The postulate distinguishes nested generation from completed observation. A functional model must specify the update, memory, readout, clock, and resource budget that make those roles concrete.
The compact presentation
DoT: The Duality of Time Postulate and Its Consequences on General Relativity and Quantum Mechanics presents the bridge from SMM to a temporal account of spatial formation. Its public introduction and A220 are the basis of this companion; the guide does not assign material to uninspected chapters.
In working language, the postulate proposes that the spatial configuration available at an outer moment is generated through nested inner activity. That sentence identifies an explanatory direction. The next step is to define the process and the condition under which its output becomes an observable record.
Write the minimal objects down
Let X be a source state space containing retained memory. Let U be its autonomous update, C a completion condition or instrument, and Π an observable readout of completed states. Specify how source histories compose and which observer procedures are allowed.
where nₖ marks a completion selected by C.
The integer n is an update index, not yet a measured time. Likewise r may be a symbol rather than a spatial location. The definitions keep these differences visible while giving the postulate something concrete to act on.
A finite completion cycle
Take a four-state cycle q=0,1,2,3 with U(q)=q+1 modulo four. Suppose only q=0 publishes a record. The source makes four updates between publications, while the observer sees a sequence of completed events.
This establishes the logical possibility of an inner/outer distinction, but the bare cycle has no counter that distinguishes successive publications. To retain event number k, the state must include memory and a rule that increments it. An unbounded perfect record requires correspondingly unbounded capacity in this idealization. The source’s resource budget cannot disappear merely because its microscopic cycle is simple.
Place the six inner roles inside the update
A richer update may contain nested dependencies associated with paired spatial ranks 1,1,2,2,3,3. The lower-level results should be retained and used by later roles, while completion certifies that the required relations are mutually consistent.
Listing six operations does not force their ranks or their geometry. A necessity argument must restrict the admissible operations enough that alternative rank patterns fail. An explicit finite construction is already useful as an existence result, provided its chosen frame, memory, and completion rules are stated honestly.
Open the full-size diagram →
Ask three independent measuring questions
What operation measures distance between completed records? What material process supplies elapsed time? What source dynamics propagates a matter excitation? These can be independently chosen in a toy model, so their agreement is the central physical task.
A hidden order also needs an observable compatibility argument if the resulting theory is to be relativistic. Calling the order inaccessible does not prove it cannot influence detector statistics. The source and observation map must jointly establish the required covariance and causal restrictions for the actual allowed procedures.
Build one result, then connect it to the next
Read A220 with A81–A83 for histories and predictive quotients, A111–A121 for autonomous completion, A126–A128 for spatial relations, and A105–A115 for material clocks and joint constraints. This route makes the postulate a practical research agenda.
A strong next theorem would use one fixed source to derive geometry, a physical clock response, and a matter propagation bound across a nonempty family of settings. Which relation becomes unavoidable because all three arise together? Which new observable remains after calibration? These are the questions that can convert the short postulate from an organizing hypothesis into a progressively more explanatory theory.
Continue with the articles
- The DoT postulate: a compact reading route
Introduce the short postulate presentation and turn its proposed consequences into a list of questions to trace through later technical work.
- One action, two temporal roles
Explain the draft’s same-cycle foundation: inner action is primitive, while outer record order comes from completed observable returns. Neither role automatically supplies a second readable laboratory clock.
- When two histories count as the same observation
Introduce completion and observational equivalence as distinct ways of identifying histories. Explain why the tests available to an observer determine which differences survive.
- A quantum source for generation and completion
Introduce the positive phase–dilation model as an explicit realization within quantum mechanics. Explain how it distinguishes inner work from completed observation without deriving quantum kinematics itself.
- A record that carries its own completion certificate
Introduce autonomous generation of a record and a flag certifying completion. Explain why the certificate must arise from the specified dynamics rather than an external declaration.
- Six inner stages and one publication interface
Explain the hierarchy of readout ranks 1, 1, 2, 2, 3, 3 followed by completion. These are nested functional roles rather than six independently readable temporal coordinates.
- What spatial readout forgets
Investigate information lost when a full generative state is reduced to spatial records. Explain why an apparently complete geometry may still be insufficient for autonomous prediction.
- What makes a clock insensitive to branching?
Explain the draft’s criterion for a clock to respond to resolution while ignoring branching. The condition is expressed through the observable algebra accessible to the clock.
- From record refinement to a joint clock–band relation
Introduce the conditional relation connecting geometry, clock response, and matter transport. Explain why the interfaces and coefficients must be independently calibrated.
Sources and reading
Read the original source for its exact formulation and edition. The examples on this page are explanatory reconstructions.