Sequential generation becomes an explanation of causality when the update law determines dependency, preserves records and bounds controllable influence in the geometry read by observers.
What does a cause change?
Ordinary causal reasoning asks what would change if a preparation, control or interaction were changed. A physical theory must specify both the intervention and the later observable that responds. Correlation alone is insufficient: two clocks can agree because they were prepared together, even when changing one clock has no effect on the other.
The question also has a cosmological form. If physical clock readings begin only within the universe, an explanation of their origin need not describe an earlier reading of the same clock. SMM places the generative source at this explanatory level. A mathematically specified source can explain why temporal and spatial relations appear, while the philosophical question of why that source exists remains a further question about grounding.
This distinction makes the research target precise: construct observable cause-and-effect relations within a generated world, and identify which structural property enforces them.
Renewed creation changes the starting point of motion
The original causality article draws on Ibn al-Arabi’s account of renewed creation. Motion is interpreted as a succession of an object’s appearances in different positions, rather than an additional entity inserted into a permanently existing object. In SMM/DTT, these appearances belong to one chronological source process; regular causal relations express how its successive configurations depend on each other. [1]
The older explanation uses the analogy of successive screen images and extends it to a universe whose constituents are jointly regenerated. Its strongest physical idea is that a common source can coordinate a complete configuration while the observed pattern of motion arises between completed configurations. Six nested inner stages organize dependent construction; outward completion makes the result available to observation. The source is prior to the assigned spatial positions, so its organizing activity need not be pictured as a signal traveling through an already finished spatial scene. A mathematical model must then explain how ordinary, controllable propagation appears within that scene. [1]
Build the causal graph from the actual update
Let a completed record contain variables r1,…,rN. For each elementary operation, draw a dependency from an input variable to an output variable whenever changing that input can change the output. The resulting graph records the mechanism itself. It should include the controller, retained memory and communication ports as well as the variables called matter.
Suppose an update at a record uses only its present state and the states of its declared neighbors. Then an intervention can advance through at most one dependency edge per completed step. If an inner controller carries a payload between distant records, its movement is another dependency channel and must enter the graph. A serial schedule does not make such a channel local simply because only one operation occurs at a time.
The source proposal becomes constructive when the same dynamics prepares the neighborhood relation and constrains later operations to respect it.
A finite chain gives an exact influence bound
Consider binary records on a ring, with synchronous completed updates qi(k+1) = qi−1(k). Two initial configurations differ only at site 0. After k updates the difference appears only at site k, with indices interpreted modulo the ring length. Repeated substitution proves the statement exactly.
If neighboring records are independently calibrated to have separation a and each completed update takes physical duration τ, the propagation speed is a/τ. A more general nearest-neighbor rule allows a growing influence region, but induction still places it inside k graph steps. This is an exact discrete causal cone.
Quantum lattice systems provide a related benchmark: finite-range interactions can yield exponentially suppressed influence outside an effective cone. The Lieb–Robinson bound makes the dependence on interaction strengths and range explicit. [2]
A common source can correlate distant records
The common-source picture naturally distinguishes formation of a joint state from later influence within it. Preparing two records in a correlated state can make their outcomes strongly related after separation. It does not follow that an observer can choose a message at one location and read it instantly at the other.
For quantum systems, the relevant test is whether changing a local operation alters a distant observer’s unconditioned statistics. Bell’s theorem additionally constrains attempts to reproduce quantum correlations using preassigned local responses and a shared classical cause. A successful temporal-source model must state its joint state and allowed interventions explicitly, so that these are calculable questions. [3]
This strengthens the older idea of synchronization: synchronization should describe a concrete correlation structure, while causal influence should describe the response to an admitted intervention. Their compatibility can then be established rather than inferred from the metaphor.
From a graph cone to a common light cone
A graph-speed bound is the first step toward relativistic causality. The next step requires clocks and rods constructed from the same source dynamics. If two particle species measure different ratios of neighboring separation to completed duration, they may inherit different effective cones. A common source does not by itself eliminate that freedom; the coupling that links their standards must do so.
A promising design is a completion rule that certifies both the transport operation and the clock record, with conservation or symmetry preventing independent retuning. One would calculate the characteristic speeds of all low-energy modes and show that the same calibrated metric governs their response. Isotropy, stability under perturbations and the continuum limit are additional properties to demonstrate for that family.
The six inner stages can organize this shared construction, but their dependency structure must survive the derivation instead of being replaced by six unrelated clocks.
The next result should survive every allowed intervention
Specify a finite autonomous source with a retained relation table, local matter records and an internal clock. Prove that two initial states agreeing on the past dependency region of an observable give the same later value, or a quantitatively bounded difference. Then include arbitrary operations that an observer is allowed to perform. This closes the gap between a background update and a causal theory of controlled experiments.
The most revealing countertest adds one permitted shortcut or one unrecorded controller memory. If that destroys the cone, the model identifies the exact protection it needs. If the protection follows from the source law and remains effective during growth, SMM/DTT gains a concrete explanation of why ordinary causal relations are stable features of generated space. The retained locality and universal-clock targets develop these two parts of the same problem.
Books, papers and further reading
- Mohamed Haj Yousef, Duality of Time, Chapters III and V–VII
Original causality article identifies Chapter III and develops its account through renewed creation, quantum interpretation and the later causality discussion.
- Elliott H. Lieb and Derek W. Robinson, The finite group velocity of quantum spin systems (1972)
Primary propagation bound for quantum systems with finite-range interactions.
- John S. Bell, On the Einstein Podolsky Rosen paradox (1964)
Constraints on a local response explanation of entangled correlations.