of this piece of work, is to synthesise advancements in stochastic dynamics and quantum foundations, forging connections between entropic stochastic resonance in Brownian transport through deformable channels and foundational quantum models.

    Read on Zenodo

  • Cosmological Instantaneous Classicalisation

    A promising, albeit speculative design, that peers through the spectrum of Cosmological Instantaneous Classicalisation by integrating the micro physics of Loop Quantum Cosmology with the entropic framework of the Event Driven First Passage Model.

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