Paper XX - Bounded Information and the Structure of Physical Theory

DOI: 10.5281/zenodo.18009267 Bounded Information and the Structure of Physical Theory Paper XX of the Ordered-Dynamics Reconstruction Program Paul Cooneya aIndependent Researcher, Innisfil, Ontario, Canada E-mail: paul.co[email protected]to.ca Contents 1 Introduction 1 1.1 Scope of the synthesis 2 1.2 Measurement and gravity 2 2 Bounded Information and Operational Locality 2 3 Dynamics as Constrained Transport 3 4 Interaction Structure and Operational Rigidity 3 5 Gauge Structure from Redundancy 3 6 Records, Probability, and Definiteness 3 7 Irreversibility and the Arrow of Time 3 8 Horizons as Operational Information Boundaries 3 9 Finite Resolution and the Limits of Description 4 10 Singularities as Descriptive Breakdowns 4 11 Conclusion 4 DOI: 10.5281/zenodo.XXXXXXXX he Emergence and Ordered-Dynamics programs develop a unified operational framework in which space, dynamics, interaction structure, gauge redundancy, measurement, horizons, and irreversibility arise from bounded information, local influence, and consistency of record formation. Across twenty papers, a sequence of structural constraints and conditional derivations are established without postulating spacetime geometry, collapse dynamics, or fundamental symmetry principles. This capstone paper provides a synthesis of those results. It does not introduce new dynamical assumptions, nor does it claim uniqueness of the underlying physical theory. Instead, it identifies which features of modern physics are shown to be structurally unavoidable within a bounded-information framework, which arise conditionally given additional assumptions, and which remain open. The synthesis clarifies how locality, gauge structure, probability, irreversibility, and horizons emerge as consistency requirements on admissible descriptions for bounded observers, and delineates the precise scope and limits of what has been proven. 1 Introduction The relationship between information, locality, and physical law has long been recognized as foundational, yet their precise operational role has remained unclear. Modern physics contains multiple structural elements whose origin is often treated as axiomatic: spatial locality, – 1 – dynamical laws, gauge symmetry, measurement rules, irreversibility, and horizon phenomena. These structures are typically introduced independently, using distinct postulates tailored to specific domains. The Emergence and Ordered-Dynamics programs investigate a different possibility: that many of these features arise as consistency requirements on admissible descriptions once information is finite, influence is local, and observers are bounded. Rather than proposing a new dynamical theory, the program reconstructs the constraints that any such theory must satisfy to remain operationally meaningful. Across the preceding nineteen papers, a sequence of results is established. Space and distance arise from bounded influence propagation. Dynamical generators are constrained by locality and information growth bounds. Interaction structure is restricted by operational no-instantaneous-influence principles. Gauge connections emerge from unavoidable local redundancy in description. Stable records, probability assignments, and effective irreversibility arise from environmental coupling under bounded information capacity. Horizons and limits of resolution appear as consistency boundaries rather than as additional postulates. The present paper does not re-derive these results. Instead, it provides a synthesis that clarifies their logical status and interdependence. 1.1 Scope of the synthesis Results summarized here fall into three categories: •Structural necessity results, which constrain all admissible bounded-information theories. •Conditional derivations, valid under explicit auxiliary assumptions. •Existence results, demonstrating internal consistency. This synthesis does not claim uniqueness of physical law, nor does it elevate conditional results to universal statements. 1.2 Measurement and gravity The program derives the operational appearance of definite outcomes, Born-rule frequencies, and irreversibility for bounded observers, without fixing a unique ontology of the quantum state. Similarly, gravitational phenomena are treated operationally: influence delay, horizons, and resolution limits are derived, without specifying metric dynamics. 2 Bounded Information and Operational Locality Both programs rest on two constraints: finite information capacity and local influence. These are not metaphysical claims, but operational limits on what can be recorded, transmitted, and compared by bounded observers. Locality itself is derived rather than assumed. Spatial structure arises from constraints on influence propagation, independent of background geometry. – 2 – 3 Dynamics as Constrained Transport Within emergent spatial structure, admissible dynamics are constrained by bounds on distinguishability growth. Under nonrelativistic assumptions, this restricts transport generators to the Schr¨odinger class. This result is conditional and kinematical: it constrains admissible dynamics without invoking measurement postulates or classical limits. 4 Interaction Structure and Operational Rigidity Operational Locality imposes a no-instantaneous-influence constraint on additional couplings. This yields a rigidity result: fundamental interaction generators must be local multiplication operators. This restriction applies to direct matter–matter interactions and does not govern compensating structures such as gauge connections. 5 Gauge Structure from Redundancy Gauge symmetry arises from unavoidable local redundancy in description. Finite influence speed prevents global coordination of internal labels, requiring connection variables to maintain consistency. Gauge fields thus function as bookkeeping structures rather than direct interaction mediators, resolving their compatibility with interaction locality. 6 Records, Probability, and Definiteness Environmental coupling under bounded information leads to unavoidable record formation. Interference between record sectors becomes operationally inaccessible, yielding definite outcomes for bounded observers. Probability assignments arise from record stability and redundancy. The squared amplitude measure emerges as the unique additive, phase-invariant quantity governing record frequency. 7 Irreversibility and the Arrow of Time Although microscopic dynamics are reversible, record accumulation induces an effective arrow of time. Reversal would require control over inaccessible environmental correlations, rendering it infeasible for bounded observers. 8 Horizons as Operational Information Boundaries Limits on accessibility arise naturally from finite information and local influence. Operational horizons mark boundaries beyond which information cannot be retrieved or coordinated within finite operations. These horizons are defined without reference to spacetime geometry, though they may coincide with geometric horizons in specific theories. – 3 – 9 Finite Resolution and the Limits of Description Bounded information density imposes limits on operational resolution. Distinctions below a certain scale cannot be reliably encoded or compared, without implying fundamental discreteness or a universal minimum length. Descriptions attempting to exceed this resolution become operationally meaningless. 10 Singularities as Descriptive Breakdowns Classical singularities correspond to operational singularities: regimes where predictive descriptions require unbounded resolution or control. Such limits do not represent physical endpoints, but the breakdown of a descriptive regime. Consistent theories must replace singularities with structures respecting bounded information, such as horizons or information-saturating regions. 11 Conclusion The Emergence and Ordered-Dynamics programs identify a common operational foundation underlying diverse physical structures. Locality, dynamics, interaction rigidity, gauge redundancy, records, probability, irreversibility, horizons, and limits of resolution arise as consistency requirements on bounded descriptions. The program does not select a unique theory of nature. Instead, it constrains the admissible structure within which any consistent physical theory must be embedded. Beyond these constraints, further refinement ceases to be physically interpretable. In this sense, the reconstruction closes not by answering every question, but by clarifying which questions can coherently be asked. – 4 –