An Ontological Audit of Temporal Structure in Physics
1. Introduction: The Question Behind “What Is Time?”
What is Time?
The question has generated an enormous literature spanning physics, metaphysics, philosophy of language and the philosophy of science. Yet the apparent simplicity of the question conceals a difficulty. The word Time is used to refer to several importantly different things: a coordinate in a mathematical theory, a parameter in a dynamical equation, a measurable interval, a component of spacetime structure, the reading of a clock, the ordering of events, the succession of physical changes, or an independently existing feature of reality.
These usages need not be mutually exclusive. But neither should they be allowed to acquire one another’s ontological status merely through linguistic familiarity.
This paper therefore begins with a narrower question:
What physical evidence requires us to add Time to our ontology?
The wording is deliberate. It does not ask whether physics uses time. Clearly it does. It does not ask whether temporal intervals can be measured. They can. It does not ask whether proper time is physically meaningful. It is. Nor does it ask whether spacetime possesses physically significant temporal structure. Modern physics provides strong reasons to say that it does.
The question is instead whether these established facts require an additional ontological commitment: that, over and above physical systems, physical change, events, relationships and temporal structure, there exists an independently existing physical reality corresponding to Time.
This is a narrower claim than the familiar proposition that “Time is not real”. It is also a more tractable philosophical question. The latter statement is ambiguous because it leaves unspecified what Time means and what sense of real is intended. The present paper seeks to avoid that ambiguity.
The aim is not to identify a single contemporary philosopher as committing an error. Rather, the audit identifies a class of inferential transitions that may occur whenever claims move from physical temporal structure to a further Time ontology.
In this paper, “additional Time” denotes an ontological posit claimed to exist over and above the physical systems, events, relations and temporal structure represented by established physical theories. The term is deliberately narrower than Time in ordinary or technical usage. If a view uses “Time” to mean physically significant temporal structure itself, that structure is accepted here and is not the target of the audit.
The paper does not assume that contemporary eternalists, substantivalists or structural realists generally posit a separate temporal substance. It asks a conditional question: when a claim moves from physically significant temporal structure to a further ontological posit, what argument warrants that move?
The qualification matters. If Time means the temporal structure of spacetime, then the paper does not dispute its physical significance. If Time means proper-time intervals associated with physical histories, those too are accepted as physically meaningful and measurable. The question arises only when the term is taken to refer to something further.
The methodological principle is therefore:
Define the term. Identify the physical referent. Show the evidence. Then justify the ontological conclusion.
This paper does not propose a new physical theory or mathematical formalism. It does not challenge the empirical success of established physical theories. Its purpose is diagnostic: to examine whether physical evidence, mathematical representation, physical structure and ontological interpretation have been sufficiently distinguished when claims about Time are made.
The central distinction can be represented as:
Physical evidence → Mathematical representation → Physical structure → Semantic interpretation → Ontological commitment
The arrows are not identities. A physical observation does not automatically become a mathematical object; a mathematical object does not automatically become a physical entity; a physical structure does not automatically become a separate substance or entity; and a conventional use of a word does not automatically establish the ontology suggested by its grammar.
The paper therefore adopts a simple rule:
Don’t dispute the physics. Audit the inference.
2. Method: An Ontological Audit
The distinction between physical evidence and ontological interpretation is familiar within philosophy of science. Mathematical representation, modelling and ontological commitment have long been recognised as separable questions. The present paper does not claim to invent that distinction. Its purpose is to apply it systematically to the ontology of Time.
The audit proceeds through five questions.
What physical phenomenon is being described?
What mathematical structure represents it?
What physical structure or relationship does that representation encode?
What does the terminology used to describe it mean?
What ontological commitment, if any, follows?
The resulting analytical sequence is:
Empirical → Mathematical → Structural → Semantic → Ontological.
Example:
| Level | Proper Time Example |
| Empirical | Clock behaviour |
| Mathematical | Proper-time integral |
| Structural | Timelike worldline |
| Semantic | “Elapsed time” |
| Ontological | What exists? |
The ordering is methodological rather than chronological. A particular scientific argument may move repeatedly between these levels. The point is to make the transitions visible.
2.1 Physical evidence comes first
Whatever ontology physics ultimately supports, its empirical access to the physical world is through physical systems, processes, interactions, differences and relationships.
Bodies move. Particles change state. Fields vary. Atoms undergo transitions. Stars form and evolve. Biological systems develop and decay. Physical systems interact.
These are physical phenomena.
The statement that physical systems change is therefore an empirical starting point. It should not yet be confused with the stronger metaphysical proposition that change is itself the fundamental constituent of reality. That is a further ontological claim.
The distinction is important because the present paper is not attempting to settle every metaphysical question about change. It begins more modestly: physical change is among the things to which our physical theories and measurements have empirical access.
2.2 Mathematical representation is not automatically ontology
Physics represents physical relationships mathematically.
For example,
v = Δx/Δt
represents a relationship between displacement and a temporal parameter.
The equation does not by itself determine the metaphysical status of the symbol (t).
Likewise, a coordinate system may contain a temporal coordinate without thereby establishing that the coordinate corresponds to an independently existing entity called Time.
This does not mean that mathematical structures are unreal or arbitrary. Quite the contrary: mathematical structures can encode highly constrained and physically successful relationships. The point is simply:
Mathematical precision does not guarantee ontological precision.
2.3 Semantic precision
Semantic precision does not require abandoning established scientific terminology. Terms such as time dilation and proper time have well-established technical meanings and are retained where they provide useful and unambiguous shorthand. Their use, however, should not be taken to settle the ontological question at issue.
The paper therefore distinguishes between the established scientific function of a term and any stronger ontological interpretation that might be inferred from its wording.
The governing principle is:
Conventional terminology is permissible as a label; it is not automatically accepted as an ontological description.
This matters because scientific language can compress several distinct claims into one expression. Time may refer to a coordinate, interval, parameter, structural feature or ontological entity. These must be disambiguated before they can be compared.
Disambiguate before you ontologise.
2.4 The burden of ontological commitment
The audit does not assume that an entity is real only if it is directly observable, independently causal, or indispensable to every successful formulation of a theory. Scientific and metaphysical commitments may be supported by explanatory, theoretical or broader ontological considerations, even when their interpretation remains contested.
The narrower issue is what warrants the claim that physics requires an additional Time ontology. The paper uses “ontological necessity” as an evidential question, not as a universal test for reality: does the proposed posit do work in the empirical or explanatory account, or is the claim supported by some other independently stated commitment?
Where rival ontologies accommodate the same established physical evidence, that evidence alone may underdetermine which ontology is correct. This does not show that the positions are equally satisfactory in every respect, or that the additional posit is false. It means only that empirical support for the shared physical structure does not by itself settle the further ontological question.
Accordingly, the working principle is modest: a claim that physics requires an additional entity needs an account of how that requirement follows from the theory or from other stated grounds. The burden discussed here attaches to the claim of physical necessity, not to every possible metaphysical belief in Time.
Additional physical ontology requires additional justification.
The audit therefore distinguishes what physical theory establishes from what an interpretation adds, while leaving room for arguments that go beyond direct empirical discrimination. This evidential use of “requires” is not a neutral or exhaustive theory of ontological commitment. Quine’s account of ontological commitment and Sider’s emphasis on objective structure marks relevant, but distinct, background debates (Quine, 1948, 1960; Sider, 2011).
3. Physical Change: The Empirical Starting Point
Whatever else physics tells us, its empirical access to the physical world is through observable physical differences, processes, interactions and relationships.
We observe physical systems in different states, interactions, and movement and transformation. We compare physical processes with one another. The concept of change is therefore unavoidable.
Suppose a physical quantity (x) has values (x1) and (x2). Its change can be represented as
Δ x=x2-x1.
If a spatial displacement occurs, a rate of change can be represented as
v = Δx/Δt
The introduction of (t) makes the relationship between displacement and rate quantitatively expressible. It does not by itself establish that (t) denotes an independently existing physical entity.
This distinction becomes clearer when we consider measurement.
A physical process can provide a reproducible standard against which other processes are compared. Historically, familiar recurring physical processes supplied practical standards: the rotation of Earth, cycles associated with the Moon and Earth’s orbit. Modern metrology replaces such everyday standards with highly reproducible physical processes.
The basic measurement sequence is therefore:
physical change → reproducible physical process → standardisation → measurement.
In this operational sense, timekeeping is fundamentally a process of comparing physical change with standardised physical change.
This does not reduce Time to “just change”. Modern physics contains temporal structure that cannot be captured by such a simple identification. The point is narrower: the empirical foundation of temporal measurement is physical processes and relationships between them.
We therefore have strong grounds for accepting:
physical change;
physical events;
relationships between events;
reproducible physical processes;
measurable intervals;
temporal structure.
The question remains whether we need to add something further.
4. Newton: From Temporal Parameter to Absolute Time
Newtonian mechanics provides a useful starting point because Newton did not merely use a temporal parameter. He explicitly distinguished mathematical time from what he regarded as absolute, true and mathematical Time.
Newtonian mechanics represents position as a function of time:
x=x(t),
with velocity and acceleration given by
v=dx/dt, ; a=d²x/dt².
The mathematical role of (t) is clear. It provides the parameter relative to which dynamical change is represented.
Newton’s philosophical claim went further. In the Principia, he distinguished absolute time from relative, apparent and common time, describing absolute time as something that “flows equably without relation to anything external” (Newton, 1999 [1687], p. 408).
The historical importance of this distinction is that Newton provides an explicit example of the transition under examination:
mathematical temporal parameter → physical theory → absolute Time.
The first two steps are uncontroversial. The third is an ontological interpretation.
The success of Newtonian mechanics demonstrates that a temporal parameter is extraordinarily useful for representing physical dynamics. It does not, by itself, demonstrate the metaphysical proposition that absolute Time exists independently of all physical processes.
The question is therefore not whether Newtonian mechanics works without its temporal parameter. Clearly, the formulation requires one. The question is whether the success of the parameter establishes the independent existence of the entity Newton associated with it.
This distinction becomes particularly important once relativity removes universal Newtonian time.
Newton supplies an historically explicit example of the audit’s final transition.
5. Special Relativity: When Universal Time Disappears
Special relativity changes the conceptual landscape.
There is no longer a single universal temporal parameter shared by all inertial observers. Temporal and spatial coordinates depend on the reference frame, while the spacetime interval remains invariant.
In one common signature convention,
ds^2=-c^2dt^2+dx^2+dy^2+dz^2.
The relativity of simultaneity demonstrates that temporal relationships cannot simply be understood as manifestations of a universal Newtonian clock. What disappears is not merely a universal clock but a frame-independent global temporal ordering for spacelike-separated events.
This is a crucial empirical and theoretical achievement. But it does not follow that Time has thereby been shown to “bend”, “slow” or “flow” as an independent entity.
What changes between observers are the coordinate descriptions and, for different physical histories, the proper-time intervals associated with those histories.
A useful way of stating the distinction is:
different histories → different proper-time intervals → different clock readings.
No additional proposition that “Time itself changed” is required.
The terminology time dilation is perfectly useful as a standard description of the phenomenon. But the phrase does not settle its ontology.
The physical content is that clocks following different worldlines can accumulate different readings. The mathematical content is represented by Lorentz transformations and the invariant spacetime interval. The ontological question is whether these facts require an independently existing entity called Time.
Special relativity therefore establishes a rich temporal structure without restoring Newtonian absolute Time.
This makes the next case particularly important.
6. Proper Time: The Strongest Case for Temporal Reality
If there is a place in modern physics where a realist about Time might reasonably expect to find direct support, it is proper time.
Proper time is a physically meaningful, invariant and measurable quantity associated with a timelike physical history.
For a timelike worldline parameterised by λ, proper time is given by
dτ² = −(1/c²) gμν dxμ dxν
with the sign convention used here.
Along a worldline,
τ = (1/c) ∫ dλ √[−gμν (dxμ/dλ)(dxν/dλ)]
An ideal clock following that worldline operationally realises the corresponding interval.
Nothing in the present argument requires us to deny this physical reality. Indeed, denying it would weaken the argument by attacking precisely the physics that provides its strongest test.
The important question is instead:
What ontological conclusion follows from the physical reality of proper time?
The answer is less straightforward than it might initially appear.
Proper time is calculated from the metric and the physical history:
g_μν + timelike worldline → τ.
The fact that the resulting quantity is invariant and measurable makes it physically significant. But derivability does not imply unreality. Nor does measurement automatically determine ontological category.
The correct conclusion is therefore conditional.
If by Time we mean the physically meaningful temporal interval associated with a timelike history, then physics provides strong evidence for its reality.
If by Time we mean an additional independently existing reality over and above the physical history and the spacetime structure that determine the interval, proper time does not by itself establish that further entity.
This is the critical distinction:
proper time is physically real ⇏ Time is an additional physical entity
The calculation contains no additional variable or entity whose independent existence must be invoked beyond the metric, the timelike worldline and the interval they determine.
This does not prove that no such (T) exists. It establishes something narrower and methodologically important:
The calculation does not require an additional ontological ingredient beyond the physical and geometrical structures already present.
Proper time therefore represents the strongest physical case considered here for temporal reality. The audit does not infer that it is unreal because it is defined through the metric and a worldline; it asks whether its physical reality establishes anything beyond the invariant interval associated with that history.
A realist may answer that proper time just is the relevant physical reality of Time. If “Time” is used to name invariant proper-time intervals and the temporal structure that relates physical events, the paper accepts the underlying physics and the disagreement is chiefly about terminology or the preferred ontology of that structure. The stronger claim examined here is that physics requires something over and above the metric, worldline, interval and physical clock behaviour.
To establish that stronger claim, an argument would need to identify what the additional posit contributes or what physical or explanatory commitment would be lost without it. The proper-time formalism establishes a measurable invariant and its relation to spacetime geometry; it does not, by itself, distinguish an additional Time entity from that established structure. This is the result of the worked audit, not a denial of proper time’s physical reality.
The audit identifies the point at which the argument moves from a physically established temporal quantity to an additional ontological commitment concerning Time.
7. Spacetime: Does Real Geometry Require Real Time?
Proper time demonstrates that temporal quantities can be physically real without thereby settling their ontological interpretation. The broader question is whether the same conclusion applies to spacetime structure itself.
The spacetime interval is represented by
ds^2=g_μνdx^μ dx^ν,
and the metric field participates directly in the gravitational dynamics through Einstein’s field equation:
Gμν + Λgμν = (8πG/c⁴)Tμν
The present argument therefore does not treat spacetime as a merely mathematical fiction.
The question is more precise:
Does the physical reality of spacetime structure require Time to be added as a further physical reality?
Several propositions must be separated.
Spacetime geometry has physical consequences.
The metric has objective physical significance.
Temporal structure is part of that spacetime structure.
The spacetime structure may be regarded as fundamental.
Time therefore exists as an independently existing entity.
The first four do not logically entail the fifth.
This is particularly important because the word fundamental can itself perform an illicit ontological escalation.
A structure can be fundamental without being a separate entity. A relation can be fundamental without being a substance. A mathematical structure can represent a physically fundamental organisation without requiring an additional object corresponding to every element of its formal description.
Thus:
fundamental temporal structure ⇏ independent Time entity
If Time means the temporal aspect of physically real spacetime structure, then the dispute is largely terminological or concerns which structural ontology is preferred.
If Time means something in addition to that structure, the ontological gap must be identified.
The question becomes:
What is the additional thing?
Many realists will identify temporal structure with spacetime structure itself. If so, the audit records that commitment at the structural level and no additional Time posit is involved.
8. Competing Ontologies of Temporal Structure
The philosophical literature contains several broad approaches to temporal ontology and the ontology of spacetime.
Substantivalist, relationist, structural realist and emergent approaches provide different accounts of the ontology of space and time. They disagree about whether priority belongs to spacetime itself, relations among physical systems, physical structure, or deeper underlying descriptions. These positions should not be treated as interchangeable commitments to an additional temporal substance (Mellor, 1998; Maudlin, 2012; Callender, 2017).These positions should not be collapsed into one another.
The purpose here is instead to ask where their disagreements occur.
A useful baseline ontology is:
physical systems + change + events + relationships + temporal structure + measurement.
A stronger ontology might add:
O₂ = O₁ + independent Time
The question is whether the additional element makes an empirically or theoretically necessary difference.
This does not mean that ontological economy automatically settles the dispute. Nor does it imply that empirically equivalent ontologies are equally satisfactory in every philosophical respect. It means that empirical evidence alone cannot establish an additional entity if that entity makes no distinguishable contribution to the empirical or explanatory account.
This provides a useful comparison:
What physical phenomenon is being described?
then:
What mathematical structure represents it?
then:
What does “Time” refer to in this account?
and finally:
What ontological commitment is actually being made?
The Block Universe
The Block Universe provides a useful test case because it is often associated with the four-dimensional interpretation of relativistic spacetime. In its standard eternalist form, the view treats past, present and future events as equally real and denies that physics identifies an objectively privileged present.
The present paper neither endorses nor rejects this interpretation. Its relevance is methodological. A four-dimensional spacetime ontology may make substantial claims about the reality and organisation of physical events without thereby requiring a further entity corresponding to Time.
T₁ = temporal structure of physical spacetime; T₂ = an additional ontological reality corresponding to Time
A Block Universe interpretation provides one account of T₁, including the ontological status assigned to events at different temporal locations. It does not, without further argument, establish T₂.
Nor does the present analysis depend upon eternalism. Presentism, growing-block theories and other interpretations may disagree about which temporal structures or events are ontologically privileged. Whatever the correct interpretation proves to be, the question pursued here remains: what physical evidence requires the addition of a further entity called Time?
The Block Universe therefore illustrates the central distinction of this paper. A theory may make a substantial ontological commitment concerning the structure and contents of spacetime without every concept used to describe that structure becoming a further ontological entity. An eternalist who identifies Time with four-dimensional temporal structure is not in disagreement with the paper’s central claim. The audit applies only if a further posit is claimed beyond that structure.
Special relativity has often been taken to support eternalist or Block Universe interpretations, but the metaphysical implications of relativistic spacetime remain contested. The present argument does not depend on resolving that debate.
The value of this sequence is that apparently profound disagreements may turn out to occur at different levels.
Two accounts may agree completely about empirical evidence while disagreeing about mathematical representation. Two may agree about the mathematics while disagreeing about structural interpretation. Two may agree about the structure while disagreeing about its ontological significance.
Agreement at one level does not entail agreement at another. The disagreement occurs at the ontological interpretation of the structure rather than at the empirical level.
9. The Category-Shift Audit
The central diagnostic question can now be stated:
Where, precisely, does the claim that Time exists enter the argument?
Consider the following progression:
physical change → temporal relationship → temporal structure → fundamental structure → Time.
The first stages may be strongly supported by observation and physical theory.
The final transition is the one that requires examination.
A particularly important distinction is between:
T_1=fundamental temporal structure
and
T_2=an additional physical reality corresponding to Time.
If Time means (T_1), then the argument concerns the physical reality and fundamentality of temporal structure.
If Time means (T_2), then an additional ontological commitment has been introduced.
The distinction can be summarised as follows: evidence for T₁ establishes physically significant temporal structure; it does not, without a further argument, establish T₂ as an additional reality.
This audit also reveals how category shifts can occur through ordinary mathematical language:
t → time coordinate → temporal dimension → temporal structure → physical reality → Time.
Each step may be reasonable in context. The problem arises if the transitions are treated as automatic.
The governing principle is:
Never let a change in terminology silently become a change in ontology. The concern has a family resemblance to Ryle’s analysis of category mistakes; recent preprints apply related diagnostics to claims about temporal asymmetry (Ryle, 1949; Borrill, 2026; Zhong, 2026).
Or more compactly:
Disambiguate before you ontologise.
The audit does not claim that every transition is mistaken. It asks which transitions are evidentially supported and which require independent philosophical justification.
10. What Does Adding Time Actually Add?
Suppose, for the sake of argument, that Time is an independently existing physical reality.
What does that addition contribute?
The question should not be interpreted as the claim that every real thing must function as a causal agent. That would be too strong. Rather, if a proposed entity is physically real, it is reasonable to ask what distinctive physical role its existence plays and what evidence identifies that role.
Energy, momentum and charge provide useful contrasts. They are not merely names attached to equations. They participate in well-defined physical relationships and have identifiable empirical consequences.
What corresponding role is played by an independently existing Time?
Consider ageing. Biological ageing involves physical processes:
biochemical processes → physical changes → ageing.
The physical mechanisms of ageing do not require Time to be inserted as an additional causal agent.
The same applies to clocks. A clock changes because its physical mechanism changes. The reading provides a standardised index of a physical process and can be compared with other physical processes.
Thus:
We observe change. We observe causes of change. We measure relationships between changes. But where, precisely, do we observe Time doing anything?
The academic version is:
If Time is proposed as an independently existing physical entity, what physical role does that entity play, and what evidence distinguishes that role from the roles already accounted for by physical systems, interactions and temporal structure?
This is a diagnostic question, not a causal criterion for reality.
It leads to a useful three-part test:
What is it? → What evidence establishes it? → What does it add?
If the answer to the third question is simply that Time provides the temporal structure already contained in the physical theory, then the additional entity has not yet been distinguished from the structure it is supposed to explain.
11. Related Approaches and the Scope of the Contribution
The literature relevant to this audit contains several debates that should be distinguished. Their relevance is not that they all defend the same ontology of Time, but that they clarify the kinds of inferential and interpretive questions the paper addresses.
Structural realism is an important background. Worrall (1989) and Ladyman (1998), and the naturalised structural realism developed by Ladyman, Ross, Spurrett and Collier (2007), make the relation between successful scientific structure and ontological commitment a central question. The present paper does not derive structural realism from its audit, nor argue that structures are the only real items or that entities must be reduced to relations. Its proposed contribution is a diagnostic procedure: it tracks empirical, mathematical, structural, semantic and ontological transitions and can be used by interpreters who disagree about the resulting ontology.
The evidential criterion used here also has a philosophical background. Quine’s account of ontological commitment makes the relation between theory and what there is explicit, while Sider argues that metaphysical description should capture objective structure (Quine, 1948, 1960; Sider, 2011). The present paper does not claim that empirical indispensability is the sole legitimate ground for ontology, or that its criterion is philosophically neutral. It uses “physics requires” in a narrower sense: the physical theory and evidence must support the claim of necessity. Other explanatory or metaphysical grounds may support an additional posit, but they should be identified as such rather than attributed to the empirical results alone.
Philosophy of time provides a second, shorter test of the audit. Mellor (1998), Callender (2017) and Maudlin (2012) address the metaphysics of time and its relation to physical theory from different positions. Maudlin’s defence of fundamental temporal structure and of taking temporal passage seriously is a more substantive challenge than an inference from clock readings alone. The audit grants the claim that temporal structure or passage may be fundamental, then asks what further step would establish an additional ontological reality over and above that structure. If “Time” names the fundamental temporal structure itself, this paper does not dispute its physical reality; if it names something further, that further commitment needs its own argument. This discussion does not attribute to Maudlin a separate temporal substance. Rovelli (2018) and Barbour (1999) offer influential, more strongly revisionary accounts of time in physics. These works locate the debate but are not treated as evidence that their authors defend an extra entity corresponding to Time beyond temporal structure.
The analysis of category mistakes also has an established history in Ryle (1949). Recent manuscripts by Borrill (2026) and Zhong (2026) apply category-error diagnoses to particular claims about temporal asymmetry. These are related applications, not identical arguments: the present paper’s concern is the broader route from physical evidence and formal representation to ontological claims about Time. Borrill’s and Zhong’s cited works are preprints, and are treated here as such.
Other recent contributions approach the question from change-centred and operational directions. Deasy (2026) defends a change-centred account; Trepp (2026) argues for an operational and relational interpretation of clock measurement. These approaches do not establish a single consensus. They help locate the present paper’s narrower contribution: a shared audit of what is physically established, mathematically represented, structurally significant, semantically asserted and ontologically added. Trepp’s cited work is an archived preprint.
The paper does not claim that the distinctions between representation, structure, semantics and ontology are new, or that it is the first to question an independent temporal reality. Nor does it claim that any of the authors discussed above infer a separate temporal substance from temporal structure. Its target is conditional: whenever an argument claims that physics requires an additional Time posit, the audit asks where that commitment enters and what warrants the transition.
The contribution claimed here is neither a new ontology of Time nor a denial of temporal reality. It is the development and application of a systematic ontological audit capable of distinguishing what is empirically established, mathematically represented, structurally encoded, semantically interpreted and ontologically added in arguments about temporal reality. The framework could in principle be applied to other ontological claims in science, but the present paper develops and assesses it only in relation to Time.
12. Limits of the Argument: Underdetermination and Ontological Choice
The argument has deliberately narrow conclusions.
Four propositions must be distinguished:
A claim has not been established.
A claim is not required by the current account.
A claim is poorly supported.
A claim has been empirically ruled out.
The present argument primarily concerns the first two.
The fact that an independent Time ontology has not been demonstrated to be necessary does not demonstrate that such an ontology is impossible.
Similarly, if two ontological accounts are empirically equivalent, O₁ and O₂, then empirical evidence alone may not distinguish them.
This is ontological underdetermination.
It follows that:
No demonstrated ontological necessity ≠ demonstrated non-existence.
But the converse methodological point remains important:
No demonstrated ontological necessity ⇒ no sufficient justification for the additional commitment.
This is not an argument for eliminating metaphysics. It is an argument for keeping empirical claims and metaphysical choices distinct.
A philosopher may reasonably choose a substantivalist ontology, a relational ontology, a structural ontology or an emergent ontology. Such choices may be motivated by explanatory, metaphysical or theoretical considerations extending beyond direct empirical discrimination.
The present paper does not attempt to prohibit those choices.
It asks that they be identified as choices.
13. What, Then, Is Time?
We can now return to the original question.
Physics establishes physical change. It establishes events and relationships between events. It establishes measurable temporal intervals. Relativity establishes that different physical histories can accumulate different proper times. General relativity establishes physically significant spacetime geometry and temporal structure.
None of this is in dispute.
The question is what Time adds.
One legitimate answer is “Time” labels an abstract framework for quantifying, ordering and relating physical change and events. Modern physics gives this framework a rich and physically significant structure.
Another legitimate use of Time refers to the succession and relationships of physical change-events that ordinary language collectively describes as “Time”.
Still another use identifies Time with physically real temporal structure.
None of these interpretations requires the additional claim that Time is an independently existing entity over and above the physical systems, events, relationships and structures to which the theory already commits us.
That final possibility remains open as a metaphysical hypothesis.
But it has not been established by the physical evidence examined here.
This gives the central distinction:
Physics establishes temporal structure.
but:
Physics does not thereby establish an additional Time ontology.
The conclusion is deliberately modest. The paper does not show that Time cannot exist.
It shows that the additional ontological reality of Time has not been demonstrated to be physically necessary.
14. Conclusion
This paper began with a deliberately narrow question:
What physical evidence requires us to add Time to our ontology?
To address that question, it developed a systematic ontological audit distinguishing five levels at which claims about Time may be made:
Empirical → Mathematical → Structural → Semantic → Ontological
The purpose of the audit was not to determine which ontology of time is ultimately correct. It was to identify what is physically established, how it is mathematically represented, what physical structure is encoded, how that structure is described, and where additional ontological commitments enter.
Applied to Newtonian mechanics, special relativity, proper time, spacetime geometry and competing interpretations of temporal structure, the audit revealed a consistent result. Physics establishes physical change, measurable temporal intervals, invariant proper time and physically significant temporal structure. None of these conclusions is disputed here. The question is whether they also establish an additional ontological reality corresponding to Time.
The analysis suggests that this further conclusion does not follow automatically from the physics. If Time is identified with temporal structure, proper time or the temporal aspect of spacetime geometry, then physics provides strong grounds for its physical significance. If Time is taken to denote an additional independently existing reality over and above those structures, an additional ontological commitment has been introduced and requires its own justification.
The principal contribution of the paper is therefore methodological rather than metaphysical. It does not propose a new ontology of Time, nor does it seek to replace existing ontologies with an alternative account. Its contribution is the development and application of a systematic audit capable of distinguishing what is empirically established, mathematically represented, structurally significant and ontologically added in arguments about temporal reality.
The resulting conclusion is deliberately limited. The audit does not demonstrate that Time does not exist. Nor does it show that broader metaphysical interpretations of temporal reality are illegitimate. It shows something narrower: the physical evidence and theoretical structures examined here do not by themselves demonstrate the necessity of an additional Time ontology beyond the temporal structure already established by contemporary physics.
The broader implication is methodological. Physical theories may underdetermine ontology. Where they do, further ontological commitments remain possible, but they should be recognised as commitments requiring additional argument rather than as conclusions already established by the empirical evidence itself.
The guiding principle of the audit may therefore be stated simply:
Physics establishes temporal structure. Additional ontology requires additional justification.
In the case of Time, that additional justification remains to be shown.
References
Barbour, J. (1999). The End of Time. Oxford University Press.
Borrill, P. (2026). The Markovianity of Time: The Category Mistake in Open Quantum Systems. arXiv:2603.13738 [preprint]. https://arxiv.org/abs/2603.13738
Callender, C. (2017). What Makes Time Special? Oxford University Press. https://doi.org/10.1093/oso/9780198797302.001.0001
Deasy, D. (2026). Time Is Change. Philosophies, 11(3), 67. https://doi.org/10.3390/philosophies11030067
Ladyman, J. (1998). What is structural realism? Studies in History and Philosophy of Science Part A, 29(3), 409–424. https://doi.org/10.1016/S0039-3681(98)80129-5
Ladyman, J., Ross, D., Spurrett, D., & Collier, J. (2007). Every Thing Must Go: Metaphysics Naturalized. Oxford University Press. https://doi.org/10.1093/acprof:oso/9780199276196.001.0001
Maudlin, T. (2012). Philosophy of Physics: Space and Time. Princeton University Press.
Mellor, D. H. (1998). Real Time II. Routledge.
Newton, I. (1999 [1687]). The Principia: Mathematical Principles of Natural Philosophy (I. B. Cohen & A. Whitman, Trans., with J. Budenz). University of California Press.
Quine, W. V. O. (1948). On what there is. The Review of Metaphysics, 2(5), 21–38.
Quine, W. V. O. (1960). Word and Object. MIT Press.
Rovelli, C. (2018). The Order of Time (E. Segre & S. Carnell, Trans.). Riverhead Books.
Ryle, G. (1949). The Concept of Mind. Hutchinson.
Sider, T. (2011). Writing the Book of the World. Oxford University Press. https://doi.org/10.1093/acprof:oso/9780199697908.001.0001
Trepp, T. C. (2026). Measuring Change, Not Time: An Existential Realism Reinterpretation of Temporal Formalism. PhilArchive [preprint]. https://philarchive.org/rec/TREMCN
Worrall, J. (1989). Structural realism: The best of both worlds? Dialectica, 43(1–2), 99–124. https://doi.org/10.1111/j.1746-8361.1989.tb00933.x
Zhong, J. (2026). Time’s Arrow as a Category Error. SSRN [preprint]. https://doi.org/10.2139/ssrn.6912318
