Author
Graham Fincham
Graham Fincham develops the PDT research programme and its conceptual interpretation.
About
The framework
and the people
behind it.
An open scientific research programme exploring Phase Differential Theory through mathematics, physics, software, simulations, experiments, and a forthcoming book. Every major idea is presented for independent scrutiny, experimental testing, and continual refinement.
How the programme started
A single question, openly investigated.
Phase Differential Theory began with a simple question.
Although quantum mechanics and general relativity are extraordinarily successful, important foundational questions remain unresolved. Could a simpler underlying physical principle provide a common explanation for phenomena that currently require separate conceptual frameworks?
The programme began by searching for the smallest possible set of physical assumptions from which a wider description of reality might emerge.
That search led to the earlier proposal that phase differential (ΔΦ) may represent a more fundamental relational quantity than many traditionally assumed physical primitives. Since then, the programme has focused on exploring the mathematical, physical, and experimental consequences of that idea while identifying the conditions under which it would need to be revised or rejected. The current R00 to R13 formulation no longer treats a single scalar ΔΦ as its sole primitive; it begins with distinctions, relational comparisons carrying phase structure, composition and retained history.
Today the research programme spans theoretical physics, mathematical development, software, simulations, experimental proposals, artificial intelligence, quantum computing, data compression, and an accessible book written for non-specialist readers. Each area develops alongside the others as the framework continues to evolve.
The philosophy of the programme
Relations, realisation and explicit assumptions.
PDT begins with a philosophical proposal about relations and realisation, then expresses that proposal through mathematical definitions and physical models. Its scientific value depends on what those constructions establish and how their physical consequences can be tested.
A relational starting point. Distinctions and relational comparisons, carrying phase, form the starting structure (PDT F). Objects are investigated as persistent relational structure rather than assumed at the outset.
The last coherent survivor. A specified model decides which candidate records remain admissible. When a process first reaches a finite stage with exactly one candidate left, A6 takes that survivor to be realised and recorded, extending the history.
Explicit assumptions. Physical models (PDT P) identify mathematics with preparations, instruments, interactions, clocks and geometry, and each identification is stated. A common realised history (PDT U) requires those models to fit together.
Results and evidence kept apart. A proved mathematical consequence, a physical model choice and an experimental observation are different things, and the programme reports them separately.
The actuality boundary. PDT adopts realisation; it does not claim to explain why anything is actual at all. Within that boundary, the apparatus, records, energy and geometry still require physical explanation (R12).
Authors
Developed through independent research, open collaboration, and ongoing scientific discussion.
Questions, constructive criticism, collaboration enquiries, and thoughtful scientific discussion are welcomed. The programme is intended to evolve through independent scrutiny and open engagement with the wider scientific community.
Co-author
Dan Hilton
Dan Hilton's principal contribution is the development and review of PDT's mathematical foundations.
Authorship of each paper is recorded on its own page from verified records. Paper authorship, mathematical collaboration and other project roles, such as website ownership or acknowledgements, are kept separate. No institutional affiliation or endorsement is claimed.
Research programme
The arc so far.
- Original idea
The phase differential idea
Development of the relational phase idea that later became PDT.
- Manuscript preparation
Original PTG and QM series prepared
The fourteen original manuscripts, PTG I to IX and QM I to V, were prepared. Preparation dates are not release dates.
- May 2026
Research library opens on this website
The website announced the PTG and QM series on 29 and 31 May 2026. Those announcements are dated records of the website, not manuscript release dates.
- Manuscript preparation
Earlier development papers
Nine development manuscripts, PTG 1 to 5, PDT I to III and PDT MC 1, extended and revised the original series.
- 13 September 2026
QM V correction notice
The experimental trio proposed in the earlier papers was withdrawn as a set of current predictions; the original manuscripts remain available.
- Current foundational organisation
R00 to R13 current foundations
The R00 to R13 suite became the current formulation of PDT. Manuscript PDFs are available on this website; release dates are still to be supplied.
- Research programme
Record, prediction and control workstreams
The research programme now centres on record formation, prediction under uncertainty and quantum control.
- Experimental or engineering result
No experimental or engineering result documented yet
No experimental measurement or benchmark result has been reported. This entry will change only when a documented result exists.
Setting expectations
What PDT is not.
Not a theory of everything
It is a candidate foundation. It needs to be tested, extended, and likely corrected.
Philosophy made precise
PDT begins with a philosophical proposal about relations and realisation, then expresses that proposal through mathematical definitions and physical models. Its scientific value depends on what those constructions establish and how their physical consequences can be tested.
Open research
Research papers, software, simulations, and supporting material are published openly wherever practical to encourage independent scrutiny, collaboration, and reproducibility.
Not finished
It is a live research programme. The framework status page tracks what is settled and what is not.
A commitment to scientific openness
Openness, criticism, and experimental testing.
Scientific progress depends upon openness, criticism, and experimental testing.
The Phase Differential Theory research programme is committed to publishing meaningful progress alongside recognised limitations. Where ideas evolve, those changes will be documented openly. Where predictions are tested, both positive and negative outcomes should help guide future development.
The purpose of publication is not to seek agreement but to encourage careful examination, independent verification, constructive criticism, and experimental investigation.
The research archive, software, simulations, and supporting material will continue to expand alongside the programme. The accompanying book is intended to make the ideas accessible to a wider audience while remaining faithful to the underlying research.
That commitment to openness, transparency, reproducibility, and continual refinement is the foundation on which this project is built. See the falsifiability commitments for the operational version.