QDST Description Quantum Discrete-Step Trajectory Dynamics (QDST) is a theoretical research program investigating whether finite intervals between localized interaction opportunities can produce experimentally distinguishable correlations in quantum propagation and scattering. The model introduces an effective discrete propagation scale L = vτ, where v is projectile velocity and τ is an update interval, without assuming that spacetime itself is fundamentally discrete. Its current formulation studies phase-averaged first-event statistics, velocity- and geometry-dependent correlations in ordered targets, quantum implementations of finite interaction schedules, and the conservation constraints that any physical discrete-update dynamics must satisfy. QDST explores possible connections to inverse-speed reaction behavior, barrier transmission, low-energy nuclear phenomena, reaction structure, and downstream interaction events, while recognizing that these phenomena already have conventional explanations and do not constitute evidence for QDST by themselves. A central objective is therefore experimental falsifiability rather than retrospective explanation. The framework seeks joint predictions across projectile velocity and target geometry that can be compared against calibrated conventional quantum and material-transport models. Its companion Discrete Trajectory Collision Experiment (DTCE) proposes site-resolved ion–graphene measurements as a possible experimental platform. The present QDST formulation is a phenomenological model and research program, not an experimentally established alternative to quantum mechanics. A complete theory would still require a microscopic conservative interaction law, treatment of localization and coherent interference, realistic material and nuclear dynamics, and experimentally calibrated predictions. Authors: Daqian Zhang, GPT6 Astra, SBIL
QDST Description Quantum Discrete-Step Trajectory Dynamics (QDST) is a theoretical research program investigating whether finite intervals between localized interaction opportunities can produce experimentally distinguishable correlations in quantum propagation and scattering. The model introduces an effective discrete propagation scale L = vτ, where v is projectile velocity and τ is an update interval, without assuming that spacetime itself is fundamentally discrete. Its current formulation studies phase-averaged first-event statistics, velocity- and geometry-dependent correlations in ordered targets, quantum implementations of finite interaction schedules, and the conservation constraints that any physical discrete-update dynamics must satisfy. QDST explores possible connections to inverse-speed reaction behavior, barrier transmission, low-energy nuclear phenomena, reaction structure, and downstream interaction events, while recognizing that these phenomena already have conventional explanations and do not constitute evidence for QDST by themselves. A central objective is therefore experimental falsifiability rather than retrospective explanation. The framework seeks joint predictions across projectile velocity and target geometry that can be compared against calibrated conventional quantum and material-transport models. Its companion Discrete Trajectory Collision Experiment (DTCE) proposes site-resolved ion–graphene measurements as a possible experimental platform. The present QDST formulation is a phenomenological model and research program, not an experimentally established alternative to quantum mechanics. A complete theory would still require a microscopic conservative interaction law, treatment of localization and coherent interference, realistic material and nuclear dynamics, and experimentally calibrated predictions. Authors: Daqian Zhang, GPT6 Astra, SBIL
This record contains a three-paper sequence developing the Field-Transport Trajectory Framework (FTTF), a field-first approach to quantum trajectories and measurement. Across the series, the central idea is that current-derived trajectories can be retained as channels of wave or field transport without assuming permanently occupied microscopic particle paths, while localized outcomes are treated as later event-forming actualizations rather than automatic consequences of interaction or decoherence. The sequence is architectural and phenomenological rather than a completed replacement for standard quantum theory. Paper I, Trajectories without Occupied Bohmian Particles, Detector Actualization, and a Conditional Lag Test, introduces the basic framework in the nonrelativistic setting. It preserves the usual current-based transport geometry but reinterprets it in field-first terms, and proposes that interaction, decoherence, and detector actualization should be treated as distinct stages. Its main empirical target is a two-path interferometer with tunable which-path probes, where the framework predicts a possible regime in which unconditional visibility loss begins before genuine branch-click events become common, while the no-click conditioned subensemble still exhibits two-channel transport. Paper II, Dirac hydrogen, coherent bound-state change, the 2p → 1s channel, and photon actualization, extends the framework to hydrogen in a Dirac-field setting. It distinguishes bound-state geometry from transport geometry, introduces transition current as the carrier of coherent bound-state reorganization, and develops the 2p→1s channel as a benchmark radiative case. Standard spontaneous-emission dynamics are retained at the microscopic level, while the framework proposes a further event layer that separates radiative feeding from photon actualization. Paper III, Resonant Thresholds, Channel-Matched Actualization, and Structured-Environment Tests of Measurement, develops a more specific and testable refinement of the event layer. Instead of treating actualization as a bare scalar threshold, it proposes that durable outcomes arise when pre-event feeding becomes sufficiently matched to a detector or environmental mode capable of record-forming stabilization. The paper formulates this as a matched-threshold law and proposes experimental tests in structured photonic environments, circuit-QED systems, interferometric detector-mode scans, and resonant atom-cloud platforms. Taken together, the three manuscripts propose a layered program separating transport, coherent change, radiative feeding, and actualization, while identifying experimental regimes in which this separation might be tested against strong conventional null models built from standard open-system dynamics and calibrated detector response.
Born's statistical interpretation of quantum mechanics transformed the wave function from a dynamical object into a quantity whose squared modulus determines the probability distribution of measurement outcomes. Since the formulation of the Born rule in 1926, the relation between a continuously evolving quantum state and discrete detection events has remained one of the central conceptual questions of quantum theory. This paper proposes a physical reconsideration of that relation. Rather than treating the appearance of a localized detection event as an immediate consequence of wave-function collapse, we distinguish two physically different stages: continuous wave-packet propagation and discrete detector readout. In the first stage, a localized wave packet evolves through an interaction potential and undergoes phase reconstruction, deflection, focusing, or redistribution. In the second stage, the continuously distributed wave amplitude interacts locally with microscopic detector degrees of freedom, producing discrete detection events. The central hypothesis explored here is that the experimentally observed distribution of individual events may arise from a local detector-response functional acting on the incident wave amplitude. In an appropriate regime, a detector response of the form R(x)∝∣ψ(x)∣2could emerge from the microscopic interaction between the wave packet and the detector, rather than being imposed as a primitive probabilistic postulate. The paper does not claim a completed derivation of Born's rule. Instead, it identifies the physical assumptions that such a derivation would require, relates them to historical electron-scattering experiments, and formulates a concrete research program for deriving the observed quadratic detection law from wave amplitude, energy transfer, phase structure, and microscopic detector dynamics.
This work proposes a theoretical framework reinterpreting particle motion andfield excitation propagation as emergent phenomena arising from sequences of discrete transition events, rather than traditional continuous trajectories or waves.We develop an operator algebra to explore how fundamental physics might emergefrom such transitions, which could operate at either discrete or infinitesimal scalesdepending on spacetime’s structure. The spacetime-agnostic architecture accommodates both continuous and discrete models while offering fresh perspectives on paradoxes of particle identity, field localization, and quantum measurement. Testable predictions for mass-dependent quantum interference phenomena are derived, providing potential experimental pathways to probe the transition-based paradigm.
Quantum Phase and Discrete Space A Channel-Based Interpretation of Time, Action, and Transport H. Bilgin Ergun, MSc.January 2026 — Bolu / TürkiyeORCID: 0009-0009-4733-4730 Abstract This book presents a unified conceptual framework for interpreting quantum and classical phenomena through discrete space, phase evolution, and channel formation. Rather than introducing new physical laws, it offers a geometrical and phase-based interpretation explaining why established principles such as least action, tunneling, interference, and lossless transport arise so robustly.Space is treated as a discrete phase-supporting structure in which physically meaningful events require completion of coherent phase cycles. Time is not assumed as a continuously flowing parameter, but emerges only after phase closure. Within this framework, transport phenomena are understood as phase-mediated channels rather than energetic violation or predefined trajectories.The approach provides a coherent interpretation of path integrals, tunneling, superconductivity, symmetry relaxation, and observer-induced decoherence, unifying them within a single phase-organized picture compatible with standard quantum formalism. Preface This book does not seek to replace established physical laws. Its purpose is to provide a geometrical and phase-based intuition explaining why those laws operate with such robustness across quantum and classical domains.The ideas presented here have been developed gradually through peer-reviewed articles and DOI-registered preprints. They are brought together in this volume to form a unified narrative accessible to physicists, engineers, and conceptually inclined readers interested in the foundations of physical theory.Author’s prior related work includes: A Phase-Coherence Interpretation of the Jahn–Teller Effect in Discrete Triadic Lattices, Zenodo (H. Bilgin Ergun), Record No: 18289641, Version 1, January 2026. Section 1 — Conceptual Interlude: Time Without Observation In phase-based descriptions, temporal ordering does not precede physical evolution; it emerges only after phase completion. Within a closed system evolving through discrete phase steps, intermediate configurations do not correspond to distinct moments in time but represent pre-temporal phase progressions.If an observer were present at every internal phase step, only the realized outcome would ever be accessible. Section 2 — Phase Selection and the Emergence of Least Action In the path–integral formulation introduced by Feynman, a system formally explores all conceivable trajectories between two configurations. Each path contributes with a phase factor determined by its action. Section 3 — Channel vs Channel-Free Propagation Energy may exist without direction, but direction does not arise without phase coherence. Section 4 — Phase-Guided Tunneling Quantum tunneling represents transport in which energetic transmission is suppressed while phase continuity persists. Section 5 — Collective Phase Locking and Lossless Transport Superconductivity represents the collective limit of phase-guided transport. Closure Note — Observation and Channel Disruption Observation disrupts phase continuity, collapsing channel multiplicity into a single route.
The characterization of the dynamics of quantum systems is a task of both fundamental and practical importance. A general class of methods which have been developed in quantum information theory to accomplish this task is known as quantum process tomography (QPT). In an earlier paper [M. Mohseni and D. A. Lidar Phys. Rev. Lett. 97, 170501 (2006)] we presented an algorithm for direct characterization of quantum dynamics (DCQD) of two-level quantum systems. Here we provide a generalization by developing a theory for direct and complete characterization of the dynamics of arbitrary quantum systems. In contrast to other QPT schemes, DCQD relies on quantum error-detection techniques and does not require any quantum state tomography. We demonstrate that for the full characterization of the dynamics of nd-level quantum systems (with d prime), the minimal number of required experimental configurations is reduced quadratically from d4n in separable QPT schemes to d2n in DCQD.
This framework preserves the empirical success of existing physical theories while proposing an alternative set of foundational assumptions from which their standard formulations emerge as effective limits. Abstract — Key Innovative Points Discrete Updating FabricThe theory postulates a fundamental discrete fabric whose elementary constituents evolve through local update processes, replacing continuous fields and background spacetime as primary entities. Irreversible Local Dynamics as FundamentalUnlike standard approaches based on unitary or reversible evolution, irreversibility is taken as ontological. Physical law emerges from irreversible local updates rather than from imposed symmetries or variational principles. Emergent Time and SpacetimeTime is not assumed as a fundamental parameter but arises from the counting of update events. Spacetime geometry emerges as a coarse-grained description of update activity across the fabric. Quantum Probability from Microstate CountingQuantum probabilities, including the Born rule, emerge from combinatorial counting of compatible microstates of the fabric, rather than being postulated axiomatically. Gravity as Update-Rate ModulationGravitational phenomena are interpreted as variations in local update rates, leading to effective curvature, time dilation, and relativistic behavior at macroscopic scales. Mass as Resistance to UpdateMass and inertia arise from stable topological structures within the fabric that resist updates, providing a dynamical origin of mass without introducing fundamental mass parameters. Fundamental Dissipation and IrreversibilityDissipation is intrinsic to the fabric dynamics and not an emergent statistical effect. The arrow of time follows directly from the irreversible nature of local updates. Extension Beyond Fundamental PhysicsThe same discrete framework accounts for macroscopic dissipative phenomena—such as friction, stick–slip dynamics, superlubricity, growth, and self-organization—linking fundamental physics and material behavior within a single process-based model. iversality Without Fundamental SymmetryLarge-scale physical laws emerge as dynamical attractors of the updating fabric, arising through elimination of unstable configurations rather than enforcement of fundamental symmetries. Emergent Rules Beyond the Born Rule in the Unified Fabric Framework The same discrete-fabric + local-update + coarse-graining structure generates multiple quantum rules without postulation. 1. Schrödinger Dynamics as an Emergent Long-Wavelength Limit Local deterministic updates on a discrete fabric admit spectral modes.In the long-wavelength limit, their evolution converges to a Schrödinger-type equation. No quantum dynamics is postulated.Only update rules and spectral structure are assumed. 2. Superposition from Coarse-Grained Microstate Counting Macroscopic amplitudes arise as sums over compatible microstates.Linearity follows from additive contributions at the amplitude level. Superposition is therefore emergent.It reflects coarse-graining, not a fundamental axiom. 3. Interference as Cross-Terms in Microstate Combinatorics Probabilities are quadratic because amplitudes sum before squaring.Cross-terms correspond exactly to interference effects. Interference is not assumed.It is a combinatorial consequence of microstate superposition. 4. Tensor Product Structure and the Origin of Entanglement Composite systems correspond to composite regions of the fabric.Global microstates factorize only if compatibility constraints separate. Entanglement arises when constraints couple subsystems.It is structural, not mysterious. 5. Decoherence from Phase Inaccessibility Observers access only coarse-grained variables.Rapidly varying microstate phases average out. Off-diagonal terms are dynamically suppressed.Decoherence emerges without postulation. 6. Measurement Collapse as Constraint Reduction Measurement is an interaction that reduces compatible microstates.The effective state updates accordingly. Collapse is not a new law.It is constraint updating under coarse-graining. 7. The Arrow of Time from Asymmetric State Counting Entropy is defined as the logarithm of compatible microstates.Local updates generically move toward larger compatible sets. Irreversibility is structural.It does not rely on subjective ignorance. 8. Coulomb Friction from Discrete Event Statistics Friction equals dissipated update energy per unit distance.The Coulomb law emerges from counting active interfacial events. The friction coefficient is not fundamental.It decomposes into microscopic event parameters. 9. Superlubricity as the Event-Free Limit Superlubricity occurs when locking events are suppressed.Dissipation is rare, not forbidden. This is a limit regime, not an exception.It confirms friction as emergent. 11. Conservation Laws from Update Invariance If the update rule is invariant under local transformations,conserved quantities emerge automatically. Noether’s theorem becomes emergent.Symmetry is a property of the update, not an axiom. 12. Classical Determinism from Phase Averaging At large scales, phase information becomes inaccessible.Only expectation values survive. Classical trajectories emerge statistically.Determinism is an effective limit. 13. Locality from Finite Update Propagation Updates propagate only through neighboring fabric nodes.Information speed is bounded. Causality is structural.Nonlocality is only apparent at coarse scales. 14. Emergent Speed Limit (c) The maximum update rate defines a universal speed.No signal can exceed it. The speed of light is not fundamental.It is a fabric update bound. 15. Metric Geometry from Update Delays Spatial curvature corresponds to spatially varying update rates.Time dilation is an update slowdown. Geometry is dynamical.The metric is emergent. 16. Gravity from Update Resistance Mass corresponds to structures resisting updates.Nearby updates slow down in response. Gravitational attraction emerges.No force field is postulated. 17. Equivalence Principle as a Structural Identity All stable update-resisting structures slow updates identically.Their response is universal. Inertial and gravitational mass coincide.Equivalence is automatic. 18. Quantization from Discrete Spectrum A finite update lattice admits discrete eigenmodes.Energy levels are quantized. Quantization is not imposed.Continuum is an approximation. 19. Noise Spectra (1/f) from Avalanche Dynamics Update cascades produce scale-free event statistics.Long-range correlations appear. 1/f noise is generic.It signals discrete underlying dynamics. 20. Criticality without Tuning The fabric naturally operates near instability thresholds.Small perturbations trigger cascades. Self-organized criticality emerges.No parameter tuning is required. 21. Thermodynamic Laws as Counting Theorems Temperature measures update activity density.Heat is disordered update flow. Thermodynamics is not independent.It is bookkeeping of updates. 22. Growth and Morphogenesis from Update Bias Directional update biases produce structured growth.Forms emerge without templates. Morphogenesis is dynamical.Shape follows update flow. 23. Fine-structure value and other unknow meaning The fine-structure value (~137) corresponds to the effective degeneracyof coherently contributing update configurations in an elementary coupling process.Proton–electron mass ratio the number of internal update cycles required to stabilize a topological vortex (proton), and a simple oscillatory update mode (electron). Mass measures cumulative resistance to updates. Lepton mass hierarchy Different stability thresholds of the same update pattern. Each mass corresponds to a different coherence regime.→ Families are metastable realizations of one structure. Reduced Planck constant Energy × time associated with one elementary update event. → ħ is the discrete unit of updating. Speed of light Maximum update propagation speed across the fabric. → c is the causal limit of the fabric. Bekenstein–Hawking entropy Number of blocked or saturated update configurations at the horizon. → An event horizon is an informational saturation boundary. Universal critical exponents They arise from the topology of update avalanches,independent of microscopic details. → Criticality is a natural fabric regime. Explanations Rarely Given in Existing Theories 1. Why probabilities are quadratic and not cubic or linear Most theories postulate P=∣ψ∣2P=|\psi|^2P=∣ψ∣2.Here it follows from coherent counting plus phase cancellation. The square is not a choice.It is the minimal stable coarse-graining. 2. Why quantum phases are physically unobservable but indispensable Phases affect interference but not outcomes directly.They label micro-configurations, not macrostates. Phase is structural memory.Measurement erases access to it. 3. Why constants are dimensionless and few Only ratios of update counts survive coarse-graining.Dimensional parameters wash out. Dimensionless constants are structural.They encode geometry, not dynamics. 4. Why “free parameters” cluster around simple numbers Many constants are order-one ratios or small inverses.They reflect combinatorial suppression. Fine tuning is apparent.It is state counting in disguise. 5. Why quantum randomness is stable and reproducible Randomness is not noise.It is deterministic micro-dynamics seen through coarse-graining. Statistics are invariant.Details are inaccessible. 6. Why identical particles are truly identical Microstates differ, macrostates do not.Labels are erased by update symmetry. Indistinguishability is enforced.It is not a postulate. 7. Why spin is quantized and half-integer values exist Spin counts topological winding in update cycles.Only discrete windings are stable. Half-integer spin reflects double-cover topology.No mystery remains. 8. Why gauge free