Glossary
Working
vocabulary.
The glossary defines the terminology used throughout the Phase Differential Theory research programme. Wherever possible, established scientific terminology is retained. New terms are introduced only where the framework requires concepts not adequately described by existing language.
Standard terms
Terms with established meanings in physics and mathematics, included here with the precise sense in which they are used across the research programme.
Coherence
The degree to which the phase relations between parts of a system remain stable over time and space. Used in the conventional optical and quantum sense, and as a central observable in PDT, where coherence is treated as the quantity that organises and sustains physical structure. See also: Coherence Threshold, Phase Locking.
Decoherence Envelope
The scale over which a coherent envelope decays under interaction with its environment. In PDT, the envelope is interpreted as the loss of phase relation between system and surroundings rather than as a fundamental collapse. Related terms: Coherence, Phase Drift.
Interference
The superposition of phase-related contributions producing characteristic patterns of reinforcement and cancellation. In PDT, interference patterns are read as direct evidence of the underlying phase relations between participating components. See also: Phase Differential, Coherence.
Measurement
In standard physics, the process by which a property of a system acquires a definite value through interaction with an apparatus. In PDT, measurement is treated as a physical interaction between phase structures rather than a privileged act of observation: it is observer-independent and described by the same phase dynamics that govern any other interaction. Related terms: Deterministic Phase Snap, Coherence Threshold.
Resonance
A condition in which a system supports a stable, self-reinforcing response at a particular frequency. In PDT, resonance is treated as a regime of sustained phase locking between coupled structures. Related terms: Phase Locking, Coherence.
PDT terms
Terminology introduced by Phase Differential Theory, or used in a specific PDT sense, to name concepts the framework requires that are not adequately described by existing language.
Canonical Phase Processes
A small set of recurring phase operations, including locking, echo, inversion, snap, and drift, that PDT uses as a common operational vocabulary across physical, biological, and cosmological contexts. See also: Phase Locking, Phase Echo, Phase Snap.
Coherence Length
A characteristic length over which phase relations remain correlated within a given structure. Coherence lengths set the scales at which PDT predicts measurable deviations from standard behaviour. See also: Coherence Threshold, Phase Locking.
Coherence Threshold
A quantitative limit on the phase differential or coherence quality that a structure can sustain before deterministic phase snap, drift, or reorganisation occurs. Coherence thresholds set many of the falsifiable scales referenced in the experimental programme. Related terms: Deterministic Phase Snap, Coherence Length.
Deterministic Phase Evolution
The principle that, at the relational level, phase configurations evolve according to deterministic dynamics, with apparent randomness recovered as a consequence of coarse-graining and limited access to the full phase structure. Related terms: Deterministic Phase Snap, Phase Transport.
Deterministic Phase Snap
The PDT mechanism in which a coherent superposition resolves into a single definite outcome through deterministic phase dynamics once a coherence threshold is met. PDT investigates whether Born-rule statistics emerge from the distribution of these deterministic events. See also: Phase Snap, Measurement, Coherence Threshold.
Drift Tensor
A second-rank object capturing how phase drift varies with direction across a region. The drift tensor plays a central role in the recovery of effective geometric and dynamical equations within PDT. Related terms: Phase Curvature, Emergent Geometry.
Emergence Chain
The ordered sequence by which physical content is reconstructed within PDT, from phase differential through coherence, geometry, matter and interactions, to time. The chain organises how the framework relates its primitive to familiar physics. Related terms: Emergent Geometry, Emergent Time.
Emergent Geometry
An effective geometric description, including notions of distance, curvature, and locality, recovered within PDT from coarse-grained behaviour of the underlying phase structure. Related terms: Relational Geometry, Phase Curvature.
Emergent Time
An effective temporal ordering derived from the sequence in which phase events are realised across coherent regions, rather than assumed as an external coordinate. PDT investigates how familiar time is recovered as a coarse-grained measure of phase event density. See also: Emergent Geometry.
Phase
The relational angle associated with an oscillating or recurrent process, defined only with respect to another phase. In PDT, phase is the basic relational quantity from which other physical properties are constructed. See also: Phase Differential, Relational Geometry.
Phase Curvature
A measure of the failure of phase transport to close around small loops in the phase structure. In PDT, phase curvature provides the relational quantity from which effective geometric curvature is reconstructed. See also: Phase Transport, Emergent Geometry.
Phase Differential
The directed difference of phase between two relations, written ΔΦ. PDT takes ΔΦ as the fundamental primitive of the framework: a minimal relational quantity that presupposes no background metric, geometry, or coordinate system. Most other quantities in the theory are constructed from operations on ΔΦ. Related terms: Phase Transport, Phase Curvature.
Phase Drift
A continuous, generally small change of phase relations across a system over time or space. In PDT, drift is the mechanism through which coherent structure gradually loses or reorganises its phase alignment. See also: Phase Shear, Decoherence Envelope.
Phase Echo
A canonical process in which a phase configuration partially reconstitutes itself after dispersal, due to underlying time-symmetric phase dynamics. Phase echoes serve as diagnostic signatures in PDT analyses of memory-like behaviour in coherent systems. Related terms: Canonical Phase Processes.
Phase Field
A continuous assignment of phase relations across a region of the underlying relational structure. In PDT, the phase field is the working object on which propagation, curvature, and locking are defined. See also: Phase Structure, Phase Propagator.
Phase Hierarchy
A layered organisation of phase structures, with each level supporting effective dynamics that feed into the next. Phase hierarchies provide the bridge in PDT between microscopic phase relations and macroscopic phenomena. Related terms: Stage, Emergence Chain.
Phase Inversion (Anti-Flip)
A canonical phase operation in which the sign of a phase relation is reversed, mapping a configuration into its anti-aligned counterpart. PDT uses phase inversion in the description of conjugate states and certain conserved relational quantities. See also: Canonical Phase Processes.
Phase Locking
A regime in which the phase differential between two or more relations is held stable over time, so that the participating structures evolve in coordinated fashion. Phase locking is central to the formation and persistence of coherent matter and macroscopic structure in PDT. Related terms: Resonance, Coherence.
Phase Network
A connected set of phase relations, often represented graph-theoretically, used in PDT to analyse propagation, locking, and information flow within complex structures. See also: Phase Structure, Phase Propagator.
Phase Pinning
A configuration in which a phase relation becomes locally fixed by the surrounding structure, resisting drift even under perturbation. Phase pinning underlies the stability of localised excitations within PDT. Related terms: Phase Locking, Phase Saturation.
Phase Propagator
The object describing how a phase configuration propagates between relations under the basic dynamics of PDT. Effective propagators in different regimes give rise to gravitational-like, electromagnetic-like, and short-range behaviours within a single framework. See also: Phase Transport, Phase Network.
Phase Saturation
The regime in which the local update rate of phase relations approaches its maximum admissible value, beyond which further coherent change cannot be supported. Phase saturation features in PDT discussions of horizons, extreme densities, and limiting dynamics. See also: Coherence Threshold.
Phase Shear
A spatially varying gradient of phase drift across neighbouring relations, producing directional differences in how phase evolves. Phase shear enters PDT analyses of decoherence, anisotropy, and structure formation. See also: Phase Drift.
Phase Snap
A localised, deterministic reconfiguration of phase relations that yields a definite outcome when a coherence threshold is reached. PDT proposes phase snap as the relational mechanism underlying measurement-like events, replacing stochastic collapse with a deterministic process. Related terms: Deterministic Phase Snap, Measurement, Coherence Threshold.
Phase Structure
The full relational network of phases, drifts, and couplings on which PDT dynamics are defined. Phase structures range from minimal local configurations to extended cosmological assemblies. Related terms: Phase Network, Phase Hierarchy.
Phase Transport
The rule that specifies how a phase value is carried from one relation to another along a path through the phase structure. Phase transport plays a role in PDT analogous to that of parallel transport in differential geometry. Related terms: Phase Curvature, Relational Geometry.
Primitive
A quantity, object, or relation treated as fundamental within a given framework, not derived from anything more basic. In PDT, the primitive is phase differential (ΔΦ). See also: Phase Differential.
Relational Geometry
A geometric description constructed entirely from relations between phases, without presupposing a background metric or coordinate system. PDT works in a relational-geometric setting from which familiar geometric notions are subsequently recovered. See also: Phase Differential, Emergent Geometry.
Rosette
A minimal, locally stable phase configuration with six-fold symmetry, used in PDT as a building block of larger phase structures. The choice is derived dynamically within the framework rather than imposed. Related terms: Six-Fold Symmetry, Phase Structure.
Six-Fold Symmetry
The discrete rotational symmetry exhibited by the minimal stable phase configuration in PDT. It constrains how phase structures combine and propagate at small scales. See also: Rosette.
Stage
A successive layer of construction within PDT, in which higher-order structures, units, or effective theories are recovered from lower-level phase relations. See also: Emergence Chain.
Vacuum Transition
A reorganisation of the underlying phase structure between distinct low-energy configurations, treated within PDT as a structured transition rather than a featureless change of state. Related terms: Phase Structure, Phase Hierarchy.
Research programme
Terms describing how the research programme itself is structured, communicated, and held open to independent scrutiny.
Active Research
Lines of investigation currently being pursued within the research programme, distinguished from results that are already well established. Active research is reported openly, including provisional findings and unresolved questions. See also: Framework Status, Open Questions.
Experimental Programme
The set of proposed and ongoing experimental investigations associated with PDT, including precision interferometry, short-range gravity tests, and entangled-photon studies. See also: Falsifiable Prediction, Independent Verification.
Falsifiability Contract
The public commitment that each component of the framework is paired with quantitative predictions whose failure would withdraw or revise that component. The falsifiability contract is recorded openly and not adjusted retroactively. Related terms: Falsifiable Prediction, Framework Status.
Falsifiable Prediction
A specific, quantitative prediction whose failure at stated precision would refute the corresponding part of the framework. PDT lists its falsifiable predictions explicitly across the experimental programme. See also: Experimental Programme, Falsifiability Contract.
Framework Status
The continuously maintained record of which parts of the framework are well developed, which are under active investigation, and which have been revised or withdrawn in response to evidence. Related terms: Active Research, Open Questions.
Independent Verification
Replication, scrutiny, and critique of PDT results by researchers outside the original collaboration. The programme is structured to invite and support such verification rather than depend on internal consensus. Related terms: Falsifiability Contract.
Laboratory
The public working environment in which simulations, visualisations, experimental proposals, and software tools associated with the programme are developed and shared. See also: Simulation, Software Platform.
Mathematical Development
The ongoing formal work that derives, extends, and audits the mathematical structures of PDT, including consistency proofs, limit theorems, and connections to established formalisms. See also: Research Papers.
Open Questions
Areas where the programme does not yet provide a complete account, including aspects of the Standard Model spectrum, detailed cosmological predictions, and the full treatment of many-body measurement. Open questions are stated explicitly rather than concealed. See also: Active Research, Framework Status.
PTG
Phase-Theoretic Gravity: the strand of the research programme that investigates whether gravitational phenomena, and ultimately general relativity in an appropriate limit, can be recovered from underlying phase dynamics. See also: Emergent Geometry, Phase Curvature.
QM Reformulation
The strand of the research programme that develops a phase-based reformulation of quantum mechanics, investigating whether standard quantum behaviour, including wavefunction evolution and Born-rule statistics, can emerge naturally from underlying phase dynamics. Related terms: Deterministic Phase Snap, Measurement.
Reader Summaries
Plain-language companions to the research papers, intended to make the structure of each result accessible to readers outside the immediate specialism without weakening the underlying technical claims. See also: Research Papers.
Research Papers
The formal, citable record of the framework, published openly with versioned updates and explicit changelogs so that the historical development of the programme remains inspectable. See also: Reader Summaries, The Book.
Simulation
A computational model used to investigate phase dynamics, coherence behaviour, or candidate phenomena within PDT. Simulations support both theoretical exploration and the design of experimental tests. Related terms: Software Platform, Laboratory.
Software Platform
The set of software tools developed in support of the research programme, including simulations, analysis utilities, and prototypes of applied technologies inspired by phase concepts. Related terms: Simulation, Laboratory.
The Book
A connected, narrative presentation of the programme that integrates the formal papers into a single argument, written for working physicists and serious general readers, and revised as the research evolves. Related terms: Research Papers.
A living vocabulary
The vocabulary grows with the research.
The terminology of Phase Differential Theory develops alongside the research programme. As new mathematical structures, experimental concepts, software tools, and applications are introduced, the glossary will continue to expand and be refined so that terminology remains consistent across the papers, the laboratory, the book, and the wider research programme.