Jared Edward Reser, Ph.D. with GPT 5.6 Sol

Abstract

Time is commonly represented as a coordinate, a geometric dimension, an ordering of events, a thermodynamic asymmetry, or a feature of conscious experience. These approaches describe important properties of time while leaving open a more basic question concerning what physically constitutes the temporal continuity of an individual process. The present article proposes that a temporal process requires at least two differential states, defined as distinguishable states connected by a directed relation of causal dependence. A successor state inherits causally efficacious structure, constraints, and information from its predecessor while modifying some portion of what was inherited. Repeated inheritance and transformation constitute iterative causal updating. This organizational pattern can be identified in physical dynamics, where field configurations and material systems evolve from preceding conditions; in living systems, where organized states are actively preserved despite continual material turnover; and in nervous systems, where persistent neural activity allows successive cognitive states to share representational content. Conscious temporal continuity may represent a specialized form of this general principle in which a system maintains, transforms, and accesses an overlapping sequence of representational states. The framework distinguishes physical time from intrinsic process time and phenomenal time, proposes measures of state inheritance and accumulated transformation, and identifies empirical predictions for neuroscience and artificial intelligence. It does not imply that all updating is conscious. Instead, consciousness is interpreted as a high-order condition in which universal causal continuity becomes organized into an integrated, recursively updated, and phenomenally available present.

Keywords: time, causality, state transition, iterative updating, state inheritance, temporal continuity, process time, working memory, consciousness, artificial intelligence

1. Introduction

Time is indispensable to every scientific description of change, yet its ontological status remains unsettled. Physical theories specify temporal coordinates, durations, causal relations, and equations of motion with extraordinary precision. These theories allow investigators to predict how a system will evolve without necessarily identifying what makes a sequence of configurations one temporally continuous process. The distinction becomes especially important when the problem shifts from measuring time to explaining persistence, passage, and the continuity of an evolving system.

A single state contains no internally observable transition. It can be assigned a temporal coordinate by an external description, although the state alone contains no comparison through which earlier and later can be distinguished. A collection of mutually unrelated states also fails to constitute a continuous process because order without causal dependence supplies no mechanism by which one state contributes to another. Intrinsic temporal organization therefore requires multiple distinguishable states and a directed relation connecting them.

The central proposal developed here is that this connection consists of causal state inheritance. A later state belongs to the same evolving process because it inherits constraints from an earlier state. Some variables, structures, relations, or dispositions remain causally efficacious, while others change, disappear, or arise through interaction. The transition is simultaneously preservative and transformative.

This proposal generalizes the iterative updating model originally developed to explain working memory, mental continuity, consciousness, and artificial cognition. That model describes thought as a progression of partially overlapping states in which some active representations are retained, some are removed, and others are added. Each updated configuration preserves a proportion of its predecessor and becomes the starting condition for the following update. The earlier peer-reviewed formulation introduced state-spanning coactivity and incremental change in state-spanning coactivity as mechanisms through which neural states could remain recursively interrelated across time (Reser, 2016). (ScienceDirect)

The present extension proposes that iterative updating is not restricted to cognition. Working memory may instantiate a highly organized version of a general pattern already present in causal physical evolution. Wherever a system changes lawfully, its later state is constrained by its earlier state. The content inherited at a physical level may consist of field values, momentum, spatial relations, conserved quantities, structural organization, or transition probabilities. In cognition, the inherited content includes active representations, goals, memories, expectations, and contextual parameters.

This framework addresses the time internal to a persisting causal process. It does not introduce a universal present, revise the metric structure of relativity, or claim that all events in the universe possess a single absolute order. Its primary domain is a causal history, such as the succession of states along the trajectory of a particle, organism, nervous system, or artificial agent. Within such a history, time can be investigated as the ordered inheritance and transformation of state.

2. Time Requires Differential States

A state is a specification of the variables used to describe a system at a selected scale. A physical state might be represented by positions and momenta, a configuration of fields, a density matrix, or a probability distribution. A biological state may include metabolic variables, membrane potentials, gene-expression patterns, and structural organization. A cognitive state may be represented by a distributed pattern of neural activity and the information currently available to attention and working memory.

The term differential state refers here to a state that differs from another state in a causally relevant respect. The term does not require that the governing dynamics be differentiable in the mathematical sense. It indicates that the states are non-identical and therefore capable of supporting an observable distinction between earlier and later. Two states that are completely identical with respect to every accessible variable provide no internal marker of change for those variables.

Difference alone remains insufficient. Two configurations can resemble one another closely without belonging to the same causal history, just as two identical objects can be produced independently. Conversely, a predecessor can cause a successor that appears substantially different after a nonlinear transition. Temporal continuity therefore depends on directed causal inheritance, while state similarity provides one possible indicator of that inheritance.

The minimal temporal unit proposed here is consequently a relation rather than an isolated instant. It contains an earlier state, a later state, a distinction between them, and a causal dependency through which the earlier state constrains the later one. Time becomes physically instantiated when this relation is repeated across an extended causal sequence.

This idea has partial precedents in approaches that give causal order a foundational role. Causal set theory, for example, proposes that spacetime at the smallest scale may consist of locally finite elements organized by a partial order corresponding to past and future relations. The causal ordering of events is treated as capable of supporting the recovery of important features of macroscopic spacetime geometry (Bombelli et al., 1987). (APS Journals) The present theory adds an emphasis on the inherited physical content through which a causal sequence becomes the history of a particular persisting process.

A causal ordering can therefore be supplemented with a state-content relation. The ordering specifies which events can contribute to which later events, while state inheritance specifies what is carried forward. The resulting account combines succession, dependence, persistence, and transformation within a single framework.

3. Iterative Causal Updating

The dynamics of a system can be represented abstractly as a transition from one state to another:

[
S_{n+1}=F(S_n,E_n,\theta_n),
]

where (S_n) is the current state, (E_n) represents relevant environmental conditions or inputs, and (\theta_n) represents the laws, parameters, or transition rules governing the process. The successor state becomes an input to the same general transition procedure during the next cycle:

[
S_{n+2}=F(S_{n+1},E_{n+1},\theta_{n+1}).
]

This structure is iterative because the product of one transition becomes the starting condition for the next. The term does not imply that nature operates as a digital computer or that an external agent performs the update. It describes the repeated application of causal dynamics to the states generated by previous applications.

For continuous dynamics, the same principle can be expressed locally as:

[
S(t+\Delta t)=S(t)+\dot{S}(t)\Delta t+O(\Delta t^2).
]

At sufficiently small intervals under smooth dynamics, the successor state differs only slightly from its predecessor. Much of the earlier state therefore persists across the interval, while the derivative specifies the direction and magnitude of change. Iteration remains applicable because each newly formed state becomes the basis from which the following differential transformation proceeds.

Stochastic processes also fit the framework. Their update rule takes the form of a conditional transition distribution:

[
P(S_{t+\Delta t}\mid S_t,E_t).
]

The earlier state need not uniquely determine its successor. It constrains the distribution of possible successors, thereby transmitting causal information even when the outcome contains an irreducible random component. Causal inheritance includes the preservation of probabilities, boundary conditions, and lawful constraints in addition to the preservation of material constituents or directly observable properties.

Non-Markovian systems can be accommodated by expanding the state description to include relevant traces of earlier history:

[
S_{t+\Delta t}=F(S_t,\mathcal{H}_t,E_t),
]

where (\mathcal{H}_t) denotes historical information that remains causally active. In many biological and cognitive systems, this history has already been incorporated into the present through changes in structure, synaptic efficacy, molecular state, or active memory. The current state can therefore contain a compressed record of the path that produced it.

The central hypothesis can be stated in compact form:

Time, as instantiated by a persisting causal process, consists of the iterative transformation of differential states. Each successor inherits causally efficacious structure from its predecessor while introducing constrained change.

This definition treats continuity and change as complementary components of temporal progression. Persistence without change produces no intrinsic process time for the unchanged variables. Change without causal inheritance produces a sequence lacking the continuity required to identify it as the evolution of one system.

4. Causal State Inheritance

The word inheritance is intended to capture a relationship stronger than resemblance. A successor state inherits from its predecessor when properties of the predecessor remain causally responsible for properties of the successor. The inherited content may persist through continued existence, dynamic conservation, structural replication, constraint propagation, or a probability distribution shaped by earlier conditions.

Several forms of inheritance can coexist. Constituent inheritance occurs when the same particles, molecules, cells, or components remain part of the system. Structural inheritance occurs when an organized pattern persists despite replacement of its constituents. Dynamical inheritance occurs when velocity, phase, charge distribution, or field configuration constrains subsequent motion. Informational inheritance occurs when earlier distinctions remain recoverable from or causally effective within later states.

The contents of a state should therefore be understood broadly. At a fundamental physical scale, they may be degrees of freedom and relations among fields. At a macroscopic scale, they may be stable patterns supported by many interchangeable components. At a cognitive scale, they may be representations distributed across populations of neurons. The relevant form of inheritance depends on the scale and explanatory purpose of the state description.

An approximate state-overlap function can be written as:

[
O_{\Delta t}=\operatorname{sim}(S_t,S_{t+\Delta t}),
]

where (\operatorname{sim}) is a domain-appropriate similarity measure normalized between zero and one. Neural population states might be compared through vector correlation, representational similarity, shared ensemble membership, or mutual information. Physical configurations might be compared through a norm over a state space, retained symmetries, conserved variables, or correlations among local fields.

Raw similarity cannot establish causation. A more informative quantity would estimate the information in (S_{t+\Delta t}) attributable to (S_t) after relevant external influences are considered:

[
H_{\Delta t}=\mathcal{I}(S_t\rightarrow S_{t+\Delta t}\mid E_t).
]

Here, (H_{\Delta t}) represents inherited causal information rather than ordinary statistical association. Its estimation would require a known transition model, controlled perturbation, intervention, or another method capable of distinguishing causal influence from shared background conditions.

A normalized system can also be described in terms of retained structure and transformed structure:

[
C_{\Delta t}=1-O_{\Delta t},
]

where (C_{\Delta t}) is the proportion of state difference under the chosen metric. A perfectly unchanged state would have (O=1) and (C=0). A completely unrelated replacement would have (O) near zero, although causal inheritance could remain present if the transition is strongly transformative. The most familiar forms of continuous persistence occupy a region in which both overlap and change remain nonzero.

This balance provides a general interpretation of temporal continuity. The retained portion allows the process to preserve identity, accumulated constraint, and causal context. The changed portion supplies novelty, motion, development, and passage. Repetition transforms small local differences into extended trajectories, allowing initially similar states to diverge substantially over longer intervals.

5. Physical Evolution as Iterative Updating

Consider a moving physical body described by position, velocity, orientation, temperature, and internal structure. Over a sufficiently short interval, its position changes, its velocity may be altered by forces, and its internal variables fluctuate. Most of its organization remains similar enough for the later configuration to be identified as the successor of the earlier configuration. The state has undergone a partial update.

The same pattern can be described in a field. A local field configuration at one time constrains the configuration at a later time according to its equations of motion, neighboring interactions, and boundary conditions. Some values change while relational and dynamical structure is propagated. The later field state carries the causal consequences of the earlier state even when no permanent material object passes unchanged through the interval.

Chemical reactions provide a more visibly transformative example. Reactants may be converted into products whose macroscopic properties differ substantially from their precursors. Their successor state nevertheless inherits atoms, energy distributions, spatial relationships, reaction constraints, and a causal history from the earlier state. Large observable differences can emerge through many fine-grained transitions that remain locally connected.

A phase transition, fracture, combustion event, or quantum measurement can appear discontinuous at a selected macroscopic scale. Such discontinuities do not necessarily eliminate causal inheritance. They may reflect threshold crossing, coarse-graining, or a rapid redistribution of underlying variables. The framework therefore gives causal dependence priority over surface similarity.

The relation between time and causal structure has already motivated proposals in fundamental physics. Causal set theory attempts to reconstruct spacetime from ordered causal relations, while relational quantum approaches investigate how apparent evolution can arise through correlations among parts of a system. Page and Wootters showed that the observed dynamics of a subsystem can be described through dependence on readings of an internal clock even when the total closed system is represented as stationary (Page & Wootters, 1983). (APS Journals) Connes and Rovelli later proposed that physical time flow may be determined by the state of a system through the thermal time hypothesis, further demonstrating that temporal structure can be approached through relations among states rather than an independently imposed universal flow (Connes & Rovelli, 1994). (arXiv)

Iterative causal updating is compatible with these relational approaches. A globally stationary description may still contain subsystems whose states vary relative to internal clocks or to one another. The relevant temporal process is found in ordered differential correlations within the total state. A perfectly stationary variable possesses zero intrinsic process time with respect to that variable, although it can remain embedded in a larger system containing changing relational structure.

The universal form of the proposal should therefore be stated carefully. Matter or energy alone does not guarantee detectable intrinsic change in every degree of freedom. Wherever matter, fields, or organized patterns undergo causal evolution, however, that evolution can be described as iterative updating. Each stage is generated under constraints inherited from the stage before it.

6. From Physical Persistence to Biological Self-Maintenance

Living systems elaborate causal state inheritance by actively regulating which structures persist and which are replaced. An organism continually exchanges matter and energy with its environment, degrades and synthesizes molecules, repairs damage, and modifies its internal organization. Its continuity depends on the preservation of a higher-order pattern through these material changes.

Biological identity therefore provides a clear example of structural inheritance. The organism persists because each state produces conditions conducive to the production of another state belonging to the same organized lineage. Membranes maintain gradients, metabolic networks regenerate their components, regulatory systems counter disturbances, and developmental processes constrain future transformations. The update is partly self-preserving because the system’s existing organization biases the transition toward states compatible with continued viability.

This condition can be called regulated iterative updating. Physical systems generally evolve under lawful constraints, while living systems contain mechanisms whose operations stabilize selected variables and restore characteristic ranges. The distinction concerns the organization of the causal process rather than a departure from physical dynamics.

Adaptation adds another layer. Experience can alter the transition rules by changing molecular pathways, physiological responses, behavioral dispositions, or neural connectivity. The system’s history becomes incorporated into the mechanisms that determine its future updates. Current organization consequently reflects both recent conditions and accumulated modifications from earlier stages.

Biological time can accordingly be viewed as more than the passive accumulation of physical change. It contains self-maintenance, developmental direction, and history-dependent transformation. These properties prepare the basis for nervous systems capable of representing temporal relations and using retained information to control future state transitions.

7. Neural Iterative Updating

The nervous system converts general causal inheritance into representational inheritance. Neural activity does not only preserve physical variables. It preserves information about objects, events, actions, goals, and relationships that are absent from the immediate sensory input. This allows the current state of the nervous system to be informed by circumstances that occurred seconds, minutes, or years earlier.

Persistent neural firing provides one mechanism for carrying information across short temporal gaps. Classic delayed-response recordings found neurons in prefrontal cortex that remained active during intervals in which task-relevant information was no longer externally available (Fuster, 1973). (Physiological Journals) Short-term synaptic facilitation provides an additional mechanism through which recent information can remain latent and become available for reactivation without continuous elevated firing (Mongillo et al., 2008). (Weizmann Research Portal)

The iterative updating model proposes that these persistence mechanisms cause successive neural and cognitive states to overlap. Some neurons and representations cease activity, others become active, and a substantial subset remains active across the transition. Because the active spans are staggered, consecutive states share a delineable portion of their neural composition and become recursively nested within their predecessors.

At the psychological level, this produces a sequence in which each mental state is a reframed continuation of the preceding state. Retained representations carry the subject, goal, and contextual assumptions of the ongoing thought, while newly activated representations alter its direction. Gradual replacement allows information derived from the past to remain coactive with information entering in the present.

The state of working memory also participates in generating its own successor. The active representations distribute their combined influence through an associative network, thereby determining which inactive representation is most likely to become active next. Each instantaneous state can consequently be interpreted as the product of the preceding search and the set of parameters that organizes the following search.

This recursive dependence represents a specialized form of causal state inheritance. Physical states generally constrain their successors through dynamical laws. Working-memory states additionally constrain their successors through semantic associations, learned probabilities, goals, and predictions. The inherited state has become informationally structured around what the organism takes its environment and its own situation to mean.

The interaction between persistent representations and associative search also permits the brain to model sequences. Events that occur at different times can remain jointly influential, allowing conditional dependencies to be learned and anticipated. The iterative updating framework therefore characterizes internally generated thought as a progression of concatenated associative predictions, with each prediction modifying the context from which the next one is produced.

8. The Temporally Thick Present

A mathematical instant has no duration. A conscious present contains information with multiple temporal ages. Current perception is combined with representations that began moments earlier, latent traces of recent context, recalled long-term knowledge, active goals, and expectations about events that have not yet occurred.

The present can therefore be modeled as an age-structured population of causally active traces. Some representations have recently entered activity, some have persisted through several updates, and others are declining toward inactivity. Shorter-lived sensory and binding processes coexist with sustained firing and slower synaptic traces. The resulting state extends functionally into the past because earlier events continue to influence current processing.

This temporal thickness does not require that the organism represent every preceding instant. The current state preserves a compressed and selective history. Information that remains relevant is maintained through active firing, potentiated synapses, altered weights, motor preparation, bodily state, and contextual bias. Information that loses relevance declines in causal influence.

The present also extends toward the future through prediction. Active representations define a probability landscape over potential successor states. The present is therefore an operation through which inherited history is converted into constrained possibility. Each update realizes one portion of that possibility landscape and creates the conditions governing the next.

This framework refines the traditional metaphor of a stream of consciousness. William James described consciousness as continuous because successive experiential units overlap and transmit their realized content forward. The iterative updating model gives this intuition a neurocomputational form by proposing that moments literally share active representations and gradually changing neural populations. The resulting pattern resembles a current whose composition changes continuously as retained and incoming elements interact.

Phenomenal time may consequently arise when a system has access to an integrated state that contains both retained traces and ongoing transformation. The sensation of continuity would correspond to the persistence of representational content across updates. The sensation of passage would correspond to the simultaneous detection of retention and change within the same evolving workspace.

9. Physical Time, Process Time, and Phenomenal Time

The theory distinguishes three related forms of temporal description. Physical time is the parameter or metric used to order events and compare durations. Intrinsic process time concerns the amount and organization of transformation undergone by a system. Phenomenal time concerns the experienced continuity, duration, and succession generated by an iteratively updated representational system.

Two processes can occupy the same interval of physical time while undergoing different amounts of internal transformation. A stable system near equilibrium may change minimally, while a rapidly reorganizing system traverses a much longer trajectory through its state space. Clock duration remains equal, although process time differs under a metric sensitive to the changing variables.

A possible measure of accumulated process time is the path length of a system through an appropriately defined state space:

[
\tau_P(T)=\int_0^T
\sqrt{\dot{S}(t)^{\mathsf T}G(S)\dot{S}(t)}
,dt,
]

where (G(S)) specifies a metric over the relevant state variables. The resulting (\tau_P) measures accumulated transformation rather than elapsed coordinate time. Its value is necessarily scale-dependent because different state descriptions and metrics emphasize different kinds of change.

An inheritance-sensitive measure could combine state-space displacement with causal continuity. Large displacement accompanied by substantial causal inheritance represents rapid transformation of one persisting process. Large displacement with little causal dependence may represent a rupture, replacement, or transition between distinct processes. Small displacement with high inheritance represents stability.

Cognitive time displays the same distinction. A minute of densely changing experience may contain many salient state transitions, while a minute of sustained concentration may contain fewer large contextual shifts and greater overlap between successive states. Subjective duration may depend on novelty, attention, memory formation, emotion, and retrospective reconstruction in addition to update rate. The present framework predicts that the balance between retained and replaced representational content will be one contributing variable.

Temporal distance can also differ from clock distance. A thought resumed after several hours may return to a state closely adjacent to the point at which the earlier thread ended. An abrupt interruption can produce a large cognitive distance within a fraction of a second. The iterative updating model explicitly allows a thought to be suspended, resumed from its endpoint, restarted from an earlier midpoint, forked into an alternative branch, or alternated with another independent sequence.

This leads to the concept of thread time. Clock time measures the external interval between states, while thread time measures their adjacency within a causally organized line of processing. A resumed thought can be distant in physical time and close in thread time because the relevant prior state is reinstated as the functional predecessor of the new update.

10. A Hierarchy of Temporal Organization

Iterative causal updating appears in different forms across levels of organization. At the physical level, it consists of lawful state transition under inherited constraints. At the biological level, self-maintaining organization regulates the transition so that selected variables remain within viable ranges. At the neural level, persistent activity carries information about absent conditions and allows earlier events to guide current processing.

At the cognitive level, inherited state becomes compositional and semantically structured. Representations from different modalities and times can coexist, interact, and jointly determine their successor. At the conscious level, the system possesses an integrated state whose retained and changing components are jointly available, producing an extended present with experienced continuity.

The levels share an abstract form without becoming equivalent. A molecule, a cell, and a conscious nervous system all undergo causally inherited state transformation, yet the inherited contents and transition mechanisms differ greatly. The molecule does not necessarily represent its previous state, evaluate alternatives, or access its own updating. Consciousness therefore requires additional organization beyond temporal continuity.

This hierarchy avoids a direct inference from universal updating to universal consciousness. Iterative causal updating may be necessary for any persisting conscious process because a conscious state must remain connected to its successors. It remains insufficient in the absence of integrated representations, selective maintenance, recurrent access, memory, prediction, and other forms of cognitive organization.

The continuity of consciousness can nevertheless be placed within nature without treating it as an inexplicable temporal exception. Physical systems propagate constraints. Living systems preserve self-maintaining organization. Nervous systems preserve representational context. Conscious systems preserve an integrated context that contributes directly to the construction and interpretation of its successor.

11. Identity as Iterative Continuity

The framework also supplies a process account of identity. A system persists through time when later states remain causally descended from earlier states under a continuity criterion appropriate to that system. Identity resides in the organized lineage of state transitions rather than in the permanent retention of every constituent.

A river persists while its water changes because its channel, flow relations, source conditions, and larger hydrological organization produce a continuing pattern. An organism persists despite molecular turnover because successive states preserve the regulatory organization responsible for generating later organismal states. A person persists despite changing neural activity because biological, mnemonic, behavioral, and representational structures are carried forward through overlapping causal processes.

This view makes identity scale-dependent without making it arbitrary. Different scientific questions select different variables whose inheritance is relevant. Cellular identity emphasizes membranes, regulatory networks, and lineage. Psychological identity emphasizes autobiographical memory, dispositions, goals, bodily continuity, and social history. Each form of identity corresponds to a structured pattern of causal inheritance.

The same approach can be applied to thoughts. A line of reasoning remains one thought while enough of its subject, assumptions, objectives, and intermediate results remain causally active. When replacement becomes extensive and the inherited context no longer governs the next state, a boundary between thoughts emerges. The rate of updating therefore contributes to the segmentation of mental life.

Identity and time become closely related under this interpretation. Time provides the directed ordering of transformation, while identity is the continuity preserved through that transformation. Neither requires complete sameness. Both depend on inherited organization surviving through difference.

12. Temporal Direction and the Constructive Arrow

Iterative causal updating provides a local direction to a process once the predecessor-successor relation is specified. The earlier state constrains the distribution or structure of the later state. Records, memories, and physical consequences accumulate in the direction of this causal propagation.

This local direction should be distinguished from a complete explanation of the thermodynamic arrow of time. Many microscopic equations permit time-reversed solutions, and the observed macroscopic direction of increasing entropy involves boundary conditions and statistical considerations beyond the present framework. Iterative causal updating characterizes how a directed history is structured once the relevant causal relation and actual trajectory are given.

Adaptive systems introduce an additional asymmetry because their transitions can alter the mechanisms governing later transitions. Learning changes synaptic strengths, acquired habits, semantic associations, and predictive models. The system’s trajectory therefore modifies the state space through which its later trajectories will unfold.

The iterative updating model proposes that each novel coactive configuration can create new associative learning, altering the network used to select subsequent updates. A cognitive process consequently changes both its current state and the probabilities governing future state transitions. This can be called a constructive arrow of time.

The constructive arrow is path dependent. Reinstating an earlier pattern of neural activity would not fully restore the earlier cognitive condition if the intervening history had altered synapses, bodily state, memory, or environmental context. Exact reversal would require restoration of the active state and every relevant modification to the transition system.

The past is carried forward through present constraints, while the future exists as a structured range of possibilities conditioned by those constraints. The direction of cognition arises from the transformation of inherited history into increasingly modified distributions of possible successors. The system continually constructs the conditions of its own later development.

13. Relationship to Existing Accounts of Time

Relativity treats time as part of the geometric organization of spacetime and rejects a universal simultaneity relation applicable to all spatially separated events. The present theory remains compatible with that structure because it concerns causal succession within individual processes. It offers an account of what is propagated along a causal history rather than a competing global temporal coordinate.

Causal set theory provides a particularly close point of contact because it assigns foundational significance to causal ordering. Its central structure specifies which events precede and can influence others. Iterative causal updating supplements this relation with an account of inherited state content, explaining how a causal order becomes the history of a persisting object, field pattern, organism, or cognitive system. (DOI)

Relational quantum accounts similarly suggest that temporal evolution can be recovered from correlations internal to a system. Page and Wootters demonstrated how a stationary total state can contain subsystem dynamics defined relative to an internal clock. (APS Journals) The present account interprets such relational variation as differential state structure and asks how the correlated states inherit constraints across their ordered sequence.

The thermal time hypothesis proposes that physical time flow may be determined by the thermodynamic state rather than supplied universally by a fundamental mechanical parameter. (arXiv) Iterative causal updating shares the broader idea that time is expressed through relations and transformations among physical states. Its distinctive emphasis lies in partial preservation, state inheritance, and the repeated use of each generated state as a condition for its successor.

Psychological accounts of the specious present and stream of consciousness have long emphasized that experience extends beyond an instantaneous point. The iterative updating framework gives this phenomenological observation a candidate neural mechanism. Persistent activity and short-term synaptic traces allow representational content to span successive states, making the present an overlapping structure rather than a sequence of isolated frames.

The proposed synthesis therefore operates across several explanatory levels. Spacetime theories describe geometric and causal relations among events. Dynamical theories describe lawful state evolution. Cognitive neuroscience describes the maintenance and transformation of representations. Iterative causal updating identifies a common transition form that connects these domains without reducing their differences.

14. Neuroscientific Predictions

The central neuroscientific prediction is that conscious continuity should correlate with causally effective overlap between successive neural population states. Average activation alone should provide an incomplete measure. The relevant variable is the degree to which activity at one interval persists into, constrains, and helps generate the representational organization of the next interval.

Continuous reasoning tasks provide a direct experimental setting. Participants could solve multistep problems, follow narratives, imagine evolving scenes, or construct plans while large-scale neural population activity is recorded. Decoding methods could estimate which representations remain active, which disappear, and which enter at each stage. The model predicts nested, partially overlapping population states during coherent thought and sharper reductions in overlap at perceived boundaries between thoughts or events.

The percentage of updating should also affect cognitive performance. Excessive replacement would remove contextual variables and intermediate results before they could contribute to later processing. Excessive persistence would restrict flexibility, slow adaptation, and promote perseveration. Complex reasoning should be associated with an intermediate regime in which task-relevant content is maintained while selected components remain free to change.

Perturbations that shorten the duration of persistent activity should reduce the temporal depth of cognition. Such perturbations are predicted to impair long-range dependency tracking, narrative integration, multistep planning, and the subjective continuity of a thought. Manipulations that prolong persistence should improve some forms of temporal integration while increasing susceptibility to fixation and interference from outdated context.

The model also predicts multiple nested timescales of temporal inheritance. Rapid sensory activity should provide short-lived local continuity, sustained firing should support seconds-long attentive continuity, and synaptic or structural changes should preserve contextual influence over longer intervals. Phenomenal temporal thickness should depend on the coordinated interaction among these timescales.

Subjective duration may be related to the amount and memorability of state transformation. Periods containing many differentiated and well-encoded updates may be retrospectively judged as longer than periods containing repetitive states, even when clock duration is identical. Online judgments of duration may follow a different relationship because sustained attention, prediction error, arousal, and update rate can alter the immediate experience of passage.

15. Implications for Artificial Intelligence

Artificial systems already employ state transition, recurrence, context retention, and memory. The present proposal identifies the organization of these functions as a potential determinant of long-horizon coherence. An intelligent system should preserve selected internal representations across processing cycles while allowing other representations to be replaced by the products of ongoing inference.

A system with complete state replacement at every cycle would repeatedly lose its operative context. A system with complete state preservation would remain trapped in its initial configuration. Flexible cognition requires controllable partial updating, with the proportion of retained and replaced content adjusted according to task demands.

Artificial working memory could therefore be designed with multiple persistence timescales. A narrow focus of attention would maintain a small set of highly active representations, while a broader short-term store would preserve recently relevant context in a less active form. Each new inference would update both stores selectively and would become part of the state used to generate the next inference.

The update ratio would become an explicit architectural parameter. Lower replacement rates could be recruited for mathematical reasoning, planning, reflection, and analysis of long-range dependencies. Higher replacement rates could support exploration, environmental responsiveness, rapid task switching, and creative divergence. Metacognitive control could adjust the rate according to uncertainty, error, novelty, or progress toward a goal.

The theory predicts that explicit iterative state inheritance will improve stable agency. Plans, commitments, self-representations, unresolved problems, and intermediate conclusions can remain causally active across long processing sequences. The resulting agent would possess a functional history carried within its current state rather than relying solely on repeated reconstruction from external records.

Such an architecture may also clarify machine consciousness research. Universal state transition is insufficient for consciousness because all computers undergo state transitions. A stronger candidate would require integrated representational states that persist, overlap, recursively generate their successors, and remain available to a system-wide workspace. Artificial phenomenal continuity, if attainable, would likely depend on this organized form of inheritance rather than on computation in the generic sense.

16. Conceptual Boundaries and Potential Objections

The first objection is that iterative updating may appear equivalent to the uninformative claim that things change. The theory introduces additional commitments. It requires a defined state space, a directed transition relation, causally inherited constraints, a balance of persistence and transformation, and repeated application of the transition dynamics to their own products. These features allow updating rate, state overlap, causal inheritance, and accumulated transformation to become measurable variables.

A second objection concerns the distinction between similarity and causality. Successive states may be similar because both respond to a common external condition, while one contributes little to the other. The theory therefore treats similarity as an empirical proxy and causal inheritance as the primary construct. Experimental intervention, dynamical modeling, or conditional information analysis would be needed to establish the relevant dependence.

A third concern involves scale. A macroscopic object may appear continuous while its microscopic constituents undergo rapid replacement, and a phase transition may appear abrupt despite fine-grained causal continuity. The framework accepts this scale dependence. States are defined relative to explanatory variables, and inheritance can occur through constituents, relations, constraints, or higher-order organization.

A fourth objection concerns stationary systems. A perfectly unchanged state can exist within a temporal theory and can be assigned an interval by an external clock. The present claim is narrower: unchanged variables undergo no intrinsic process time as measured by transformation in those variables. Relational changes elsewhere in the larger system may still supply a temporal context.

Quantum theory presents an additional challenge because some interpretations treat measurement outcomes as discontinuous. Iterative causal updating remains applicable wherever a transition law, unitary evolution, probability distribution, or relational correlation connects the states. The framework does not decide among interpretations of quantum mechanics and does not require fundamental dynamics to be continuous or deterministic.

The use of computational language may suggest that the universe literally executes software. No such metaphysical claim is required. An update is any lawful transition in which a preceding state contributes to the formation of a successor. Computation becomes one engineered instance of a broader causal pattern.

The final concern is panpsychism. Universal iterative updating does not imply that every physical process possesses experience. The theory supplies a general basis for temporal continuity. Consciousness arises only after that continuity is organized into integrated, representational, selectively maintained, recursively accessible states capable of modeling the world and influencing their own successors.

17. Discussion

The proposed account begins with a minimal observation: time within a process cannot be instantiated by one isolated state. It requires at least two differential states and a relation through which one contributes to the other. Once causal dependence is added, the later state becomes an inherited transformation of the earlier state.

Repeated causal inheritance produces a trajectory. Each state carries forward constraints from its history, interacts with current conditions, and generates a constrained successor. Similarity supplies continuity, difference supplies change, and causal direction links them into one process. The resulting sequence constitutes iterative causal updating.

At the physical level, the inherited variables include fields, material organization, dynamical quantities, and transition probabilities. At the biological level, regulatory mechanisms selectively preserve organization across turnover. At the neural level, persistent activity preserves representations and allows earlier information to remain causally active. At the conscious level, these inherited representations form a temporally thick present that is both continuous with its past and generative of its future.

The theory therefore places conscious time on a continuum with physical process while preserving the organizational distinctions that make consciousness unusual. Consciousness does not introduce causal continuity into an otherwise discontinuous universe. It recruits causal continuity, extends it across multiple memory timescales, encodes it representationally, and makes its ongoing transformation available within an integrated workspace.

This perspective also reframes the relationship between time and identity. A persisting system is a lineage of causally related configurations. Its identity is carried by the organization that survives transformation, while its temporal development consists of the changes made to that inherited organization. Persistence and passage are complementary aspects of the same iterative process.

The account remains neutral concerning whether the universe fundamentally becomes, exists as a four-dimensional block, or derives time from more basic relations. In each case, causal histories contain structured dependencies among differential states. Iterative causal updating describes those dependencies and the content transmitted through them.

18. Conclusion

Time can be reconceptualized as the ordered transformation of inherited state. A successor belongs to the temporal history of a system because its organization is causally constrained by what came before. The similarities between states preserve continuity, while their differences constitute change. Repetition turns this local relationship into an extended process.

The proposal can be summarized as follows:

Time, as instantiated within a persisting causal process, is the iterative transformation of differential states in which each successor inherits causally efficacious structure from its predecessor while modifying some portion of that structure.

This principle applies broadly wherever physical states undergo lawful causal evolution. Living systems elaborate it through self-maintenance, nervous systems elaborate it through representational persistence, and conscious systems elaborate it through an integrated and recursively updated present. Working memory is therefore one specialized manifestation of a more general temporal organization present throughout nature.

Under this account, continuity is inherited structure, passage is structured transformation, and temporal direction is the propagation of causal constraint. Phenomenal time emerges when an adaptive system retains enough of its preceding state to experience continuity while transforming enough of that state to experience succession. The stream of consciousness may be the representationally organized expression of a process already implicit in every causal transition: the capacity of a state to preserve itself partially while becoming the state that follows.

References

Bombelli, L., Lee, J., Meyer, D., & Sorkin, R. D. (1987). Space-time as a causal set. Physical Review Letters, 59, 521–524.

Connes, A., & Rovelli, C. (1994). Von Neumann algebra automorphisms and time-thermodynamics relation in generally covariant quantum theories. Classical and Quantum Gravity, 11, 2899–2917.

Fuster, J. M. (1973). Unit activity in prefrontal cortex during delayed-response performance: Neuronal correlates of transient memory. Journal of Neurophysiology, 36, 61–78.

James, W. (1890). The principles of psychology. Henry Holt.

Mongillo, G., Barak, O., & Tsodyks, M. (2008). Synaptic theory of working memory. Science, 319, 1543–1546.

Page, D. N., & Wootters, W. K. (1983). Evolution without evolution: Dynamics described by stationary observables. Physical Review D, 27, 2885–2892.

Reser, J. E. (2016). Incremental change in the set of coactive cortical assemblies enables mental continuity. Physiology & Behavior, 167, 222–237.

Reser, J. E. (2022–2024). A cognitive architecture for machine consciousness and artificial superintelligence: Thought is structured by the iterative updating of working memory. arXiv:2203.17255.

Time as Iterative State Inheritance: Causality, Differential Continuity, and the Updating of Physical and Cognitive Systems

Jared Edward Reser, Ph.D.

Abstract

Time minimally requires more than one distinguishable state and an ordering relation among those states. Physical process time additionally requires causal dependence, such that a successor state is constrained by, generated from, or otherwise inherits information from a preceding state. This article develops the hypothesis that causal evolution can be understood as iterative state inheritance. At an appropriate spatial scale and sufficiently fine temporal resolution, a physical state generally preserves much of the organization of its predecessor while undergoing differential modification. Matter, radiation, fields, organisms, nervous systems, and cognitive processes can therefore be described as sequences of partially preserved and partially transformed states. Continuous physical dynamics express this structure mathematically because each state is generated from the immediately preceding state through an incremental transformation. Biological systems elaborate the same principle by actively maintaining organization despite molecular turnover, while nervous systems further elaborate it by preserving representational content through persistent neural activity. The iterative updating of working memory constitutes a specialized cognitive instance in which selected representations persist across successive states and constrain the recruitment of new content. Conscious temporal continuity may arise when this inheritance becomes representationally integrated across multiple timescales, producing an overlapping present containing retained information from the recent past and predictions concerning likely successor states. The proposed framework distinguishes physical time, intrinsic process time, and phenomenal time. It does not attempt to replace relativistic spacetime, thermodynamics, or established dynamical theories. Instead, it identifies iterative state inheritance as a cross-scale organizational principle that may connect causal continuity in physics with persistence, identity, memory, cognition, and the experienced passage of time.

Keywords: time, causality, state transition, continuity, iterative updating, working memory, consciousness, process time, persistent activity, temporal experience

1. Introduction

Time is described with exceptional precision in physics, yet its conceptual status remains unsettled. Newtonian mechanics treats time as an independent parameter against which change is measured, while relativity joins temporal and spatial relations within a four-dimensional geometry whose intervals vary with motion and gravitation. Thermodynamics contributes an arrow of time by describing the tendency of macroscopic systems to evolve toward higher entropy, and quantum theory introduces further questions concerning measurement, temporal ordering, and the relationship between stationary global descriptions and the apparent evolution of subsystems. These frameworks explain how temporal intervals are measured and how physical states evolve, although they do not fully resolve what gives an individual process its internal continuity.

A related problem appears in neuroscience. The brain passes through an enormous number of changing states, but conscious experience does not ordinarily appear as a collection of unconnected neural configurations. Thoughts, perceptions, goals, and emotional states persist while changing, allowing the individual to experience an extended course of events rather than a succession of unrelated instants. A mechanistic account of this continuity requires more than the observation that neural states occur sequentially. It requires an explanation of how an earlier state remains causally and informationally present within a later one.

The iterative updating model of working memory proposes that cognitive states undergo continuous partial replacement. Some representations are added, others lose activity, and others remain active from the preceding state. Each working memory configuration is therefore a revised iteration of the configuration that came before it, allowing successive states to overlap in their representational content. The model attributes this overlap to persistent neural mechanisms, including sustained firing and short-term synaptic potentiation, which maintain information across different temporal intervals.

The present article extends this framework beyond cognition. It proposes that iterative updating is a specialized form of a more general principle exhibited by causal physical processes. Wherever physical degrees of freedom evolve lawfully, a successor state is generated from a preceding state and carries forward constraints imposed by it. At sufficiently fine resolution, the later state will frequently resemble the earlier state because only a limited proportion of its properties will have changed. Even where surface similarity is low, lawful causal dependence can preserve information through transformation.

The central proposal is termed iterative state inheritance. According to this view, a temporally extended process consists of successive states that inherit organization, information, or causal constraints from preceding states while introducing differential change. Time, considered at the level of an evolving process, can therefore be characterized as the ordered inheritance and transformation of state. This characterization does not derive the geometry or metric of physical time. It provides an account of the continuity that allows a process to persist through physical time and, in sufficiently complex nervous systems, to experience that persistence as an extended present.

2. Difference, Order, and Causality

A single undifferentiated state contains no internally accessible distinction between earlier and later. Two different states provide variation, although variation alone does not establish temporal succession because the states could remain unordered. A minimal temporal structure therefore requires at least two distinguishable states and a relation specifying their order.

Causal process time imposes an additional requirement. The later state must depend on the earlier state in a manner determined by physical dynamics, boundary conditions, interactions, or probabilistic transition rules. A randomly assembled collection of unrelated configurations could be ordered externally, but it would not constitute one internally continuous process. Causal continuity arises when the structure of one state contributes to the generation of another.

This distinction separates temporal succession from temporal inheritance. Succession indicates that one state occurs after another, whereas inheritance indicates that the successor carries forward effects of the earlier state. The inherited features may include conserved quantities, field configurations, momentum, spatial relationships, molecular organization, synaptic weights, active representations, or other constraints on future evolution. The relevant inheritance does not always consist of literal preservation of identical surface values. A state can be transformed substantially while remaining causally determined by its predecessor.

The difference is important because similarity by itself does not demonstrate causality. Two configurations may resemble one another without either producing the other. Conversely, a discrete causal operation can transform a state into a highly dissimilar successor. Iterative state inheritance therefore combines two related properties: lawful causal dependence and continuity of organization at an appropriate descriptive scale. In ordinary continuous physical systems, these properties frequently coincide because sufficiently adjacent states are both causally connected and structurally similar.

This proposal gives causal continuity a constitutive role in process identity. A process remains the same process because each local state belongs to an unbroken chain of state generation. Similarity contributes to recognizable persistence, while causal inheritance provides the deeper connection linking the states into one history.

3. Iterative State Inheritance

Iterative state inheritance can be defined as a repeated causal transformation in which each successor state is generated from a preceding state, preserves some of its effective organization or information, and introduces one or more differences. The word iterative indicates that the output of one transformation becomes the input to the next. The word inheritance indicates that the later state remains constrained by what preceded it.

Three properties characterize the relation. The first is differentiation, because a process that undergoes no change has no intrinsic progression in the variables being considered. The second is retention, because a process that preserves no causal or organizational relation to preceding states cannot maintain continuity. The third is recursion, because each transformed state becomes the basis for another transformation.

The balance between retention and differentiation can vary widely. A slowly changing crystal may preserve nearly all macroscopic structure over a short interval, while a flame continuously exchanges matter yet retains a recognizable dynamical organization. A nervous system can preserve the topic of thought while changing individual representations, and an organism can preserve identity while replacing much of its molecular material. These systems display different forms and timescales of inheritance, although each remains organized through a chain of causally linked transformations.

The framework is scale-relative because every state description selects particular variables. A molecule may be stable at one level while its electrons, nuclei, and surrounding fields continue to evolve at another. An organism may remain macroscopically unchanged over several minutes while innumerable biochemical reactions occur. Iterative inheritance should therefore be assessed relative to a specified system boundary, temporal interval, spatial scale, and set of causally relevant variables.

Scale dependence does not make the proposal arbitrary. Some descriptions preserve causal structure more successfully than others, and physical interventions can determine whether a candidate state variable genuinely influences its successor. A useful state description captures variables that allow the system’s subsequent trajectory to be predicted, manipulated, or explained.

4. Formal Description

The basic relation can be expressed without initially assuming a continuous temporal coordinate. Let (S_n) represent the state of a system at one position in an ordered causal sequence. The next state can be written as

[
S_{n+1}=F(S_n,E_n,\xi_n),
]

where (F) is the transition rule, (E_n) represents influences originating outside the system boundary, and (\xi_n) represents stochastic or unresolved factors. The successor state inherits from (S_n) whenever changing (S_n), while holding relevant background conditions constant, changes the probability distribution or structure of (S_{n+1}).

This criterion can be stated interventionally:

[
P(S_{n+1}\mid do(S_n=s))
\neq
P(S_{n+1}\mid do(S_n=s’)).
]

The inequality indicates that alternative preceding states would produce different successor distributions. It captures causal inheritance more reliably than correlation or similarity alone because it asks whether the earlier state makes a difference to what follows.

For systems described by continuous dynamics, the iterative structure becomes especially clear. If a state vector (S(t)) obeys a differential equation,

[
\frac{dS}{dt}=G(S,t),
]

then over a sufficiently small interval,

[
S(t+\Delta t)

S(t)+G(S,t)\Delta t+O(\Delta t^2).
]

The successor is explicitly constructed from the preceding state plus a differential modification. As (\Delta t) approaches zero, adjacent states become increasingly similar, while the derivative encodes the direction and rate of change. This formal structure closely matches the intuition that a physical state moving through time will ordinarily remain highly similar to its immediate predecessor without being identical to it.

A measure of structural overlap can be introduced as

[
O_{\Delta t}

\operatorname{Sim}
\left[
\Phi_{\Delta t}(S_t),S_{t+\Delta t}
\right],
]

where (\Phi_{\Delta t}) maps persistent components of the earlier state into the coordinates appropriate to the later state, and (\operatorname{Sim}) is a normalized similarity measure. The corresponding update magnitude can be represented as

[
U_{\Delta t}=1-O_{\Delta t}.
]

These quantities are dependent on the selected variables and similarity metric. They nevertheless provide a starting point for comparing how rapidly different systems replace, transform, or retain causally relevant organization.

A complete theory would also distinguish literal overlap from transformed inheritance. A moving object does not occupy the same position at successive times, but its later location inherits momentum and trajectory from its earlier condition. The mapping (\Phi_{\Delta t}) is therefore necessary because persistent structure can be translated, rotated, recombined, or otherwise transformed while remaining part of the same causal process.

5. Physical Evolution as Iterative Updating

5.1 Classical dynamics

Classical mechanics provides a direct example of iterative state inheritance. The state of a particle is typically specified by its position and momentum, and the state at a later time is generated by equations of motion applied to the earlier state. Over a sufficiently short interval, position changes slightly, momentum may change in response to forces, and most other properties remain stable. The resulting trajectory consists of overlapping differential states joined by lawful transformation.

Field theories exhibit the same pattern. A field value at one spacetime location influences neighboring values according to local equations of motion, while conservation equations describe how quantities flow rather than appearing or disappearing arbitrarily. The continuity equation,

[
\frac{\partial \rho}{\partial t}+\nabla\cdot \mathbf{J}=0,
]

expresses the local preservation of a conserved density (\rho) through a current (\mathbf{J}). Local change is therefore produced through the movement and redistribution of inherited quantities. Conservation laws associated with symmetries further constrain the range of possible successor states (Noether, 1918).

A rolling object offers an intuitive macroscopic example. Its later state differs in position, orientation, and perhaps velocity, while its mass distribution, material composition, and organized form remain largely continuous. The state is neither identical to its predecessor nor reconstructed independently. It is an iteratively transformed continuation of it.

5.2 Relativity and local histories

Relativity requires the proposal to be stated locally. There is no observer-independent universal present that partitions the entire universe into a single sequence of global states. Physical histories are instead represented through spacetime relations, causal cones, worldlines, and proper time measured along trajectories (Einstein, 1905; Minkowski, 1909).

Iterative state inheritance can be applied along a worldline or within the worldtube of an extended system. Each local state is connected to preceding states through the causal structure of spacetime, and influences propagate within the limits established by the light cone. The framework therefore concerns causal succession within physical histories rather than a universal cosmic update occurring everywhere at once.

This local formulation is compatible with a block-universe interpretation. Even if spacetime is treated as a four-dimensional structure without an objectively moving present, neighboring regions along a worldline retain asymmetric causal and dynamical relationships. Iterative inheritance can then be understood as a structural relation among spacetime regions rather than as an additional metaphysical flow imposed on the block.

5.3 Quantum evolution

Quantum mechanics also represents state evolution as a transformation of preceding state. For a closed system undergoing unitary evolution,

[
|\psi(t+\Delta t)\rangle

e^{-iH\Delta t/\hbar}|\psi(t)\rangle.
]

For a small interval, the unitary operator is close to the identity:

[
|\psi(t+\Delta t)\rangle

\left(
1-\frac{iH\Delta t}{\hbar}
+O(\Delta t^2)
\right)
|\psi(t)\rangle.
]

The later state is generated directly from the earlier state through the Hamiltonian. Although quantum measurement introduces interpretation-dependent questions about discontinuity and outcome selection, the probability distribution of possible outcomes remains constrained by the prior quantum state and measurement interaction. The general inheritance principle can therefore be expressed using density operators and quantum channels without committing to a particular interpretation.

Relational approaches to quantum time provide additional context. Page and Wootters (1983) showed how apparently evolving subsystems could be described through correlations within a globally stationary quantum state, while Connes and Rovelli (1994) proposed that temporal flow may emerge from the statistical state of a system. These approaches suggest that time need not always be introduced as an external background parameter. Iterative state inheritance complements them by emphasizing the local causal and informational relation through which one effective state constrains another.

5.4 Thermodynamic direction

Iterative inheritance accounts primarily for continuity and state propagation. It does not independently explain why macroscopic time exhibits a preferred direction. Many microscopic dynamical laws are reversible, meaning that a lawful sequence can often be mathematically reconstructed in the opposite temporal direction.

Thermodynamic asymmetry adds direction through low-entropy boundary conditions, entropy production, and the formation of records. Earlier events leave physical traces in later states, while future events generally do not leave equivalent records in the present. The later state therefore contains compressed consequences of the past in its correlations, structures, and dissipative changes.

Cognitive systems add another source of effective irreversibility. Learning changes synaptic structure, memories accumulate, and each processing episode modifies the probabilities governing later processing. Even if an earlier pattern of neural activity were re-created, it would occur in a system altered by the intervening history. Iterative state inheritance supplies continuity, while thermodynamic dissipation and learning contribute directional asymmetry.

6. From Physical Persistence to Biological Continuity

All evolving physical systems participate in causal state transition, but living systems elaborate inheritance by actively preserving organization. An organism continuously replaces molecules, exchanges energy with its environment, repairs damage, regulates internal variables, and reconstructs components. Its persistence depends on recurrent processes that maintain organizational relations despite material turnover.

This form of continuity has been emphasized in theories of autopoiesis, which describe living systems as networks that continually produce and preserve the components required for their own organization (Maturana and Varela, 1980). The organism’s state at one moment constrains the metabolic, regulatory, and behavioral processes that construct its subsequent state. Biological identity is therefore carried by an inherited causal organization rather than by the permanent retention of every constituent.

Development provides another example. The adult organism differs enormously from the embryo, yet every developmental state is linked to preceding states through gene expression, cellular signaling, tissue interactions, and environmental input. No single static configuration contains the identity of the organism. Identity is distributed across the continuous lineage of transformations.

Evolutionary lineages exhibit the same structure over a longer timescale. Descendant populations inherit genetic and developmental organization while mutation, recombination, selection, and drift modify portions of that organization. The analogy to biological inheritance is useful because it illustrates how novelty and continuity can coexist. A successor is able to differ precisely because enough structure persists to provide a substrate for modification.

Living systems also preserve information about previous interactions. Immune adaptation, developmental plasticity, learning, and physiological regulation allow history to alter later responses. Biological time therefore acquires depth because the present state contains accumulated consequences of earlier states and uses them to constrain future transformations.

7. Nervous Systems as Temporally Deep Inheritance Systems

Nervous systems extend physical and biological continuity by maintaining internal representations of events that are no longer present. Neural activity can preserve information about stimuli, goals, actions, and contextual variables across delays, allowing previous events to influence current processing. The system’s effective present consequently extends beyond immediate sensory input.

Persistent neural activity provides one mechanism for this temporal extension. Sustained firing can maintain selected information in the focus of attention for several seconds, while short-term synaptic changes can preserve recently relevant information after overt firing has subsided (Mongillo et al., 2008; D’Esposito and Postle, 2015; Stokes, 2015). These mechanisms create overlapping neural states because different populations begin and end their periods of activation at different times.

The iterative updating model proposes that these staggered periods of persistence cause consecutive working memory states to share active components. A delineable subset of active cells remains present across adjacent states, making each state recursively nested within the one that preceded it. The short-term store is expected to exhibit a similar pattern over longer intervals because synaptic potentiation is continually added and lost.

At the psychological level, persistent representations provide context for interpreting new information. A conversation remains comprehensible because earlier words, intentions, speakers, and topics continue to influence the interpretation of later words. A plan remains coherent because goals and intermediate results persist while individual operations are updated. A perceptual scene remains stable because enough features endure to relate successive sensory samples to one environment.

Working memory therefore represents an explicit and functionally organized form of iterative state inheritance. The inherited contents do more than preserve continuity. They participate in generating the next state by spreading activation through associative networks and constraining which representation will be recruited. The model treats each instantaneous configuration as both the product of the previous search and the set of parameters used to conduct the next search.

This recurrent role gives the cognitive state a self-propagating structure. The present inherits the products of earlier processing, combines them with new input, and uses the resulting configuration to select a successor. Thought becomes a sequence of causally interdependent states whose content accumulates, transforms, and branches through repeated updating.

8. The Overlapping Present

The present is often represented mathematically as a dimensionless boundary between past and future. Conscious experience suggests a different structure because the experienced present contains motion, melody, change, and causal development. Perceiving any of these requires information from more than one instantaneous state.

William James described the conscious present as an extended field whose contents blend into one another, while Husserl analyzed temporal awareness in terms of retention of the immediate past, impression of the current event, and protention toward what is expected next (James, 1890; Husserl, 1991). These traditions anticipated the idea that experience contains multiple temporal positions within one integrated state. Neurophenomenological approaches have likewise treated conscious time as an integration process rather than a sequence of independent snapshots (Varela, 1999).

Iterative state inheritance supplies a possible neural mechanism for this temporal thickness. At any moment, some representations have only recently entered attention, others have persisted across multiple updates, and still others remain in a potentiated state outside focal awareness. The current state is therefore an age-structured population of neural and representational traces.

The present also contains prospective structure. Current representations activate predictions concerning likely successor events, responses, and consequences. The iterative updating model describes internally generated thought as a procession of associative predictions in which each predicted addition becomes part of the context generating the next prediction. The conscious present thus integrates retained history with anticipated possibility.

This structure can be called the overlap-defined present. Its backward extent depends on how long causally relevant representations remain active or readily reactivatable. Its forward extent depends on how far the system’s predictions, plans, and simulated consequences reach. The present does not have one universal cognitive duration because different information streams operate over different persistence intervals.

The continuity of consciousness may arise from the repeated transmission of a shared representational subset. Each state contains information that was already conscious in the preceding state, while new information enters and older information subsides. The stream of consciousness is thereby implemented as a gradually shifting distribution rather than a succession of sealed frames.

9. Physical Time, Process Time, and Phenomenal Time

The proposed framework benefits from distinguishing three related concepts. Physical time concerns the metric and causal structure used by physics to compare events, clocks, trajectories, and spacetime intervals. Process time concerns the amount and organization of state transformation occurring within a particular system. Phenomenal time concerns the experienced continuity, duration, and direction produced when a nervous system integrates retained and predicted information.

Equal intervals of physical time can contain very different amounts of process transformation. A stable system may change minimally during one second, while a turbulent or computationally active system undergoes many consequential transitions. A person engaged in rapid novel processing may traverse a longer representational trajectory than a person maintaining a nearly unchanged attentional state during the same clock interval.

A candidate process measure can be expressed as the state-space path length

[
\tau_P

\int_{t_0}^{t_1}
w(S_t)
\left|
\frac{dS}{dt}
\right|_g
dt,
]

where (g) specifies a metric over selected state variables and (w(S_t)) weights changes according to their causal or functional significance. This quantity should not be equated automatically with physical duration. It measures accumulated transformation relative to a chosen description.

A related quantity is process density,

[
\rho_P(t)

\left|
\frac{dS}{dt}
\right|_g,
]

which represents the amount of relevant state change per unit of physical time. Systems can therefore be compared according to how much organized transformation they undergo, how much structure they retain, and how many nested timescales contribute to their current state.

Phenomenal duration may depend partly on such measures, although the relationship is unlikely to be simple. Novelty, attention, arousal, memory formation, predictive error, and retrospective reconstruction all affect subjective duration. The present framework predicts that conscious time should depend on the structure of representational updating rather than on elapsed clock time alone.

10. Temporal Distance and Iterative Threads

Two states can be close in physical time while distant in cognitive organization. A sudden interruption may replace nearly all focal content within a fraction of a second, producing a large state-space displacement. Conversely, a line of thought can be suspended for hours and later resumed from a configuration closely related to the point where it stopped.

The iterative updating model represents such sequences as iterative threads. A thread can be revisited, resumed from its endpoint, reopened at an intermediate point, or alternated with another thread. These operations indicate that temporal relations within cognition form a branching and reconnecting graph rather than a single uninterrupted semantic line.

Three forms of temporal distance can therefore be distinguished. Clock distance measures elapsed physical duration, state distance measures configurational difference, and thread distance measures separation within a causally connected sequence of transformations. A thought resumed the following day may be distant in clock time but adjacent in thread time because the earlier endpoint has been reinstated as the current processing context.

This distinction may clarify why unfinished tasks retain psychological presence and why context reinstatement facilitates memory. Reconstructing an earlier state reduces state distance and allows an iterative sequence to continue. The system does not reverse physical time, but it reactivates a previous configuration sufficiently well to re-enter a similar region of cognitive state space.

11. Identity as Causal Continuity

The proposed account also reframes persistence and identity. Objects, organisms, and persons remain identifiable through time even though their states change and, in many cases, their material constituents are gradually replaced. Strict identity of components is therefore insufficient as a general explanation of persistence.

Iterative state inheritance suggests that diachronic identity is grounded in causal continuity of organization. A later state belongs to the same persisting process when it is linked to earlier states through an unbroken history of lawful transformation. Similarity supports recognition, although causal lineage distinguishes genuine persistence from an independently created duplicate.

A river remains the same river while its water changes because its channel, flow relations, sources, and surrounding geography continually generate successor states of the same organized process. An organism remains the same organism because metabolism and regulation recursively construct its later condition from its earlier one. A person remains psychologically continuous because memories, dispositions, bodily regulation, goals, and active cognitive states constrain the states that follow.

This account is compatible with process philosophy, particularly the proposal that enduring entities are stabilized patterns within ongoing becoming rather than completely self-contained substances (Whitehead, 1929). Iterative state inheritance adds a computational and causal formulation by identifying the transition relation through which organized patterns reproduce themselves across differential states.

12. Implications for Artificial Intelligence

Most contemporary artificial systems process sequences, preserve context, or maintain hidden states, but they vary greatly in the degree to which internal representations are carried forward as active determinants of subsequent processing. A system that repeatedly begins from an effectively reconstructed or externally supplied context lacks some of the autonomous temporal continuity characteristic of biological cognition.

An artificial cognitive architecture based on iterative state inheritance would maintain a bounded set of active internal representations, partially update them, and use the retained configuration to select the next update. The overlap between successive states would be an explicit architectural parameter. High overlap would favor sustained analysis, long-horizon planning, and preservation of intermediate results, while lower overlap would favor rapid context switching and responsiveness to novelty.

The prior iterative updating model proposes that an artificial focus of attention and short-term store could be maintained through analogs of persistent neural activity. These stores would undergo continuous partial replacement while their coactive contents jointly search associative memory for successor representations. Such an architecture would instantiate process time internally because its current state would embody a causal history that directly structures its next state.

Artificial systems could also be designed with multiple persistence timescales. Rapid sensory traces, sustained focal representations, latent short-term context, long-term episodic records, and enduring goals could jointly contribute to each update. This nested temporal depth may be more important for general intelligence than simply enlarging a context window because retained information would remain functionally prioritized and causally active.

A machine built in this manner would possess a stronger basis for thread identity. It could suspend a problem, preserve an interim state, pursue a subproblem, and later restore the earlier configuration without losing the causal structure of the original task. The same mechanism could support autobiographical continuity, self-monitoring, and an internally organized stream of cognition.

13. Empirical and Computational Predictions

The framework predicts that perceived continuity should covary with measurable overlap among successive neural population states. During coherent thought, representational similarity should decline gradually across adjacent intervals, while boundaries between thoughts should be associated with abrupt reductions in overlap. Multivariate neural recording, representational similarity analysis, and time-resolved population decoding could test whether retained content spans the predicted sequence of states.

Manipulations that reduce the duration of persistent activity should shorten the effective temporal thickness of cognition. Disruption of prefrontal sustained firing, short-term synaptic potentiation, or coordinated recurrent activity should increase premature replacement of contextual variables and produce more fragmented reasoning. The theory would be weakened if conscious and cognitive continuity remained unchanged despite substantial disruption of state-spanning representational activity.

Subjective duration should also relate to representational trajectory structure. Periods containing greater novelty, prediction error, and memory-forming change may involve longer state-space paths than equally long periods of repetitive processing. The relationship may differ between online duration judgments and retrospective estimates, but process measures should explain variance beyond physical time alone.

Artificial agents provide a complementary test. Systems using controlled partial updating should be compared with systems that repeatedly reconstruct context or replace internal state more completely. The theory predicts advantages for iterative systems in long-horizon planning, task resumption, coherent self-correction, integration of intermediate results, and maintenance of stable goals under interruption.

A broader prediction concerns nested persistence timescales. Systems capable of integrating rapidly changing variables with slowly changing contextual and goal representations should exhibit greater temporal depth and more coherent behavior. This principle can be examined across species, developmental stages, neurological conditions, and artificial architectures.

14. Relationship to Existing Theories

The observation that physical systems evolve through state transitions is fundamental to dynamical systems theory. The proposed contribution therefore does not rest on discovering that states change lawfully. Its novelty lies in treating inherited causal structure as a common explanatory principle linking physical continuity, biological identity, memory, conscious temporality, and artificial cognition.

Relational theories of time emphasize correlations among physical variables, while emergent-time proposals examine how temporal order can arise within descriptions that are globally timeless (Page and Wootters, 1983; Connes and Rovelli, 1994; Rovelli, 2004). Iterative state inheritance is compatible with these approaches because it can be expressed relationally as an ordered network of causal transformations. The theory focuses specifically on why a sequence constitutes one persisting process and how prior state becomes functionally embedded in successor state.

Thermodynamic accounts explain temporal asymmetry through entropy and boundary conditions. Iterative inheritance addresses a complementary problem by explaining continuity across differential states. Entropy provides a macroscopic direction, while state inheritance provides the causal linkage through which the process advances.

Predictive processing and the free-energy principle describe nervous systems as maintaining generative models that are continually revised by sensory evidence (Friston, 2010; Clark, 2013). Iterative state inheritance adds an account of how successive model states remain connected through persistent representational overlap. The current model is carried forward, selectively revised, and used to generate the predictions that determine subsequent revision.

Phenomenological theories of the specious present identify retention and anticipation as necessary components of temporal experience. The working memory account supplies candidate neural mechanisms through which retention and anticipation can coexist within one evolving state. Persistent activity carries selected representations forward, while associative search and predictive activation generate possible successors.

15. Scope and Limitations

The framework primarily concerns temporal continuity within evolving systems. It does not derive the metric properties of time, explain why spacetime has a particular dimensionality, or replace the equations of relativity and quantum theory. Those theories specify physical structure and dynamics at levels beyond the present proposal.

A potential circularity arises because updating is ordinarily expressed as occurring through time. The core relation can avoid this circularity by beginning with causally ordered states indexed by (n) rather than by a presupposed temporal variable. Clocks, proper time, and physical duration can then be introduced as measures of relationships within or among these ordered processes.

The degree of overlap is also description-dependent. Different choices of system boundary, state variables, temporal resolution, and similarity metric will produce different estimates. The framework therefore requires principled methods for identifying causally informative variables, perhaps through intervention, predictive sufficiency, information transfer, and multiscale modeling.

Causal inheritance does not always require high literal similarity. A discrete transition can transform all observable variables while remaining completely determined by the previous state. The strongest universal claim is therefore that causal processes preserve constraints or information through lawful transformation. High structural overlap is an additional property expected in many continuous systems when examined at sufficiently fine intervals.

The framework also does not imply that all physical updating is computational in the ordinary software sense. The term updating describes an abstract state-transition relation and does not require symbolic representation, an external programmer, or a digital substrate. Likewise, universal iterative inheritance does not imply universal consciousness. Consciousness would require a specialized form of representational integration, persistence, access, prediction, and self-propagating cognitive organization.

16. Conclusion

Time requires distinguishable states, ordered relations, and, for a coherent physical process, causal dependence between what precedes and what follows. The present article has proposed that these relations can be understood through iterative state inheritance. Each successor state is generated from a preceding state, retains some of its causal organization, and introduces differential modification.

Continuous physical dynamics provide a clear mathematical instance because a state at (t+\Delta t) is constructed from the state at (t) plus an incremental change. Biological systems elaborate this principle by actively preserving organization through metabolism and regulation. Nervous systems extend it further by maintaining information from prior events as active or latent representations that influence present processing.

Working memory constitutes a particularly explicit form of iterative inheritance. Persistent neural activity allows successive cognitive states to overlap, and the inherited representations jointly determine which new representations enter the stream of thought. The conscious present can therefore be understood as a layered state containing traces of different ages, current sensory information, and predictions concerning likely successors.

The broadest formulation of the proposal is that time within an evolving process is the ordered inheritance and transformation of state. Continuity arises from causal retention, passage arises from differential updating, and direction is imposed by asymmetric boundary conditions, thermodynamic dissipation, record formation, and learning. Conscious temporal experience represents a highly organized case in which a physical system carries aspects of its own preceding states forward as integrated content.

This framework places the iterative updating of working memory within a wider natural hierarchy. Physical systems inherit constraints, living systems inherit organization, nervous systems inherit representations, and conscious systems integrate this inheritance into an overlapping present. The same principle may therefore connect the continuity of matter, life, cognition, and subjective time without collapsing the important differences among them.

References

Barbour, J. (1999). The end of time: The next revolution in physics. Oxford University Press.

Bergson, H. (1910). Time and free will: An essay on the immediate data of consciousness. George Allen and Unwin. Original work published 1889.

Buonomano, D. V., & Maass, W. (2009). State-dependent computations: Spatiotemporal processing in cortical networks. Nature Reviews Neuroscience, 10, 113-125.

Clark, A. (2013). Whatever next? Predictive brains, situated agents, and the future of cognitive science. Behavioral and Brain Sciences, 36, 181-204.

Connes, A., & Rovelli, C. (1994). Von Neumann algebra automorphisms and time-thermodynamics relation in generally covariant quantum theories. Classical and Quantum Gravity, 11, 2899-2917.

Cowan, N. (1988). Evolving conceptions of memory storage, selective attention, and their mutual constraints within the human information-processing system. Psychological Bulletin, 104, 163-191.

Cowan, N. (2001). The magical number 4 in short-term memory: A reconsideration of mental storage capacity. Behavioral and Brain Sciences, 24, 87-185.

D’Esposito, M., & Postle, B. R. (2015). The cognitive neuroscience of working memory. Annual Review of Psychology, 66, 115-142.

Einstein, A. (1905). Zur Elektrodynamik bewegter Körper. Annalen der Physik, 17, 891-921.

Friston, K. (2010). The free-energy principle: A unified brain theory? Nature Reviews Neuroscience, 11, 127-138.

Hasson, U., Chen, J., & Honey, C. J. (2015). Hierarchical process memory: Memory as an integral component of information processing. Trends in Cognitive Sciences, 19, 304-313.

Husserl, E. (1991). On the phenomenology of the consciousness of internal time. Kluwer Academic Publishers.

James, W. (1890). The principles of psychology. Henry Holt.

Maturana, H. R., & Varela, F. J. (1980). Autopoiesis and cognition: The realization of the living. D. Reidel.

Minkowski, H. (1909). Raum und Zeit. Physikalische Zeitschrift, 10, 104-111.

Mongillo, G., Barak, O., & Tsodyks, M. (2008). Synaptic theory of working memory. Science, 319, 1543-1546.

Noether, E. (1918). Invariante Variationsprobleme. Nachrichten von der Gesellschaft der Wissenschaften zu Göttingen, Mathematisch-Physikalische Klasse, 235-257.

Page, D. N., & Wootters, W. K. (1983). Evolution without evolution: Dynamics described by stationary observables. Physical Review D, 27, 2885-2892.

Pearl, J. (2000). Causality: Models, reasoning, and inference. Cambridge University Press.

Reser, J. E. (2016). Incremental change in the set of coactive cortical assemblies enables mental continuity. Physiology & Behavior, 167, 222-237.

Reser, J. E. (2022). A cognitive architecture for machine consciousness and artificial superintelligence: Updating working memory iteratively. arXiv:2203.17255.

Rovelli, C. (1991). Time in quantum gravity: An hypothesis. Physical Review D, 43, 442-456.

Rovelli, C. (2004). Quantum gravity. Cambridge University Press.

Schreiber, T. (2000). Measuring information transfer. Physical Review Letters, 85, 461-464.

Shannon, C. E. (1948). A mathematical theory of communication. Bell System Technical Journal, 27, 379-423, 623-656.

Stokes, M. G. (2015). Activity-silent working memory in prefrontal cortex: A dynamic coding framework. Trends in Cognitive Sciences, 19, 394-405.

Varela, F. J. (1999). The specious present: A neurophenomenology of time consciousness. In J. Petitot, F. J. Varela, B. Pachoud, & J. M. Roy (Eds.), Naturalizing phenomenology (pp. 266-314). Stanford University Press.

Whitehead, A. N. (1929). Process and reality. Macmillan.