Honest
answers.

Phase Differential Theory is a research programme exploring how relational phase structures can support mathematical constructions and physical models. Its conclusions depend on the axioms and additional assumptions used in each construction. Establishing which physical laws follow from the foundations, and which require further inputs, remains a central task.

PDT investigates connections to quantum and gravitational descriptions through explicit mathematical constructions and conditional models. A complete derivation of both theories from the foundational axioms alone has not been established. Each claimed connection should be assessed using its stated assumptions, proof and physical interpretation.

Two audiences. Curious readers who want to understand the ideas without graduate physics, and working physicists who want to read the equations and check the derivations and their assumptions. Every page on the site is signposted for one of those two paths.

The programme began historically with the phase differential (ΔΦ) as its starting quantity. The current R00 to R13 formulation does not treat a single scalar ΔΦ as its sole primitive: it begins with distinctions, relational comparisons carrying phase structure, composition and retained history, under the assumptions stated in the foundations. Geometry, dynamics and units then require further, explicitly stated physical identifications (R01, R02, R07, R08).

No. PDT is a research programme that seeks to recover established results within a relational framework, under stated assumptions. Established physics is the benchmark. Distinctive testable predictions remain to be established.

No. PDT is an active research programme. Significant portions of the formalism are well developed, others are under construction, and several questions remain genuinely open. The framework is treated as a living body of work rather than a finished theory.

No. The current foundations recover quantum results within explicitly stated operational assumptions, while preserving the successful predictions of standard quantum mechanics. Earlier proposals for departures from standard quantum mechanics are not current predictions of the foundational suite.

Phase Differential Theory (PDT) was initiated by Graham Fincham and is being developed through an ongoing collaboration with Dan Hilton, together with continuing input from reviewers, collaborators, and independent contributors. The programme combines theoretical development, mathematical review, software, simulations, experimental planning, and open scientific discussion. The contact channel is monitored and triaged within a working week.

The current foundations establish quantum probability and dynamics within explicitly stated operational assumptions (R04 to R06), including composite systems and a conditional Bell-nonlocal completion subject to no-signalling. These are conditional results: the operational premises are stated, not derived from phase alone. The earlier proposals for departures from standard quantum mechanics are not current predictions.

The gravitational construction in R10 uses declared geometry, action and matter assumptions, and must account for total stress. Within that declared class, conditional Einstein dynamics follow. It is not claimed that a universal physical spacetime has already followed from relational phase alone, and no current corrections to general relativity are predicted.

The current foundations distinguish record order, the development of episodes and physical clocks (R08). Record order does not by itself supply a clock: a physical clock requires identification and calibration, and calibration leaves some freedoms unresolved.

The six-fold rosette is a model or visualisation. A unique sixfold structure, physical three-dimensional space, the observed gauge groups and the particle spectrum do not follow from the minimal phase axioms alone; where a construction uses such structure, the chosen input must be named.

R09 sets out compatible interaction and matter models, with the assumptions and limits involved in refinement. The observed particle spectrum and its properties are not derived from the minimal axioms alone; a common matter, geometry and record model with consistent stress accounting remains open.

Measured constants and particle masses currently enter as empirical calibration. Calibration fixes scales; it is not a prediction. Predicting dimensionless constants and mass ratios would require independent selection of physical parameters, which remains open.

Black holes and horizons were studied in earlier papers through transport horizons, whose limiting construction still requires stated convergence and regularity conditions. Current cosmological and gravitational work is conditional (R10, R11). This remains an open area rather than a closed result.

The principal open questions are: an independently justified physical record law and robustness under noise; a common matter, geometry and record model with consistent stress accounting; and independent selection of physical parameters and dimensionless relations, rather than empirical calibration.

Gravity is treated through a conditional construction (R10) that uses declared geometry, action and matter assumptions. It is not claimed that curvature or a universal physical spacetime follows from relational phase alone. This is not a finished theory of quantum gravity.

PDT does not yet provide an independently justified physical record law, a common matter, geometry and record model with consistent stress accounting, or independent selection of physical parameters and dimensionless relations. It does not derive particle masses, mixing angles or cosmological parameters. A positive threshold within a model is not a continuum Yang-Mills spectral-gap proof.

Some of what is attributed to dark matter could in principle relate to phase structure, but no such model is currently established. R11 sets out conditional cosmological models and the stress requirements any proposal must meet.

Earlier PDT papers proposed a matter-wave coherence floor, a short-range Yukawa-type deviation and photon parity or helicity effects. These are earlier proposals, withdrawn from the current prediction list pending a matching derivation and experimental protocol. They are not confirmed, not established, and not currently testable predictions of the R00 to R13 foundations, and their absence alone would not falsify those foundations. A testable prediction requires a specified physical model, a quantitative calculation and an experimental protocol. See the Falsifiability page and the Framework Status page for the correction record.

A6 adopts the first attained singleton as the realisation event: when a specified admissibility process reaches a first finite stage with exactly one candidate remaining, that candidate is taken to be realised and recorded. The physical law governing the candidate process must also be specified. A6 alone does not guarantee that every process terminates, supply a universal numerical coherence threshold, determine the apparatus interaction, establish universal determinism or derive quantum probabilities without additional premises. See R01, R03 and R05. "Phase snap" is book vocabulary for this proposed realisation boundary. It is a proposal that still needs a physical trigger, dynamics and evidence, not an established physical mechanism.

No. A positive threshold within a model is distinct from a proof of a spectral gap for continuum Yang-Mills theory. No continuum Yang-Mills spectral-gap proof is claimed.

Yes. Phase Differential Theory: A Relational Framework for Quantum Mechanics, Gravity and Cosmology, by Graham Fincham, runs to 72 chapters in nine parts. The book page gives a summary of every chapter.

Start on the book page, which summarises all 72 chapters. Purchase options for the full book will be listed there once they are ready.

The papers present results in technical form. The book provides a connected narrative across the programme, accessible to readers who want the argument and its consequences without working through every derivation. The two are complementary.

The book is written for serious general readers, students, and researchers from neighbouring fields. Mathematical detail is signposted but kept out of the main flow, so the argument can be followed without specialised background.

Yes. The book is treated as a living document. Revisions will track significant developments in the underlying research, with changes recorded transparently rather than absorbed silently.

The Lab is the public working environment for the programme. It hosts interactive visualisations, simulations and software that make models inspectable by others. Software demonstrations illustrate models; they are not experimental confirmation.

Current and planned simulations cover phase lattices, coherence dynamics within chosen models, and exploratory models of electromagnetic and gravitational behaviour. Some earlier illustrations use threshold rules chosen for the model; these are illustrations, not a derived physical mechanism. Unless a simulation page says otherwise, a simulation is not derived from the R00 to R13 foundations, and simulations are not experimental confirmation.

Yes. The tools in the Lab are intended for use by researchers, students, and independent investigators. Where licences apply, they are stated alongside each tool.

Yes. New simulations are added as new aspects of the framework reach the stage where numerical investigation is meaningful. The Lab is intended to grow with the programme.

The simulations and visualisations built around the framework are being released as the lab page matures. The aim is for every computational claim to be reproducible from published code.

Several tools developed for PDT, particularly those concerned with coherence, signal structure, and high-density information representation, have potential applications beyond the framework itself. Such applications are explored where they arise.

Quantum computing is an applied research direction, not a result of PDT. Current work evaluates specified controllers under matched resources, latency and performance criteria; no control advantage is claimed without benchmark evidence.

Artificial intelligence is an applied research direction inspired by PDT rather than a core component of the physical theory. Work in this area explores phase-structured representations relevant to learning systems, with a focus on stability, generalisation, and the limits of coherence in large models. Findings here do not stand or fall with PDT itself.

Data compression research is an applied technology inspired by relational phase concepts rather than a foundational element of PDT. The framework motivates exploratory compression schemes based on phase relations rather than raw amplitudes, and prototypes are part of the active software work.

The news feed posts programme milestones: paper releases, book progress, software releases and replies to serious critique. The mailing list mirrors the same updates by email.

The papers are the formal, citable record, with the R00 to R13 suite as the current foundations. The book is the continuous narrative. The lab hosts simulations, visualisations and software, which illustrate models rather than confirm them.

Active work spans the R00 to R13 foundations (relational comparisons, phase structure, composition and records), conditional constructions connecting to quantum and gravitational descriptions, cosmological models under stated premises, the requirements for experimental proposals, and applied software in coherence-sensitive domains.

The R00 to R13 current foundations are the most developed part of the programme: the relational axioms, phase transport, selection and records, quantum probability and dynamics under stated operational premises, and conditional constructions of geometry and gravity. The A6 realisation commitment is adopted as an axiom; the physical law governing the candidate process must be specified separately.

Work remains on: an independently justified physical record law and its robustness under noise; a common matter, geometry and record model with consistent stress accounting; and independent selection of physical parameters and dimensionless relations. Detailed cosmological models and many-body measurement also remain under investigation.

Refuted components are withdrawn or revised, and the change is recorded openly in the framework status. The programme is structured so that local failures do not require concealment, and global failure remains a possible outcome.

Earlier PDT papers proposed a matter-wave coherence floor, a short-range Yukawa-type deviation and photon parity or helicity effects. These are earlier proposals, withdrawn from the current prediction list pending a matching derivation and experimental protocol. They are not confirmed, not established, and not currently testable predictions of the R00 to R13 foundations, and their absence alone would not falsify those foundations. A testable prediction requires a specified physical model, a quantitative calculation and an experimental protocol. See the Falsifiability page and the Framework Status page for the correction record.

Yes. We welcome precision interferometry, short-range gravity and quantum optics groups who can help turn a specified physical model into a quantitative calculation and an experimental protocol. The earlier proposals are not current predictions of the foundational suite. Write through the contact page and describe the capability you bring.

Potentially. University laboratories in optics, condensed matter and precision metrology could help once a specified physical model has a quantitative calculation and a defined protocol. No current prediction of the foundational suite is yet ready for testing. Collaboration on developing such proposals is welcomed.

Independent scrutiny is invited. The current foundations and the earlier papers are public so that arguments can be checked. Experimental proposals must first be developed into a specified model, calculation and protocol before independent replication is meaningful.

Rejection criteria apply to the specified model and assumptions being tested. A clean null result can reject a stated model only when its observable, assumptions, procedure, uncertainties and rejection criterion have been fixed in advance. A null result against one historical proposal does not by itself refute the framework as a whole. The earlier coherence-floor, Yukawa-type and photon parity or helicity proposals are not current predictions of the foundational suite.

Publication and journal-review status are recorded separately for each paper where verified. Public release in a repository does not itself constitute journal peer review. Where a journal-review stage has not been confirmed, the site identifies that uncertainty.

For the current formulation, cite the R00 to R13 foundational suite at /foundations. For an earlier paper, use the citation on its page, which reflects only verified records. No repository DOI is currently verified for these papers, so do not cite a Zenodo DOI unless one appears on the paper page.

Open publication allows the work to be checked, criticised, and built upon without gatekeeping. It also makes the historical record of the programme inspectable, which is essential for any claim to scientific seriousness.

Mathematical review within the programme and formal journal peer review are separate processes. The publication record identifies a paper's journal-review stage where that information has been confirmed.

Documented scientific corrections are listed on the Framework Status page with the affected paper, the change, the recorded update date and a link to the relevant notice or revised material. Website wording changes are not presented as revised manuscripts.

Yes. Negative results, failed predictions, and abandoned lines of work are published alongside positive results. A research programme that hides its failures cannot be trusted with its successes.

Distinctive experimental confirmation remains outstanding. Mathematical proofs and numerical checks establish properties of specified constructions; simulations examine their behaviour under chosen conditions. Experimental support requires measurements and comparison with credible conventional explanations.

On this site. The current foundations are at /foundations. Each earlier paper has its own page with the abstract, reader summary, any context notices, the claims stated in the original paper, a citation and a download.

Purchase options will be announced on the book page when they are ready. Until then, the book page is the place to read the chapter summaries.

Use the contact page and choose the enquiry type that fits your question.

Translation rights are available subject to agreement. Enquiries from translators and foreign-language publishers are welcomed.

Universities interested in using the material for teaching, seminars, or discussion are encouraged to contact the PDT team regarding appropriate use and supporting resources. The aim is to support genuine educational engagement while keeping a clear record of how the material is used and cited.

A conditional result follows when its stated assumptions hold. The proof establishes the implication, but does not by itself establish that every assumption describes nature. Physical assumptions, empirical calibration and mathematical hypotheses should therefore be identified explicitly.

Falsifiability applies to a specified model and test, not automatically to an entire research programme. A proposal must identify a versioned source, define its observable and procedure, state its assumed coupling and parameter range, distinguish calibration inputs from predictions, specify a conventional comparison model, and give the expected uncertainty and a pre-specified rejection criterion.

PDT is independent. The research is currently self funded with a small group of supporters. The support and investors pages describe how additional funding would accelerate the manuscript, the experimental collaborations, and the software programme.

The programme spans theoretical physics, mathematics, software, simulations and a forthcoming book, providing several avenues for scientific and technological development. It states openly what each model assumes and what a test would require; distinctive experimental predictions remain to be established. The investors page sets out the full thesis.

Plausible applied directions include phase-coherent communications, coherence-preserving quantum computing components, phase-based data compression, and learning systems built on phase-structured representations. These are research directions, not promises.

Use the contact form. Messages are read directly by the PDT team and routed to the most appropriate author or collaborator. State plainly whether you are a reader, a researcher, a journalist, or a collaborator, and a reply will come back through the same channel.

The fastest way is to read a paper and tell someone about it. Beyond that, join the mailing list for major releases, introduce the work to researchers who could help develop models into testable proposals, and consider direct support through the Support page.

Yes. Contributions from physicists, mathematicians, engineers, and software researchers are welcomed. The contact page is the appropriate first point of entry.

Yes. Errors in the papers, software, or website are taken seriously and corrected openly. Reports through the contact page are appreciated.

Yes. Collaboration proposals from individuals, research groups, and institutions are welcomed and reviewed in good faith.