Phase Differential Theory
Phase Differential
A Framework for Reality
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The theory explained

From relations
to records.

PDT starts from distinctions and relationships, gives their comparisons a phase structure, lets a specified model decide which candidate records remain admissible, and adopts the first unique survivor as a realised record that extends the history.

Current foundations →Worked example →

The thread in five steps

  1. 01

    Relations

    Distinctions and relationships form the starting structure, with phase part of that structure.

  2. 02

    Composition

    Phase comparisons compose according to explicit rules.

  3. 03

    Admissibility

    A specified model supplies the candidate records and the law deciding which remain admissible.

  4. 04

    Realisation

    If the process first reaches a finite stage with exactly one candidate, A6 takes that survivor to be realised.

  5. 05

    Records

    The record extends the history. Physical models must explain how records are produced, stored and maintained.

A

Why begin with relations?

Physics usually describes objects, their properties and their behaviour. PDT investigates a more primitive description in which distinctions and relational comparisons provide the starting structure. Its phase structure is an explicit assumption whose consequences can then be studied mathematically.

Adopting relational phase is part of the foundations. It is not claimed that circle-valued phase follows from the bare fact that there are many things to compare; it is a chosen starting structure, and the work lies in showing what it supports.

R00R01

B

What does phase mean here?

A phase can be represented by an angle around a circle. In PDT, phase information is assigned to relational comparisons, with rules for composing successive comparisons. Clock faces and waves can help illustrate relative phase, but the foundational definition is given by the comparison structure.

Going round a closed sequence of comparisons, and composing each step, gives a loop phase. That loop phase can carry information that a simple list of phases attached to individual points does not capture.

R01R02

C

What remains admissible?

A candidate is one of the possible records considered in a specified episode. The model supplies a rule, fixed from antecedent information, determining which candidates remain admissible as the episode develops.

The phrase ‘coherent survivor’ refers to survival under that stated admissibility rule. The rule must be defined within the model.

Antecedent information means information specified before the eventual outcome is used. The rule cannot be adjusted after the fact to favour the answer that occurred.

R03

Theorem R03.1 statement

D

What does realisation add?

The mathematics can establish whether a specified process reaches a first unique survivor. A6 adds the realisation commitment: at that first attained singleton, the surviving candidate is taken to become an actual record.

A6 does not by itself guarantee that every process reaches a singleton, establish universal determinism or supply a probability law. Changing an apparatus or interaction can change a model’s outcomes or probabilities; merely knowing a prediction does not by itself change nature’s answer.

R01R03R05

Theorem R05.1 statementTheorem R05.4 statement

Worked example

How a candidate becomes a record

Rule At stage 1, B becomes inadmissible. At stage 2, A becomes inadmissible. C remains admissible through these stages.

Candidates · Initial state

  • A admissible
  • B admissible
  • C admissible

A, B and C are admissible.

  1. Initial state ·
  2. Stage 1 ·
  3. Stage 2

Recorded history

No record yet.

Stages order the steps of the example. A stage is not automatically a physical clock reading.

These examples supply their own exclusion rules. They illustrate when the realisation principle applies. A physical model must also explain the rule governing an actual apparatus.

E

How do records relate to time?

Records establish an order of realised events. A physical clock requires an additional identification between a process and measured duration. PDT therefore distinguishes the order of records, the development of a selection episode and calibrated clock time.

The history retains its earlier entries as part of the mathematical description. The reliability of a physical memory depends on the dynamics of the system storing it.

R03R08

F

How does this connect to physics?

The foundations build physical models by identifying mathematical structures with preparations, instruments, interactions, clocks and geometry. Each identification is an additional, stated assumption.

Quantum probabilities and dynamics
Results under stated operational premises
R04R05R06
Record formation
Specified exclusion instruments and their limits under noise
R03R05
Spatial structure and clocks
Conditional carriers, physical identification and calibration
R07R08
Interactions and matter
Declared representations, dynamics and refinement assumptions
R09
Gravity
Einstein dynamics within a stated geometry and action class
R10
Cosmology
Evolution models with specified matter, stress and initial data
R11
A common physical theory
Compatibility of the modules within one realised history
R12
  • PDT F: structural foundations.
  • PDT P: physical models.
  • PDT U: realised physical history.

The foundational boundary

Where the explanation stops

PDT adopts realisation through A6. It does not claim that identifying a surviving mathematical candidate explains why actuality exists at all. This is the foundational boundary of the proposal.

Physical explanations still have work to do within that boundary. A model must specify the apparatus interaction, the production and stability of records, the exchange of energy and the relationship to the geometry used by other physical systems.

The foundations make these questions explicit so that mathematical results, physical model choices and experimental tests can be assessed separately.

R12

Development references

Earlier papers

The account above follows the R00 to R13 current foundations. These earlier papers record how the ideas developed and remain available in their original form.

Continue to the precise constructions.

Current foundationsThe mathematicsQuestions and answers