Relations before objects
PDT takes relationships as its starting point. It investigates how persistent patterns of relationships can account for what we recognise as objects.
Research programme
Phase Differential Theory
Can one physical mechanism unify quantum mechanics and general relativity?
Explore phase, persistence and time in a six-minute film.
PDT begins with a philosophical proposal: relationships are fundamental, and objects can be understood through structures that persist within those relationships. It asks how space, time, matter and definite events can be understood within a common relational framework.
At its centre is the last coherent survivor principle. When a specified process first reaches a finite stage with exactly one admissible candidate remaining, that survivor is taken to be realised and recorded.
The current R00–R13 foundations give this proposal an explicit mathematical formulation. They distinguish the starting assumptions, the results that follow from them, and the additional premises used to construct physical models.
Three ideas
The last coherent survivor
A candidate is admissible while it remains allowed by the model’s specified rules. The realisation principle, A6, takes the sole remaining candidate to be realised and recorded when a first finite singleton stage is reached.
Records and continuity
Each realised event adds a record to a growing history. The mathematical history retains earlier entries; the physical reliability of a stored record depends on the dynamics of the system carrying it.
Worked example
How a candidate becomes a record
Stage 0
C(0) = {A, B, C}
Stage 1
C(1) = {A, C}
Stage 2
C(2) = {C}
C(s) is the set of candidates still admissible at stage s. In this example, the supplied rule excludes B at stage 1 and A at stage 2. Stage 2 is the first stage with exactly one candidate remaining. Under A6, C is realised and recorded at that stage.
This example supplies its own exclusion rule. A physical model must specify the rule governing the actual system. A stage in this example is not automatically a physical clock reading.
Current foundations
The R00–R13 foundational suite
The R00–R13 foundational suite provides the current formulation of Phase Differential Theory. R00 guides the reader through the suite; R01–R13 set out its axioms, mathematical results and physical constructions, with their assumptions and scope. Earlier papers remain available as part of the historical development of the programme.
R00
Foundational suite and review guide
The guide to the suite, its reading order, the three PDT layers and the additional premises used in physical models.
R01
Core axioms and consistency
The relational primitives, phase composition, retained history and the additional A6 realisation commitment.
R02
Phase transport and complex structure
Loop phase, the minimal real phase carrier and the limits of what scalar phase information determines.
Choose a reading path
Start at the right level.
For readers
Start with the central ideas, follow a worked example, and understand the distinction between mathematical support and experimental evidence.
Follow the reader’s pathFor physicists
Examine the definitions, assumptions, mathematical results and the physical models built on them.
Follow the technical pathResearch status
Current scientific status
The R00–R13 suite is the current foundational formulation of PDT. Its mathematical results hold under stated assumptions, and its physical models declare the premises that connect them to observable quantities. Physical dynamics, calibration and distinctive experimental confirmation remain the subject of continuing research.
Explore the research statusCurrent foundations
R00–R13 is the current formulation.
A6 realisation
An explicitly adopted realisation principle.
Selection mathematics
Results proved under stated assumptions.
Physical models
Constructions with declared physical premises.
Experimental evidence
Distinctive confirmation remains an open goal.
Continuing research
Dynamics, calibration and testable predictions.
Open work
Current research questions
Question 01
Physical interpretation
Which mathematical structures can be consistently identified with measurable physical quantities?
Question 02
Dynamics and scale
Which evolution laws and physical calibrations follow from the framework, and which remain additional inputs?
Question 03
Experimental discrimination
Which specified models lead to outcomes that can be distinguished from conventional explanations?
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Get involved
Discuss the mathematics, suggest a test, or explore a defined research collaboration.