Paper XXIII - Dynamical Mass Inference in History-Dependent Time

DOI: 10.5281/zenodo.18009306 Dynamical Mass Inference in History-Dependent Time Paper XXIII 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 2 Standard Assumptions in Dynamical Mass Inference 2 2.1 Single operational time standard 2 2.2 History-independent reconstruction 2 2.3 Instantaneous equilibration 2 2.4 Operational neutrality of clocks 2 3 Operational Time and Dynamical Observables 3 3.1 Ordering time versus operational time 3 3.2 Observed velocities and accelerations 3 4 Bias in Dynamical Mass Inference 3 5 Separation of Dynamical and Lensing Mass 3 6 Predictions and Falsifiability 3 7 Conclusion 4 strophysical evidence for dark matter is primarily inferred from dynamical measurements interpreted under the assumption of a single, globally consistent operational time. In the Ordered-Dynamics Reconstruction Program, this assumption need not hold: finite clocks reconstruct time from bounded records, incurring processing overhead quantified by a dimensionless coefficient αeff (Papers XI and XXI). Paper XXII formalized the accumulation of this overhead as a cumulative operational lag ∆T, a history-dependent bookkeeping functional. In this paper we show that when dynamical evolution is analyzed using clocks whose operational time reconstruction is history-dependent, standard mass inference procedures acquire a systematic, environment-dependent bias. The effect is operational: it does not require new matter, modified forces, or changes to propagation geometry. Lensing-based inference, which depends only on propagation delay, remains insensitive, while dynamical probes inherit a bias through the time variable entering observed accelerations. This provides an operational reinterpretation of a class of late-time dark-matter–like phenomenology, without addressing primordial matter content or early-universe physics. 1 Introduction The observational case for dark matter is built largely on discrepancies between mass inferred from dynamical motion and mass inferred from luminous baryons. Across galaxies and clusters, observed velocities, velocity dispersions, and accelerations exceed those predicted by visible matter under standard gravity. The conventional interpretation attributes the discrepancy to additional, non-luminous gravitating matter. An alternative possibility is that the inference procedure itself relies on operational assumptions that need not hold universally. In particular, standard dynamical mass inference presumes that motion is measured with respect to a single operational time standard that is effectively global, path-independent, and history-independent across the system. – 1 – The Ordered-Dynamics Reconstruction Program challenges this presumption. In the program, reversible microscopic dynamics are indexed by an abstract ordering parameter λ, while physical clocks reconstruct operational time ˜ tfrom locally stabilized records. Finite clocks incur unavoidable processing overhead due to bounded information-processing capacity (Papers XI and XXI). Paper XXII made explicit the accumulation of this overhead as the cumulative operational lag ∆T, a history-dependent bookkeeping functional determined by the clock’s interaction with its informational environment. The purpose of the present paper is to examine consequences of this structure for dynamical mass inference. We show that when motion is analyzed using clocks whose operational time carries history dependence, the standard mapping from observed acceleration to inferred mass acquires a systematic bias. This produces an apparent mass excess without modifying gravitational propagation, introducing new matter components, or altering force laws. A key feature of the framework is the clean separation between dynamical and geometric probes. Lensing-based mass inference depends on propagation delay encoded by the influencedelay factor Z(x) (Paper XIII) and is insensitive to clock reconstruction overhead. Dynamical probes, by contrast, depend explicitly on ˜ tand therefore inherit history-dependent bias when αeff varies along the relevant history. Remark 1 (Scope and intent).This paper addresses late-time dynamical mass inference only. It does not address primordial dark matter, early-universe cosmology, or particle candidates. The goal is not to replace dark matter as a fundamental concept, but to clarify how operational assumptions about time enter dynamical inference. 2 Standard Assumptions in Dynamical Mass Inference Dynamical mass inference relates observed motion to gravitational acceleration. Beyond the dynamical equations themselves, practical inference relies on operational assumptions about time and measurement that are often implicit. 2.1 Single operational time standard Observed velocities and accelerations are computed with respect to an operationally reconstructed time coordinate assumed to be shared across subsystems and effectively pathindependent. 2.2 History-independent reconstruction Clock reconstruction overhead is assumed not to accumulate systematically with system age or dynamical history. 2.3 Instantaneous equilibration Temporal memory in clock–environment coupling is neglected. 2.4 Operational neutrality of clocks Clocks are treated as passive probes, introducing no systematic bias correlated with environment or history. Remark 2.These assumptions are operational rather than dynamical; they concern how motion is measured, not how gravity acts. If operational time reconstruction is history-dependent, standard dynamical mass inference is generically biased. – 2 – 3 Operational Time and Dynamical Observables 3.1 Ordering time versus operational time Let λdenote the ordering parameter governing reversible microscopic dynamics, and ˜ tthe operational time reconstructed by clocks. Following Paper XXII, processing overhead is encoded by dλ d˜ t=1+αeff , αeff ≥0.(3.1) 3.2 Observed velocities and accelerations For a trajectory x(λ), the observed velocity and acceleration with respect to operational time are vobs =dx d˜ t, aobs =d2x d˜ t2. One finds aobs = (1 + αeff )2d2x dλ2+ (1 + αeff )dαeff d˜ t dx dλ.(3.2) Remark 3.The ordered trajectory x(λ) and gravitational dynamics are unchanged. All additional structure enters through the operational time variable used in inference. Remark 4 (Stationary overhead).If αeff is effectively constant over the inference interval, the response term vanishes and standard dynamical inference is recovered. Systematic bias requires nontrivial history dependence. 4 Bias in Dynamical Mass Inference [Dynamical inference bias] When αeff varies along the relevant history, part of the observed acceleration is misattributed to gravitational mass, producing an apparent mass excess relative to inference performed in ordering time. Remark 5.Operationally, the “mass excess” refers to the mass parameter inferred by equating aobs to a force law expressed in ordering time. 5 Separation of Dynamical and Lensing Mass [Lensing insensitivity] Lensing-based mass inference, governed by propagation delay Z(x), is insensitive to αeff and to cumulative operational lag ∆T. Remark 6.Agreement or tension between lensing and dynamical mass channels therefore directly constrains operational time reconstruction effects. 6 Predictions and Falsifiability The framework predicts: •discrepancies between dynamical and lensing mass inference, •historyand environment-dependent scatter in dynamical relations, •recovery of standard inference in screened or stationary regimes, – 3 – •absence of corresponding signals in particle-physics observables. Observation of strictly universal acceleration scales or force-law modifications independent of history would falsify this framework. 7 Conclusion We have shown that history-dependent reconstruction of operational time induces a systematic bias in dynamical mass inference without modifying gravity or introducing new matter components. The effect arises because observed accelerations computed with respect to ˜ t include a response term when processing overhead varies along the system’s history. Geometric probes such as lensing remain insensitive, providing a clean operational separation between dynamical and propagation-based inference. Quantitative confrontation with astrophysical data is deferred to subsequent papers. – 4 –