Time is global: one time encompasses the whole universe, and no region, system, frame, observer, or worldline has a time of its own. Time is the fixed, non-reversed, non-metric succession of the common stages of change of all physical systems in the universe. It causes nothing: physical systems change through physical causes. It is not a substance, a field, a container, a clock reading, a coordinate, or a geometric dimension, and physical change does not produce it.
ℰC is the cosmic extension, 𝒮Ctot the one domain of the common stages of the universe, and ≺C their objective earlier–later order; no length, rate, or duration belongs to the order. The Ordinal Succession convention 0 ≺C 1 ≺C 2 ≺C 3 ≺C 4 ≺C … ∞ (conditional) names the stages by their places: stage 0 is the first stage of change, at the formation and genesis of the universe, with no date fixed for that beginning; the numerals are ordinal names, not quantities, and are not added, and they do not determine the stage of any given change, since change continues without stopping, observed or not; no stage, named or lying between named stages, is empty of change or static; no stage is major or minor; and ∞ is neither a stage, a limit, nor a greatest member, and is conditional because current science does not establish whether the succession ends. Invariance is the fixed succession of the change realized through its stages, and its non-reversal: what succeeds is dynamic, a change that never stops; what is fixed is the order of its succession, never interrupted by a static or empty stage. Because change never stops, the place in the succession of the stage of any given change cannot be determined.
Every stage is a stage at which physical systems are realized and change is realized. A stage is the formal expression of the realization of a change within the unceasing chain of change, by comparison between the earlier change and the later (stage 0 has no earlier change before it), and not a container that change occupies. UCC states that change never stops; invariance is the fixed and non-reversed succession of that unceasing change; its predicate is derivable from temporal constitution and UCC, but invariance is not produced by them. Physical factors acting at a stage are causes of the change of its systems, not members of its population.
The Cosmic Moment Axiom: every physical system of the universe realizes its changes on the one common succession. Its realization succession 𝒲A contains no private stage, and its own earlier–later order is the cosmic order. At each stage, all the physical systems qualified at it gather at that same stage; the systems of all stages do not gather at one stage. Co-presence is not synchronization, signal access, spatial coincidence, or coordinate equality.
Universal Change Continuity, the postulate of change: physical change continues without interruption in every physical system of the universe, without exception, whether observed, unobserved, or below any detection threshold. The change is that of each system itself, internal or external: where a constitution is unchanged, the change is realized in the state of motion and coupling that the acting influences change.
A changed relation to another system is not by itself a change of A; calling one system older, smaller, or slower only because another has changed attributes no change to it. The contrary of UCC is warranted complete physical non-change of a system at a stage of its existence.
The cosmic moment is the conjunction of co-presence and change: at each stage, all systems realized there are together and every one of them realizes its own change there. With the common-stage condition, it makes every stage of the universe a stage of change of all its systems. Change of every system is stated by a postulate, not written into the definition of a stage, so that UCC keeps a contrary that physical evidence could establish.
CMA and UCC are logically independent: CMA ⊬ UCC and UCC ⊬ CMA, each proved by a countermodel that satisfies every other governing postulate. Beginning and end are not treated alike: the first stage is adopted as the revisable Cosmic Origin postulate, anchored in the early hot and dense state; its contrary is a succession with no least member. Non-termination remains a revisable hypothesis, because current evidence establishes neither a terminal stage nor an unbounded future.
𝒰phys is the totality of the physical systems of the universe. Each system has its own structure, history, and accumulated change, and all these histories pass through the same common stages: many histories, one succession, and no private times.
The physical universe is the totality of physical systems and physically realized physical factors. It is neither a container nor a single system.
Four commitments carry the framework. Each has its own status and its own contrary, and none is derived from another.
Strict Cosmic Ordering: the later never becomes earlier under any observer, coordinate, clock, condition, or description. A system that recovers an earlier state realizes a new later change; no stage goes backward, because a stage is the formal expression of a change realized in the succession.
There are no separate times on Earth and in space. Clocks there run at different rates as physical systems under different conditions. A common stage implies no equal states, rates, causes, locations, clock readings, or histories.
Between any two stages of a system's existence there is no stage at which it is absent or unchanging. Observation is not a condition of change, and non-detection does not establish non-change.
The Causal Realization Principle requires a nonempty set of actual physical contributors without requiring determinism, uniqueness, or one universal mechanism. Time, stage, and order are not causes.
Change has three classes of contributors: the internal structure and properties of the changing system; influencing physical systems, which remain systems and cannot be enumerated; and physical factors, which have no structural constitution or identity range and whose families are listed near-exhaustively. A medium, body, lattice, or boundary is a system; its temperature or pressure is a state of that system, not a factor. Influences do not act singly: they combine qualitatively, under an environment that differs from place to place.
Every contributor is realized at the stage of the change it contributes to, and an external influence acts only as it reaches the system, by contact or through a physical pathway. The Sun influences a system on the Earth at the stage at which its radiation and gravitational field arrive, a later stage than the one at which they left it; the passage is not counted in stages, and the stage that bears on the change is the stage of arrival. The same influence produces different changes in different systems, according to constitution, cohesion, susceptibility, capacity, thresholds, and kind; it may be supportive or adverse. The variation of a factor is not counted as change.
Each physical system has a realized identity range IA in the common domain. At its ending, the cumulative resultant of its earlier change and its final change are present together at one and the same stage. The ending of one system does not stop the succession or the change of any other.
A successor exists only where a new identity is physically produced. Absorption into a persisting system ends the absorbed identity without a successor; the absorbing system may change its character or keep it, and retains its numerical identity either way. Universal eventual ending of every system is an optional module, not a core commitment.
Constituents, subsystems, and composites coexist at the same common stage. Composition does not transfer state, change content, causation, numerical identity, or history between levels. Across stages, the population of the universe gains, loses, absorbs, and transforms identities within one ordering.
Composition is physical organization, not temporal hierarchy, and population change is not motion through a temporal container.
Spatial relations hold among systems realized together at one stage; the earlier–later order relates distinct stages. A coordinate tuple that merges the two into one homogeneous type does not preserve this distinction. Two states belong to one cosmic moment only at one and the same stage.
Systems far apart are co-present at the same stage without spatial coincidence. Records do not identify stages, because change never stops, so an actual comparison is made at the stage of reception, between a received record and a local state.
Sample, apparatus, detector, record, observer, and laboratory are physical systems of the universe, and they change under UCC. Because change continues in everything, the stage at which a change first appears cannot be identified. A clock is a physical system made of matter: vibration, heat, pressure, shock, motion, and gravitational conditions act on its bearer and record chain.
Observed light deflection is a property of a signal path or of its reconstruction, attributed to declared contributors: medium, gravitational relation, motion and rotation, scattering and refraction, and transmission. Rotation is one contributor, not the explanation of every deflection. “Bending of time” is a type error, because time carries no direction or curvature.
The geometric reading of relativity has no time for the whole universe: it assigns a proper time to each worldline and a coordinate time to each chart, and a global time function, where one exists, is one choice among infinitely many. ITOF affirms what that reading denies: one global time, without reservation. The proper and coordinate times are kept as quantities of clocks and charts, and each phenomenon is read through its bearers, conditions, model, prediction map, and records.
The Lorentz transformations are derived from homogeneity, isotropy, the relativity principle with reciprocity, record-order preservation, and continuity, with no premise about time, CMA, or UCC. Under identical physics ITOF is empirically equivalent to special relativity; the equivalence concerns records and does not qualify the global time. CMA entails a frame-independent co-presence that no record determines, and any association σ of events with stages preserves the causal order strictly. Differential ageing is a different amount of change between the same common stages, not “less time”; a horizon is a coordinate divergence, not a stop of change.
Curved, warped, dilated, contracted, stretched, compactified, and bent are not false of time but inapplicable to it; each belongs to a definite bearer: model geometry, clock and rod records, received light, or signal paths. Spacetime represents the gravitational relation among physical systems; time is not a component of a physical spacetime entity.
The succession of change is never reversed, along a closed timelike curve or through a wormhole or warp-drive time machine; consistency paradoxes therefore have no physical realization. Records do not require a geometry of time, and predictive success does not transfer to a physical property of time; mathematical consistency does not establish physical existence, including that of higher dimensions.
UCC does not contradict the mathematics of stationary states. An exactly isolated eigenstate is an idealization: the influences acting on a realized system are not constant. By the equivalence principle a uniform gravitational field produces no local change in a freely falling system; the tidal part, which moving and distant masses always produce, does. A ground state certified under complete isolation is where UCC is exposed to adverse evidence.
A global phase is not counted as change, and finite measurement yields bounds, not certified zeros. The constitution-dependent clock hypothesis HCR has the clock bound kα = (14 ± 11) × 10−9; in its minimal field model the MICROSCOPE test gives |kα| < 3.4 × 10−12 (95%), below its withdrawal threshold. A result for HCR does not test the governing commitments.
V40/F20 keeps one non-metric, non-causal temporal referent and assigns every other content to the commitment that states it: common stages to temporal constitution, unity to CMA, uninterrupted change to UCC, causes to CRP, and every quantitative relativistic result to independently warranted physics.
The governing division is exact: time is the global succession; temporal constitution makes every stage a stage of change; CMA forbids private stages; UCC requires uninterrupted change; CRP assigns every change to physical causes. No one of them substitutes for another, and none makes time a cause.