1. Introduction

Time and spacetime occupy central roles in both the history and philosophy of science, yet their ontological status remains contested. From Aristotle’s analysis of time as a measure of motion to Leibniz’s relational critique of Newtonian absolutism, and from Mach’s empiricism to Einstein’s geometric reformulation, the concepts of time, space, and spacetime have repeatedly shifted in meaning and function. Contemporary physics continues this trajectory: General Relativity treats spacetime as a dynamical geometric structure, while many approaches to quantum gravity omit time as a fundamental parameter. These developments have generated a rich literature on relationalism, emergent spacetime, and the representational roles of temporal and spatiotemporal frameworks.

This paper contributes to that tradition by offering an empirically grounded metaphysical reconstruction of time and spacetime. The central claim is simple: all empirical evidence typically taken to support temporal or spatiotemporal structure—ageing, decay, motion, oscillation, and gravitational phenomena—is evidence of change and relational organisation, not of independent temporal or spatiotemporal entities. Clocks register regular change‑events; spacetime geometry encodes relations among such events. Neither measurement detects a substance with causal powers.

A key source of confusion, I argue, is semantic. The words time and space are polysemous, and their abstract, indexing senses are routinely conflated with their experiential or metaphorical senses. This conflation encourages the reification of coordinate structures in physical models, generating familiar pseudo‑problems concerning temporal passage, spacetime “flow,” and the ontology of the metric field. By distinguishing these meanings, we can dissolve these puzzles and clarify the conceptual commitments of physical theory.

The positive programme of the paper reconstructs duration, persistence, spatiality, and spacetime structure in terms of change‑events and their relations. This reconstruction aligns with relational and emergent approaches in contemporary philosophy of physics (e.g., Barbour, Rovelli, Lam & Wüthrich, Knox, Huggett), while offering a simpler metaphysical grounding in the primacy of change. The resulting Redundancy Thesis holds that if every empirical and explanatory role attributed to time or spacetime can be discharged by change and relational organisation, then time and spacetime are representational tools rather than fundamental constituents of the physical world.

The remainder of the paper develops this argument through an integrated historical, semantic, and conceptual analysis, clarifying the status of temporal and spatiotemporal parameters in scientific practice and contributing to ongoing debates in the history and philosophy of science.

Author note: Portions of this manuscript were revised with the assistance of a large language model (Microsoft Copilot) for restructuring and clarifying author‑generated content. All conceptual claims and arguments are the author’s own.

2. Historical and Philosophical Context

The conceptual foundations of time and spacetime have been central concerns in both the history and philosophy of science. The present reconstruction builds on, and departs from, several major strands in this tradition. This section situates the Redundancy Thesis within that broader intellectual landscape.

A natural starting point is Aristotle’s analysis of time as “the number of motion with respect to before and after,” which treats time not as an independent entity but as a measure of change. This relational and non-substantival conception was later developed by Leibniz, who argued that time (and space) are systems of relations among events rather than substances or containers. Leibniz’s correspondence with Clarke, and his critique of Newtonian absolute time, established a framework in which temporal structure is derivative of change rather than fundamental. The present account aligns with this tradition by grounding temporal concepts in differences between states of systems, rather than in an independently existing temporal dimension.

Nineteenth‑century empiricists such as Mach reinforced this relational perspective by emphasising the primacy of observable change and the dangers of reifying abstract parameters. Mach’s critique of absolute space and time influenced Einstein’s development of General Relativity, in which spacetime is represented by a dynamical metric field whose structure depends on matter and energy. Although GR is often interpreted substantivally, Einstein himself repeatedly stressed that spacetime has no independent existence apart from physical processes. This relational reading of GR provides historical support for the view that spacetime geometry encodes relations among events rather than describing a physical medium.

Twentieth‑century philosophy of science introduced further conceptual tools relevant to the present analysis. Reichenbach and Grünbaum emphasised the conventional and representational aspects of temporal and spatial coordinates, arguing that simultaneity, temporal order, and metric structure depend on definitional choices and modelling practices. Their work highlights the importance of distinguishing empirical content from representational conventions—an issue that becomes central once the polysemy of time and space is recognised. McTaggart’s argument for the unreality of time, based on contradictions in the A‑series, also plays a role here: if the experiential sense of temporal flow is a cognitive phenomenon rather than a metaphysical structure, then the contradictions he identified dissolve.

Contemporary philosophy of physics has continued to explore the relational and representational dimensions of temporal and spatiotemporal structure. Barbour’s timeless configuration‑space ontology and Rovelli’s relational quantum mechanics both argue that change, not time, is fundamental, and that temporal parameters emerge from correlations among physical variables. These approaches resonate with the empirical minimalism developed in this paper, though the present account grounds the emergence of temporal structure in the semantics of time and the primacy of change rather than in specific physical formalisms. In the context of spacetime, Knox’s spacetime functionalism and Huggett’s representational analysis of quantum gravity emphasise the role of spacetime as a tool for organising physical information rather than as a fundamental entity. Lam and Wüthrich’s work on emergent spacetime in quantum gravity further supports the idea that spatiotemporal structure may arise from non‑spatiotemporal relations.

The Redundancy Thesis developed in this paper draws together these historical and contemporary strands. It agrees with Aristotle, Leibniz, Mach, and Einstein that temporal and spatiotemporal structures are derivative of physical processes; it aligns with Reichenbach and Grünbaum in emphasising the representational role of temporal and spatial parameters; and it complements contemporary relational and emergent approaches by grounding temporal and spatiotemporal concepts in the primacy of change. At the same time, it offers a distinctive contribution by showing that many familiar puzzles about time and spacetime arise from semantic conflation rather than from empirical or theoretical difficulties. By clarifying the conceptual roles of time and spacetime, the Redundancy Thesis provides a unified framework for interpreting temporal and spatiotemporal structure across classical, relativistic, and quantum contexts.

These historical and philosophical developments motivate the methodological stance adopted in the present paper, which treats conceptual clarification, empirical minimalism, and relational reconstruction as central tools for analysing temporal and spatiotemporal structure.

3. Methodological Approach

The analysis that follows adopts a conceptual and metaphysical methodology informed by both the historical development of temporal and spatiotemporal concepts and by contemporary scientific practice. The preceding section showed that questions about the nature of time and spacetime have long turned on the relation between empirical phenomena, representational frameworks, and linguistic usage. The present approach builds on this tradition by treating conceptual clarification as a legitimate and necessary component of the philosophy of science.

The method proceeds from a simple starting point: the empirical record consists of observable changes in physical systems, and any adequate metaphysics of time or spacetime must be accountable to this record. This commitment to empirical minimalism aligns with the relational insights of Aristotle, Leibniz, Mach, and Einstein, and with contemporary approaches that treat temporal and spatiotemporal parameters as representational rather than ontological. The aim is not to propose new physical models, but to clarify the ontological commitments that arise when temporal and spatiotemporal vocabulary is used to describe physical processes.

A second methodological commitment concerns the role of language. The polysemy of time and space has played a significant role in the historical development of temporal and spatiotemporal concepts, and continues to shape contemporary debates. The present analysis therefore treats semantic clarification as a central philosophical task. By distinguishing the abstract, indexing uses of temporal and spatial terms from their experiential and metaphorical uses, the method seeks to dissolve pseudo‑problems that arise from conflating these meanings.

A third component of the methodology is relational reconstruction. Rather than taking temporal or spatiotemporal structure as primitive, the analysis reconstructs duration, persistence, spatiality, and spacetime structure from patterns of change and relations among change‑events. This approach is compatible with, but not dependent on, specific physical frameworks such as relational quantum mechanics, timeless configuration‑space dynamics, or emergent spacetime programmes in quantum gravity. The aim is to articulate a metaphysically parsimonious framework that clarifies the representational role of temporal and spatiotemporal parameters across physical theories.

Taken together, these methodological commitments—empirical minimalism, semantic clarification, and relational reconstruction—provide the basis for the Redundancy Thesis developed in the remainder of the paper. The following sections apply this framework to the empirical, semantic, and structural features of temporal and spatiotemporal discourse, showing how they can be understood without positing time or spacetime as fundamental constituents of the physical world.

4. Results

4.1 The Empirical Constraint: All Evidence of Time Is Evidence of Change

Any adequate account of time must begin with the empirical data. Whatever time is, if it is anything at all, it must be something for which we have evidence. Yet when we examine the empirical record with care, a striking fact emerges: there is no direct empirical evidence for time itself. There is abundant evidence for change—for motion, transformation, decay, growth, oscillation, vibration, and evolution—but none for a substance, entity, or medium called “time.” This observation is so simple that it is easy to overlook, yet it has profound implications for the metaphysics of time.

Consider the phenomena that are typically cited as evidence of time’s passage. We age. The Earth rotates. Clocks tick. Atoms transition between energy levels. Radioactive nuclei decay. Stars burn their fuel. Thermodynamic systems evolve toward equilibrium. In each case, what we observe is change: a difference between one state of a system and a later state of that same system. We do not observe time flowing, moving, or exerting influence. We observe systems undergoing transformations.

This point is not merely linguistic. It is empirical. If time were a substance or medium that flows, we might expect to detect it in the same way we detect other physical phenomena: through its interactions, its causal powers, or its measurable effects. But time has no such signature. It does not push, pull, bend, vibrate, emit, absorb, or scatter. It does not appear in any list of fundamental forces or fields. It is not detected by any instrument except insofar as that instrument measures change.

This is not to deny that clocks measure something. They do. But what they measure is not time as an independent entity; they measure regular, periodic change in a physical system. A pendulum clock measures the oscillation of a pendulum. A quartz clock measures the vibration of a crystal. An atomic clock measures the frequency of electromagnetic radiation associated with transitions between energy levels in caesium atoms. In each case, the clock’s reading is a count of change-events. The clock does not detect time; it detects change and then uses an agreed-upon calibration to express that change in units we call “seconds.”

This observation aligns with a long tradition in physics and philosophy. Aristotle argued that time is “the number of motion with respect to before and after,” meaning that time is a measure of change, not a thing in itself. Leibniz insisted that time is not a substance but a system of relations among events. In modern physics, Julian Barbour has argued that time is an emergent abstraction arising from correlations among timeless configurations of the universe. Carlo Rovelli has argued that time is relational and that the fundamental equations of physics do not require a global time parameter. Even Lee Smolin, who argues for the fundamentality of time, acknowledges that the empirical evidence for time is always mediated by change.

The empirical record therefore supports a simple but powerful thesis:

All empirical evidence for “time passing” is evidence of change. There is no empirical evidence for time as an independent entity.

This thesis has several important consequences.

Time Has No Causal Powers

If time were a substance or medium, we might expect it to cause things to happen. But nothing in the empirical record suggests that time has causal efficacy. When people say “time causes ageing,” they are speaking metaphorically. Ageing is caused by biochemical processes: DNA replication errors, oxidative stress, telomere shortening, and other molecular mechanisms. These processes unfold due to energy differentials and physical interactions, not because time “makes” them happen.

Similarly, radioactive decay is not caused by time. It is caused by quantum mechanical processes governed by the structure of the nucleus and the probabilistic nature of quantum transitions. The fact that decay rates can be expressed in units of time does not mean that time causes decay. It means only that decay is a process that can be measured.

Motion is not caused by time. It is caused by forces. A ball rolls down a hill because gravity accelerates it, not because time pushes it forward. A planet orbits a star because of gravitational attraction, not because time “moves” it along its trajectory.

In every case, time is not a cause but a measure. It quantifies the rate at which change occurs. To mistake the measure for the cause is to commit a category error.

Change Requires Energy Differentials, Not Time

If time does not cause change, what does? The answer, well-established in physics, is energy differentials. Systems change because they are not in equilibrium. Heat flows from hot to cold. Objects accelerate when forces act on them. Chemical reactions occur when reactants have higher free energy than products. Quantum transitions occur when energy levels differ.

Julian Barbour (The End of Time, Phoenix, London,1999, p231) captures this point succinctly when he writes that “all true change in quantum mechanics comes from interference between stationary states with different energies.” In a system described by a stationary state, no change occurs. Change arises only when energy differences exist.

This observation reinforces the empirical thesis. Change is driven by physical interactions and energy gradients. Time plays no causal role. It is a parameter used to describe the evolution of systems, not a force that drives that evolution.

The Illusion of Time’s Flow

If time has no causal powers and no empirical signature, why do we experience it as flowing? The answer lies in the structure of change itself. We are organisms embedded in a world of continual change. Our bodies change, our memories accumulate, our perceptions update, and our environment evolves. The brain integrates these changes into a coherent narrative, giving rise to the subjective impression of a “flow” from past to future.

But this flow is not a feature of the world; it is a feature of our cognition. It is the way a change-detecting organism experiences change. The world does not flow; it changes. The flow of time is a psychological interpretation of physical processes, not a physical process in its own right.

This distinction is crucial. If we mistake the subjective flow for an objective feature of reality, we are led to reify time as a substance that “moves.” But nothing in the empirical record supports this reification. The flow is an illusion created by the brain’s integration of change.

The Empirical Minimalism of Change

The empirical evidence therefore supports a minimalist ontology: Change is real, Time is not independently observable, Time has no causal powers, Time is a measure of change, not a cause of it.

This empirical minimalism is consistent with standard practice in physics, where unobservable structures are not posited unless required for explanatory or predictive success. Many fundamental equations—most notably the Wheeler–DeWitt equation in canonical QG—omit time entirely, describing change through correlations among physical variables rather than evolution with respect to an external parameter. Even in GR, the dynamical metric encodes relational structure rather than a substance with independent causal powers. These features of contemporary physics support the view that change, not time, is the primary empirical datum, and that temporal structure is a representational framework rather than a fundamental entity.

This empirical minimalism also echoes Barbour’s argument that change, not time, is the primary physical datum (Barbour 1999) and aligns with Rovelli’s relational account of temporal structure (Rovelli 1996).

Taken together, these empirical considerations motivate a conceptual analysis of the term ‘time’ itself, for many of the puzzles surrounding time arise not from observation but from linguistic and conceptual conflation.

4.2 The Semantic Constraint: Time as a Polysemous Word

A striking feature of the word time—one that is rarely acknowledged in scientific or philosophical discussions—is that it is polysemous. Polysemy is a well-established phenomenon in linguistics: a single word can have multiple, related meanings that share a conceptual core but diverge in usage. Classic examples include “bank” (financial institution vs. riverbank) or “light” (not heavy vs. illumination). In the case of time, the polysemy is more subtle, because the meanings are historically intertwined and conceptually adjacent. Yet the failure to distinguish them has led to profound confusion.

This semantic ambiguity has direct consequences for interpreting physical theories. Treating the experiential sense of time as if it were the abstract parameter of physics leads to reifying the coordinate 𝑡 in dynamical equations into a physical entity. Much confusion about temporal passage, time dilation, and the ontology of spacetime arises from this conflation.

Yet beneath this diversity, a pattern emerges. The definitions cluster around two core meanings, which correspond to two distinct conceptual roles that the word time plays in our thought: Time as a dimension of change and Time as the perceived flow of change.

These two meanings are related but not identical. They share a conceptual core—both concern the ordering of events—but they differ in their ontological commitments and their linguistic behaviour. The first is abstract, quantitative, and structural; the second is experiential, qualitative, and metaphorical. Confusing them leads to conceptual errors.

If the empirical and semantic records both point toward the primacy of change, the next step is to examine the nature of change itself.

Time as a Dimension of Change

The first core meaning of time is the one employed in physics and mathematics. In this sense, time is an abstract indexing framework used to order events and measure rates of change. It is a dimension in the same sense that space is a dimension: a coordinate system that allows us to specify where and when events occur.

This meaning is explicit in the equations of classical mechanics, where time appears as a parameter in differential equations describing motion. It is explicit in thermodynamics, where time indexes the evolution of macroscopic variables. It is explicit in quantum mechanics, where time appears in the Schrödinger equation as a parameter governing the evolution of the wavefunction. And it is explicit in relativity, where time is one coordinate in a four-dimensional geometric manifold.

In all these cases, time functions as a dimension of change. It does not cause change; it measures it. It does not flow; it indexes the evolution of systems. It is not a substance; it is a coordinate.

This meaning aligns with Aristotle’s definition of time as “the number of motion with respect to before and after.” Aristotle recognised that time is not motion itself but a measure of motion. Leibniz, too, insisted that time is not a substance but a system of relations among events. In modern physics, Carlo Rovelli’s relational interpretation of time emphasises that time is not an independent background but a parameter that emerges from the relations among physical systems.

In this sense, time is an abstraction. It is a conceptual tool that allows us to quantify change. It is indispensable for describing physical processes, but it has no independent ontological status.

Time as the Perceived Flow of Change

The second core meaning of time is the one employed in everyday discourse. In this sense, time is something that “passes,” “flows,” or “moves forward.” We speak of time dragging, racing, slipping away, or standing still. We experience time as a kind of medium through which we move, or as a river that carries us along.

This meaning is not abstract or quantitative. It is qualitative and experiential. It reflects the way we, as change-detecting organisms, experience the continual succession of events. Our memories accumulate, our perceptions update, and our environment evolves. The brain integrates these changes into a coherent narrative, giving rise to the subjective impression of a “flow” from past to future.

In this sense, time functions as a mass noun, like “traffic,” “weather,” or “music.” A mass noun refers to a non-specific collection of underlying events or processes. Traffic is not a substance; it is a collective term for the movement of vehicles. Weather is not a substance; it is a collective term for atmospheric processes. Music is not a substance; it is a collective term for sequences of sound.

Similarly, time is not a substance; it is a collective term for the ongoing succession of change-events. What “flows” is not time but change. The flow of time is a metaphorical interpretation of the continual occurrence of change.

This meaning aligns with McTaggart’s A-series, which concerns the subjective experience of past, present, and future. McTaggart argued that the contradictions inherent in the A-series render time unreal. But his argument presupposes that the A-series reflects an objective feature of reality. If the A-series reflects a cognitive interpretation of change rather than a metaphysical structure, then the contradictions dissolve.

The Dangers of Conflating the Two Meanings

The polysemy of time becomes problematic when the two meanings are conflated. This happens frequently in both physics and philosophy.

Physicists often slide from the abstract dimension to the experiential flow. When they speak of “time dilation,” they sometimes describe it as if time itself were stretching or compressing, as if time were a physical substance. But time dilation is a difference in rates of change between reference frames, not a literal stretching of time. (Here ‘reference frame’ refers to a state description, not a coordinate frame).

Philosophers often slide from the experiential flow to the abstract dimension. When they debate whether the past and future “exist,” they treat the mass-noun sense of time as if it were a literal entity with ontological status. But the existence of past and future events is a question about the structure of change, not about the existence of a substance called time.

Everyday speakers slide between the meanings constantly. When we say “time flies when you’re having fun,” we are speaking metaphorically. When we say “the meeting lasted an hour,” we are speaking abstractly. The same word is doing different conceptual work.

The failure to distinguish these meanings leads to pseudo-problems. For example:

• The question “Does time flow?” is ambiguous. The abstract dimension does not flow; the experiential interpretation does.
• The question “Does time exist?” is ambiguous. The abstract dimension exists as a conceptual tool; the experiential flow exists as a cognitive phenomenon; neither exists as a physical substance.
• The question “Can we travel in time?” is ambiguous. We can ‘move’ through the abstract dimension by changing (empirically, we don’t ‘move’ through time, we change); we cannot move through the experiential flow as if it were a medium.

Similar concerns about conceptual conflation have been raised in discussions of spacetime functionalism (Knox 2013) and in Huggett’s analysis of representational structure in quantum gravity (Huggett 2017).

Recognising the polysemy dissolves these puzzles.

Polysemy as a Guide to Conceptual Clarity

The semantic analysis therefore yields a clear conclusion:

The word time is polysemous. It has at least two core meanings—time as a dimension of change and time as the perceived flow of change—and many puzzles about time arise from conflating them.

This conclusion is not merely linguistic. It has profound implications for the metaphysics of time. If the abstract dimension is a conceptual tool and the experiential flow is a cognitive interpretation, then time is not a fundamental feature of reality. The fundamental feature is change. Time is a way of describing change, not a thing that exists independently of it.

If the empirical record shows that all evidence for time reduces to evidence of change, then the next step is to examine the conceptual structure of the word time. For even if time has no independent empirical signature, it may still play an indispensable conceptual role. But to understand that role, we must understand what the word actually means. This requires a semantic analysis.

The next section develops this point by examining the nature of change and the role of dimensions as abstract indexing frameworks.

4.3 Change as the Underlying Reality

If the empirical record shows that all evidence for time reduces to evidence of change, and if the semantic record shows that the word time is polysemous, then the next step is to examine the nature of change itself. For if time is not fundamental, then change must be. This section develops a rigorous account of change and clarifies the role of dimensions—space, time, temperature, and others—as abstract indexing frameworks used to quantify aspects of change.

Many fundamental equations—most notably the Wheeler–DeWitt equation—omit time entirely. In such formulations, change is encoded in correlations among physical variables rather than in evolution with respect to an external parameter. This supports the view that change, not time, is the primary empirical datum.

The central thesis of this section is simple: change is the underlying empirical reality, and dimensions are abstract tools for indexing different aspects of that reality. Time is one such dimension, but it is not unique. It is one of many abstract frameworks we use to describe how systems evolve.

What Is Change?

Change is one of the most basic features of the world. It is the difference between one state of a system and another. This difference may be spatial, thermal, energetic, structural, chemical, biological, or quantum. It may be continuous or discrete, reversible or irreversible, relative or absolute. But in every case, change is a transition between states.

A simple definition captures this:

Change is the occurrence of a difference between two reference frames of a system.

A reference frame, in this context, is not a coordinate system but a state description. Reference frame 1 describes the system at one moment; reference frame 2 describes it at another. If the descriptions differ, change has occurred. If they do not, no change has occurred.

This definition aligns with Aristotle’s insight that change is the actualisation of potential. It aligns with Leibniz’s view that change consists in the succession of states. It aligns with modern physics, where change is described by the evolution of dynamical variables. And it aligns with everyday experience, where change is simply the difference between “before” and “after.”

Importantly, change does not require time. It requires only difference. Time is a way of measuring difference, not a precondition for it.

Types of Change: Quantum and Compound

Change can occur at different levels of complexity.

Quantum change

Quantum change occurs at the level of fundamental particles. Examples include: a quark changing flavour, an electron transitioning between energy levels, a photon being emitted or absorbed, a quantum state collapsing upon measurement

These changes are discrete and governed by probabilistic laws. They are the building blocks of all higher-level change.

It’s worth noting here something that we will come back to, that is that quantum change may be reversible (or “time-symmetric” as it is often—misleadingly—described).

Compound change

Compound change occurs at the level of composite systems. Examples include the Earth rotating, a chemical reaction proceeding, a biological organism ageing, a star undergoing nuclear fusion.

These changes are continuous (or appear continuous) and governed by classical or statistical laws. They arise from the aggregation of quantum changes.

The distinction between quantum and compound change is important because it shows that change is not a monolithic phenomenon. It has structure. But in every case, change is the transition between states.

Whereas quantum change may be reversible, complex sequentially dependent change-series are not. You can’t unscramble an egg.

So, not one arrow of time, but multiple arrows of change.

Relative and Absolute Change

Change can be relative or absolute.

Relative change

Relative change occurs when the state of a system changes relative to another system. For example: a car moves relative to the road, a planet moves relative to a star, a sound wave propagates relative to the air

Relative change is ubiquitous. It is the basis of relational theories of space and time, such as those advocated by Leibniz and Rovelli.

Absolute change

Absolute change occurs when the state of a system changes independently of any external reference. For example: a particle decays, a chemical bond breaks, a quantum state transitions.

Absolute change is internal to the system. It does not require an external reference.

The distinction matters because it shows that change does not depend on a universal time. It depends only on the structure of the system and its interactions.

Dimensions as Abstract Indexing Frameworks

To describe change, we need ways of quantifying it. This is where dimensions come in. A dimension is an abstract calibration framework used to index some aspect of reality. It is not a physical substance; it is a conceptual tool.

Examples include: Space: indexes position, Temperature: indexes heat, Mass: indexes inertia, Charge: indexes electromagnetic interaction, Time: indexes change

Each dimension corresponds to a measurable aspect of reality, but the dimension itself is not the reality. Space is not position; it is the framework for describing position. Temperature is not heat; it is the framework for describing heat. Time is not change; it is the framework for describing change.

This distinction is crucial. It shows that dimensions are abstractions, not entities. They are ways of organising information about the world, not components of the world itself.

The Dimension of Time

Time, in its abstract sense, is the dimension of change. It indexes the rate at which change occurs. It allows us to quantify how quickly or slowly systems evolve.

For example: A pendulum oscillates with a certain frequency, a chemical reaction proceeds at a certain rate, a radioactive nucleus decays with a certain half-life, a planet orbits a star with a certain period.

In each case, time is the dimension used to quantify the rate of change. But the change itself is driven by physical interactions, not by time.

This aligns with Aristotle’s definition of time as the “number of motion.” It aligns with Leibniz’s relationalism. It aligns with Rovelli’s relational time. And it aligns with Barbour’s view that time is an emergent abstraction.

Higher-Order Dimensions: Spacetime and Beyond

If space is the dimension of position and time is the dimension of change, then spacetime is the dimension of changing position. It is a compound dimension that indexes motion.

Similarly, acceleration is the dimension of changing motion. Jerk is the dimension of changing acceleration. And so on.

These higher-order dimensions show that dimensions are not physical entities but conceptual tools. They are ways of describing patterns of change.

Change Without Time

A key implication of this analysis is that change does not require time. It requires only difference. Time is a way of describing change, not a precondition for it.

This is not a radical claim. It is implicit in much of modern physics. For example:

• The Wheeler–DeWitt equation in QG has no time parameter.
• Barbour’s “timeless” configuration space describes change without time.
• Rovelli’s relational quantum mechanics describes events without a global time.

These theories show that time is not fundamental. It is an emergent abstraction.

This relational reconstruction resonates with Lam and Wüthrich’s account of spacetime emergence in quantum gravity (Lam & Wüthrich 2018), though the present framework grounds relational structure directly in change rather than in specific physical models.

The Primacy of Change

The analysis therefore yields a clear conclusion:

Change is the fundamental empirical reality. Time is an abstract dimension used to describe change.

This conclusion sets the stage for the next section, which examines the polysemy of the word space and the nature of spacetime.

4.4 Space, Spatiality, and Spacetime

If time is a polysemous term whose meanings must be disentangled before we can understand its role in physics and metaphysics, the same is true of space. The two concepts have evolved together, and their conflation has generated parallel confusions. Just as time is often treated as a substance that “flows,” space is often treated as a substance that “extends,” “contains,” or “expands.” And just as time is often reified into a medium with causal powers, space is often reified into a container or fabric. These reifications are not supported by the empirical record. They arise from semantic ambiguity.

In GR, spacetime geometry encodes relations among events and the dynamical behaviour of the metric field. Nothing in the formalism requires interpreting spacetime as a substance. QG approaches that treat spacetime as emergent reinforce this relational reading.

This section reconstructs the concepts of space and spatiality, showing that they are polysemous in ways analogous to time, and that spacetime is best understood as a compound indexing framework for relational structure, not as a physical entity. The goal is to clarify the conceptual landscape so that the redundancy thesis can be applied symmetrically to time, space, and spacetime.

The Polysemy of Space

Like time, the word space has multiple, related meanings. Dictionaries list dozens of definitions: space as “the three‑dimensional extent in which objects exist,” space as “a region,” space as “an interval,” space as “emptiness,” space as “outer space,” and so on. These definitions fall into two broad categories:

• Space as an abstract coordinate framework
• Space as a physical region or container

These two meanings are conceptually distinct but routinely conflated.

Space as an Abstract coordinate framework

In physics, space is typically used in an abstract sense: it is a dimension of position, a coordinate system that allows us to specify where objects are located relative to one another. This is the sense in which Euclidean geometry, Newtonian mechanics, and even GR employ the term. Space, in this sense, is not a substance. It is a mathematical structure.

This meaning aligns with the relational tradition of Leibniz, Mach, and Rovelli. On this view, space is not an independently existing entity but a system of relations among material objects. To say that an object is “in space” is simply to say that it has spatial relations to other objects.

Space as a physical region or container

In everyday discourse, space is often treated as a container: a physical expanse that objects occupy. We speak of “empty space,” “outer space,” “making space,” or “running out of space.” This usage treats space as a kind of physical medium or volume.

This meaning is metaphorical. It arises from our embodied experience of moving through environments. But it is not a literal description of a physical entity. There is no empirical evidence for a substance called “space” that contains objects. What we observe are objects and the relations among them.

The Dangers of Conflating the Two Meanings

The conflation of these two meanings leads to conceptual errors analogous to those that arise from conflating the two meanings of time.

For example:

• When physicists speak of “space expanding,” they sometimes slide from the abstract coordinate sense to the container sense, as if space were a physical medium that stretches. But what expands is not a substance; it is the distance relations between galaxies in a dynamical metric.
• When philosophers debate whether space is “substantival” or “relational,” they often conflate the abstract coordinate sense with the container sense, treating the mathematical structure as if it were a physical object.
• When popular accounts describe space as a “fabric” that “bends,” they reify the coordinate framework into a physical material.

These confusions mirror those surrounding time. Just as time does not flow, space does not extend. Both are abstractions used to describe aspects of change.

Spatiality as a Feature of Change

If space is not a substance, what is spatiality? Spatiality is a feature of change‑events. It is the pattern of relative positions among changing systems. We infer spatial structure from the trajectories of moving objects or the distances between interacting systems or the propagation of signals or the geometry of relational networks.

• Spatiality is not an independently existing entity. It is a structural feature of the world’s change‑patterns.

This aligns with the relational tradition. Leibniz argued that space is “the order of coexistences.” Rovelli argues that spatial relations are primary and that space emerges from the network of interactions among physical systems. In QG, many approaches treat spatial geometry as emergent from more fundamental relational structures.

On this view, space is not a container but a pattern.

Spacetime as a Compound Indexing Framework

If time is the dimension of change and space is the dimension of position, then spacetime is the dimension of changing position. It is a compound indexing framework that combines spatial and temporal coordinates into a unified structure.

This structure is extraordinarily powerful. It allows us to describe: motion, acceleration, causal structure, light cones, gravitational effects, or the geometry of the universe.

But its power does not entail its fundamentality. Spacetime is a model, not a substance. It is a mathematical representation of relational structure, not a physical fabric.

This is explicit in GR. The metric tensor describes the geometry of spacetime, but the geometry is determined by the distribution of matter and energy. There is no independent spacetime substance. The geometry is relational.

This is also explicit in QG. Many approaches—loop Quantum Gravity, causal set theory, spin networks, and others—treat spacetime as emergent from more fundamental structures. In these theories, spacetime is not a background but a derived concept.

The Reification Error

The most persistent confusion in discussions of spacetime is the reification error: treating an abstract indexing framework as if it were a physical entity. This error arises from semantic ambiguity. When we speak of “spacetime curvature,” we use a metaphor that suggests a physical fabric. But curvature is a property of a mathematical manifold, not a physical substance.

Similarly, when we speak of “spacetime expanding,” we use a metaphor that suggests a physical medium. But expansion is a change in the metric relations among galaxies, not a stretching of a material.

The reification error is the spatial analogue of the temporal error that treats time as a flowing substance. Both errors arise from conflating abstract and experiential meanings.

Spacetime Without Substance

If spacetime is not a substance, what is it? It is a relational structure. It is the pattern of spatial and temporal relations among change‑events. It is a way of organising information about the world, not a component of the world.

This view dissolves many puzzles:

• The “flow” of time is not a physical process.
• The “expansion” of space is not a stretching of a medium.
• The “curvature” of spacetime is not a bending of a fabric.
• The “beginning” of spacetime is not the creation of a container.

These puzzles arise only if we reify the abstractions.

The Symmetry Between Time and Space

The analysis of space mirrors the analysis of time: both are polysemous, both have abstract and experiential meanings, both are indexing frameworks, not substances, both are derived from patterns of change, both are reified when their meanings are conflated.

This symmetry is not accidental. It reflects the fact that both concepts arise from the same underlying reality: change.

Spacetime as a Derived Concept

The analysis therefore yields a clear conclusion:

Spacetime is not a fundamental entity. It is a derived concept that models the relational structure of change‑events.

This conclusion sets the stage for the next section, which shows how duration, period, and persistence can be defined without invoking time or spacetime as fundamental entities.

This analysis of spatial and spatiotemporal concepts mirrors the earlier analysis of time and prepares the ground for reconstructing the central temporal notions—duration, period, and persistence—without presupposing time as fundamental.

4.5 Duration, Period, and Persistence Without Time

If time is not fundamental, then the central temporal concepts must be reconstructed without presupposing time. This section shows that duration, period, and persistence are already defined in terms of change, even when we mistakenly believe otherwise. This section develops that reconstruction. The goal is not merely to show that these concepts can be defined without time, but that they already are defined in terms of change, even when we mistakenly believe otherwise.

The argument proceeds in three steps:

• Duration is the amount of change in a system or between systems.
• Period is the recurrence of a regular change-pattern.
• Persistence is the continuity of change within a system’s identity-conditions.

None of these require time as a fundamental entity. All can be defined entirely in terms of change-events and their relations.

Duration as the Amount of Change

Duration is typically defined as “the length of time during which something continues.” This definition is circular: it defines duration in terms of time, which is itself defined in terms of duration. To break the circle, we must define duration without presupposing time.

The empirical record provides the key. When we measure duration, what we actually measure is the amount of change in a reference system. For example: a pendulum swings a certain number of times, a quartz crystal vibrates a certain number of cycles, a caesium atom undergoes a certain number of transitions, a heart beats a certain number of times, the Earth rotates a certain fraction of a turn.

In each case, duration is quantified by counting change-events. The unit (second, minute, hour) is a conventional calibration of these events. There is no independent entity called “time” that duration measures. Duration is the amount of change.

This is not a revisionary claim. It is how clocks work. A clock does not detect time; it detects change. The “duration” between two events is the number of change-events in a reference system that occur between them.

Thus: Duration = the quantity of change in a reference system between two states of another system.

This definition is empirical, not metaphysical. It captures what we actually do when we measure duration.

Period as Recurrence of a Change-Pattern

A period is typically defined as “the time taken for one complete cycle of a repeating process.” Again, this definition is circular. But the empirical basis of period is clear: it is the recurrence of a regular change-pattern.

Examples include: the oscillation of a pendulum,  the vibration of a crystal, the rotation of a planet, the orbit of a moon, the cycle of a heartbeat, the recurrence of a wave crest.

In each case, the “period” is the pattern of change itself, not a duration measured against an independent temporal entity. The period of a pendulum is the pendulum’s oscillation. The period of the Earth’s rotation is the Earth’s rotation. The period of a wave is the wave’s recurrence.

Thus: Period = the recurrence interval of a regular change-pattern, defined by the pattern itself.

This definition does not require time. It requires only change and recurrence.

Persistence as Continuity of Change

Persistence is typically defined as “continued existence through time.” This definition presupposes time as a container in which objects endure. But persistence can be defined without invoking time.

Persistence is the continuity of change within a system’s identity-conditions. A system persists if: its internal change-patterns remain coherent, its structural relations remain within the bounds of its identity, and its interactions with other systems maintain continuity.

For example: A river persists because its flow-pattern remains coherent, a biological organism persists because its metabolic processes remain continuous, a planet persists because its mass-energy distribution remains stable, a quantum particle persists because its state-relations remain coherent.

Persistence is not “existence through time.” It is the maintenance of change-patterns that constitute identity. Thus: Persistence = the continuity of a system’s identity-constituting change-patterns.

This definition is empirical and structural. It does not require time as a container.

The Illusion of Temporal Necessity

If duration, period, and persistence can all be defined in terms of change, why do we believe they require time?

The answer lies in the semantic ambiguity identified earlier. Because the word time is polysemous, we mistakenly treat the abstract dimension of change as if it were a physical entity. We then assume that duration, period, and persistence must be defined in terms of this entity. But this assumption is unwarranted.

The empirical record shows that: duration is measured by change, period is defined by change, persistence is constituted by change. Time plays no independent role.

The Symmetry with Space

The same analysis applies to spatial concepts.

• Distance is the amount of spatial change between states.
• Location is a relational property defined by spatial relations.
• Extension is the structural spread of a system’s components.

None of these require space as a substance. All can be defined in terms of relational structure and change.

This symmetry reinforces the central thesis: time and space are conceptual frameworks derived from change, not fundamental entities.

Just as temporal concepts reduce to patterns of change, spatial concepts reduce to relational structure among change‑events.

The Conceptual Payoff

By reconstructing duration, period, and persistence in terms of change, we achieve three things:

• We dissolve the circularity in traditional definitions of temporal concepts.
• We show that time is not required to define the phenomena it is supposed to explain.
• We prepare the ground for the redundancy thesis, which argues that if time and spacetime can always be expressed in terms of change, they are not fundamental.

This sets the stage for Section 7, where the redundancy thesis is formulated explicitly.

4.6 The Redundancy Thesis: Time and Spacetime as Non-Fundamental

The preceding sections have established two key results:

• Empirical: All evidence for time and spacetime reduces to evidence of change and relational structure.
• Semantic: The words time and space are polysemous, and their abstract senses function as indexing frameworks rather than as names for physical substances.

These results jointly motivate a stronger claim: time and spacetime are not fundamental features of reality. They are conceptual tools derived from patterns of change. This section formulates that claim precisely and defends it against potential objections.

Formulating the Redundancy Thesis

The Redundancy Thesis can be stated succinctly:

If every empirical and explanatory role attributed to time or spacetime can be discharged by change and relational structure, then time and spacetime are not fundamental.

This is a standard form of argument in metaphysics and philosophy of science. When a posited entity does no independent explanatory work—when its roles can be fully discharged by other, better-grounded entities—it is deemed ontologically redundant. Classic examples include: phlogiston (replaced by oxygen and combustion chemistry), the luminiferous aether (replaced by electromagnetic field theory), absolute space (replaced by relational structure), vital forces (replaced by biochemical processes)

The same logic applies to time and spacetime. If time and spacetime add nothing to our explanations beyond what change and relational structure already provide, then they are not fundamental constituents of reality.

The Explanatory Work Attributed to Time

To evaluate the redundancy of time, we must examine the explanatory roles it is supposed to play. These typically include: ordering events, measuring duration, explaining rates of change, providing a background for dynamics, grounding persistence, generating temporal asymmetry.

Each of these roles can be discharged without positing time as a fundamental entity.

(1) Ordering events: Events can be ordered by their causal or structural relations, not by time. Causal order is primitive; temporal order is derived.

(2) Measuring duration: Duration is the amount of change in a reference system. Clocks measure change, not time.

(3) Explaining rates of change: Rates of change are ratios of one change-pattern to another. No independent temporal entity is required.

(4) Providing a background for dynamics: Dynamics can be formulated relationally, as in: Barbour’s timeless configuration space, Rovelli’s relational quantum mechanics, the Wheeler–DeWitt equation, Machian dynamics, causal set theory. None require a fundamental time.

(5) Grounding persistence: Persistence is the continuity of identity-constituting change-patterns, not endurance through a temporal medium.

(6) Generating temporal asymmetry: Temporal asymmetry arises from irreversible change-series, not from time itself.

Thus, time performs no indispensable explanatory work.

The Explanatory Work Attributed to Spacetime

A parallel analysis applies to spacetime. Spacetime is typically said to: Provide a geometric structure for physical processes, explain gravitational phenomena, define causal structure, serve as the arena for fields and particles and expand, curve, or evolve

But each of these roles can be discharged by relational structure and change-patterns.

(1) Geometric structure: Geometry describes relations among events, not a substance.

(2) Gravity: In GR, gravity is the manifestation of relational curvature, not a force exerted by a medium.

(3) Causal structure: Causal structure is primitive; spacetime geometry encodes it, but does not generate it.

(4) Arena for fields: Fields interact with one another; spacetime is a coordinate representation of those interactions.

(5) Expansion and curvature: Expansion and curvature are changes in relational metrics, not deformations of a physical fabric.

Thus, spacetime also performs no indispensable explanatory work.

The Redundancy Argument

We can now state the redundancy argument formally:

• All empirical evidence for time and spacetime is evidence of change and relational structure.
• All explanatory roles attributed to time and spacetime can be discharged by change and relational structure.
• No empirical or explanatory role remains that requires time or spacetime as fundamental entities.
• Therefore, time and spacetime are ontologically redundant.

This is not eliminativism in the sense of denying the usefulness of temporal or spacetime concepts. It is ontological minimalism: we retain the concepts as tools, but we do not treat them as fundamental constituents of reality.

Why Redundancy Matters

The redundancy of time and spacetime has significant implications:

• It dissolves pseudo-problems generated by reification.
• It clarifies the conceptual foundations of physics.
• It aligns with relational and emergent approaches in QG.
• It unifies the treatment of time and space under a single framework: change.
• It removes metaphysical baggage that has accumulated over centuries.

Most importantly, it allows us to reconstruct the ontology of physics in a way that is empirically grounded, conceptually coherent, and free of unnecessary abstractions.

The Positive Ontology: Change and Relation

If time and spacetime are not fundamental, what is?

The answer is already implicit in the preceding sections:

The fundamental ontology consists of change-events and the relational structure among them.

Everything else—time, space, spacetime, geometry, duration, persistence—is derived.

This is not a speculative metaphysics. It is an empirically grounded reconstruction of the conceptual framework of physics.

Transition to Objections

These considerations set the stage for addressing the most common objections to the Redundancy Thesis, which often arise from reifying temporal or spatiotemporal vocabulary.

5. Discussion

This section addresses the three strongest objections to the redundancy thesis.

5.1 Objection: “Change requires time.”

This objection presupposes precisely what is at issue. It builds time into the definition of change by stipulating that change is being one way at one time and another way at another time. On the present account, change is simply a difference between two states of a system; time is the abstract indexing of that difference, not its precondition. To insist that change requires time is to reify an indexing framework into a metaphysical entity. The ontology is difference; temporal vocabulary is a representational convenience.

5.2 Objection: “Physics uses time; therefore, time must be real.”

Physics uses many indispensable parameters—temperature, pressure, gauge choices, coordinate systems—that play essential roles in modelling but are not ontologically fundamental. Time functions in the same way: as a parameter that indexes change, not as a physical entity with causal powers. Moreover, several major frameworks in contemporary physics (the Wheeler–DeWitt equation, Barbour’s relational dynamics, Rovelli’s relational quantum mechanics, causal set theory) formulate dynamics without a fundamental time parameter. The presence of time in many equations reflects modelling practice, not metaphysical commitment.

5.3 Objection: “General Relativity treats spacetime as dynamical, therefore spacetime is real”

GR describes a dynamical metric field, but this does not entail a substantival spacetime. The metric encodes relational structure among events; curvature is a property of a mathematical manifold, not a physical medium. Einstein himself emphasised that spacetime has no independent existence apart from matter and energy. Contemporary approaches in quantum gravity reinforce this relational reading by treating spacetime as emergent. GR therefore supports the view that spacetime is a representational structure, not a fundamental entity.

6. Conclusion

This paper has argued that the empirical and conceptual roles attributed to time and spacetime can be reconstructed entirely from change and relational structure. All evidence typically taken to support temporal or spacetime ontology—ageing, decay, motion, oscillation, and gravitational phenomena—is evidence of change, not of independent temporal or spatiotemporal entities. Clocks register regular change‑events, and spacetime geometry encodes relations among such events; neither measurement detects a substance with causal powers.

A semantic analysis shows that the polysemy of time and space has encouraged the reification of coordinate structures in physical models. Distinguishing the abstract, indexing sense of these terms from their experiential, metaphorical senses dissolves familiar pseudo‑problems concerning temporal passage, spacetime “flow,” and the ontology of the metric field. Once these ambiguities are removed, the empirical record supports a minimalist ontology in which change is primary and temporal and spatiotemporal concepts are representational tools.

Reconstructing duration, period, persistence, spatiality, and spacetime structure in terms of change‑events and their relations yields the Redundancy Thesis: if every empirical and explanatory role attributed to time or spacetime can be discharged by change and relational organisation, then time and spacetime are not fundamental constituents of the physical world. This perspective coheres with time‑free or relational formulations in quantum gravity and with the dynamical spacetime of GR, both of which treat temporal and spatiotemporal structure as emergent or representational rather than primitive.

The resulting framework clarifies the conceptual status of temporal and spatiotemporal parameters in physical theory. It supports relational and emergent approaches to spacetime, dissolves pseudo‑problems generated by semantic conflation, and offers a unified, empirically grounded basis for interpreting the structure of physical models. If change is the fundamental empirical datum, then time and spacetime are best understood as abstractions we impose to organise patterns of change, not as elements of the ontology of nature.

This reconstruction fulfils the programme outlined in the introduction: to clarify the empirical and conceptual roles of time and spacetime by grounding them in change and relational structure, and to dissolve the pseudo‑problems that arise from reifying representational frameworks.

References

Aristotle. Physics, Book IV. Translated in various editions. (Primary source for the definition of time as “the number of motion with respect to before and after.”)

Barbour, Julian. The End of Time: The Next Revolution in Physics. Oxford University Press, 1999. (Develops the timeless “Platonia” view and argues that time is an emergent abstraction from correlations among configurations.)

Barbour, Julian. “The Nature of Time.” arXiv:0903.3489 (2009). (A concise technical statement of Barbour’s timeless approach.)

Carroll, Sean. From Eternity to Here: The Quest for the Ultimate Theory of Time. Dutton, 2010. (Discusses entropy, the arrow of time, and the cosmological origins of temporal asymmetry.)

Coope, Ursula. Time for Aristotle: Physics IV.10–14. Oxford University Press, 2005. (Authoritative analysis of Aristotle’s account of time and change.)

Einstein, Albert. “Relativity: The Special and General Theory.” 1916. (Popular exposition of relativity; clarifies that spacetime is a geometric model, not a physical substance.)

Einstein, Albert. “The Meaning of Relativity.” Princeton University Press, 1922. (Technical lectures clarifying the geometric interpretation of spacetime.)

Knox, Eleanor. “Effective Spacetime Geometry.” Studies in History and Philosophy of Modern Physics 44 (2013): 346–356

Lam, Vincent, and Christian Wüthrich. “Spacetime is as Spacetime Does.” Studies in History and Philosophy of Modern Physics 64 (2018): 39–5

Leibniz, Gottfried Wilhelm. “The Leibniz–Clarke Correspondence.” 1715–1716. (Foundational articulation of relational space and time.)

Huggett, Nick. “Target Space ≠ Spacetime.” Studies in History and Philosophy of Modern Physics 59 (2017): 81–88.

McTaggart, J. M. E. “The Unreality of Time.” Mind 17 (1908): 457–474. (Argues that the A-series is contradictory and that time is unreal.)

Rovelli, Carlo. The Order of Time. Allen Lane, 2018. (Presents the relational and thermodynamic view of time; argues that time is not fundamental.)

Rovelli, Carlo. “Relational Quantum Mechanics.” International Journal of Theoretical Physics 35 (1996): 1637–1678. (Foundational paper on relational quantum mechanics; time is not fundamental.)

Smolin, Lee. Time Reborn: From the Crisis in Physics to the Future of the Universe. Houghton Mifflin Harcourt, 2013. (Argues that physics has erred by treating time as non-fundamental; proposes restoring time to fundamental status.)

Smolin, Lee. The Singular Universe and the Reality of Time. Cambridge University Press, 2014. (Co-authored with Roberto Mangabeira Unger; argues for the reality of time and the uniqueness of the universe.)

Wheeler, John A., and Bryce DeWitt. “Quantum Theory of Gravity I: The Canonical Theory.” Physical Review 160 (1967): 1113–1148. (Contains the Wheeler–DeWitt equation, which famously lacks a time parameter.)

Whitehead, Alfred North. Process and Reality. Macmillan, 1929. (Develops a process-based metaphysics in which events and change are fundamental.)

Additional Linguistic Sources (for polysemy):

• Oxford English Dictionary, entries for “time” and “space.”
• Merriam-Webster Dictionary, entries for “time” and “space.”

Dictionary.com, entries for “time” and “space.” (Used to demonstrate the polysemous structure of temporal and spatial vocabulary.)