Temporal Ontology and Non-Markovian Quantum Dynamics

Abstract

Recent arguments in favor of Presentism leverage Markovianity, the principle of the future’s events being able to be determined/influenced only by current events (and sufficiently near events). These approaches, however, leave the room open for objections centered around recent speculative non-Markovian foundations of our physical theories. Using insights from Builes and Impagnatiello’s argument and drawing on recent quantum foundations, I explore how non-Markovian quantum dynamics may constrain metaphysical accounts of time. I compare rough versions of Eternalism and Presentism in their ability to accommodate temporally extended correlations and motivate further development with explicit treatment of non-Markovian physics in the metaphysics of time.

1. Introduction

In the philosophy of time, roughly speaking, Presentism holds that only present events exist. The contrastive view Eternalism says that past, present, and future events all equally exist. Philosophers have long debated which view better fits with modern physics. Markovian processes are usually taken to be central to many physical theories, including classical mechanics and quantum mechanics [1]. In these models, the system evolves in such a way that the future state is fully determined by the present, making the past irrelevant. As with any philosophical discourse regarding physical laws, theories, and time, it is important to distinguish and clarify our notions. As Lettie puts it:

“Processes which adhere to Markovianism, such as Brownian motion, are commonly called ‘Markovian’. But Markovianism is a general claim about temporal processes, and if our physical theories are right, this general claim is true. We can put this by saying that the universe is Markovian, and/or the laws of physics are Markovian, and/or time is Markovian. I use these interchangeably to express endorsement of Markovianism, a universe-wide claim about processes, laws, and time.”

[2] (p. 1)

I adopt this vocabulary throughout this paper. This feature of time evolution fits naturally with Presentism’s view that only the present is real and causally relevant.

It then is not surprising that a recent argument, by Builes and Impagnatiello (B&I), affirms that Markovianism supports Presentism [3]. According to the account, Presentism naturally explains the supposed Markovian nature of our laws. The general argument structure employed by B&I takes this form:

(P1) A theory of time that explains why time is Markovian is preferable to one that does not.

(P2) Particular versions of Presentism (plus non-Humeanism) explain why time is Markovian.

(P3) No versions of Eternalism (even with non-Humeanism) explain why time is Markovian.

(C) Thus, we should reject Eternalism and endorse one of those particular versions of Presentism.

P1 is defended by drawing upon our physical theories, which are (roughly) Markovian according to B&I. However, recent speculative approaches in quantum foundations suggest that fundamental physics may exhibit non-Markovian features under specific interpretations. Examples of such ongoing research topics include applications of modular flow in quantum gravity [4], the thermal time hypothesis [5], Barandes’s [6] indivisible stochastic correspondence, and the vast literature of quantum open systems. This calls for an examination of the metaphysics of time from a non-Markovian perspective.

In this paper, I investigate what metaphysical accounts of time might look like if we take non-Markovian assumptions seriously. While the dialectical structure parallels Builes and Impagnatiello’s argument for Presentism from Markovianity, my aim is solely to offer a preliminary map of the explanatory strategies available to different ontologies of time under non-Markovian assumptions. To illustrate how non-Markovian assumptions might shift the dialectical landscape, consider how a proponent of Eternalism might construct a parallel argument:

(P1’) A theory of time that explains why time is non-Markovian at the foundational level of quantum mechanics is preferable to one that does not.1

(P2’) Particular versions of Eternalism explain why time is non-Markovian.

(P3’) No versions of Presentism explain why time is non-Markovian.

(C) Thus, we should reject Presentism and endorse one of those particular versions of Eternalism.

This argument structure highlights how Eternalism and Presentism differ in their explanatory prospects under non-Markovian assumptions, even if one does not endorse the conclusion as definitive. Throughout the paper, I assume the argument from B&I, and this parallel one, to represent the two opposing views. In Section 2, I explore the possibility of P1’ through a brief distinction of non-Markovianism. Section 3 then discusses non-Markovian quantum foundations. In Section 4, I present P2’ and discuss various versions of Eternalism and objections. I do the same for Presentism in Section 5 and P3’. I conclude with future directions in Section 6.

2. Non-Markovian Distinction

In this section, I motivate premise P1′ by examining recent developments in quantum foundations that suggest time evolution is non-Markovian at a fundamental level. I begin by characterizing non-Markovianism in probabilistic terms, then survey physical models that embody this feature. Finally, I argue that such models warrant metaphysical explanation if we take their foundational status seriously.

2.1. Non-Markovianism

Let us consider the following proposition introduced earlier.

P1’: A theory of time that explains why time is non-Markovian is ceteris paribus preferable to a theory that does not.

Usually, we take non-Markovianism to be the thesis that the temporal evolution of a physical system is such that the present state does not screen off the past from the future. More precisely, for stochastic processes, letting $S_t$ denote the complete physical state of the system at time t, a Markovian process satisfies

$$P(S_{t_2}\mid S_{t_1}, S_{t_0})=P\left(S_{t_2}\right|S_{t_1})$$

for all t₀ < t₁ < t₂. That is, the probability of some event at t₂ given information of another state at t₁ is the same as having t₁ and another state at t₀. In short, having more information about the past does not influence the probability of some future state happening; it is only the current physical state that determines probabilities for a future state. Non-Markovian processes violate this condition: the future conditional on the present depends non-trivially on earlier states. In probabilistic terms, the present is not a sufficient statistic for the future.

This stochastic notion is relevant for the examples to come. Throughout the paper, I adopt a notion of quantum non-Markovianity that emerges in three distinct contexts:

• Open quantum systems: When a quantum system interacts with an environment, its reduced dynamics often exhibit genuine memory effects where past system–environment correlations influence future evolution beyond what the present reduced state encodes [7].2
• Foundational reformulations: Some interpretations of quantum mechanics, like Barandes’s [6] stochastic correspondence, treat quantum evolution as fundamentally non-Markovian at the level of configuration space histories, where interference prevents factorization of transition amplitudes.
• Emergent time in quantum gravity: In interpretations where time itself emerges from entanglement structure (as in the Tomita–Takesaki framework), the resulting dynamics can exhibit non-Markovian features because temporal evolution depends on global quantum correlations rather than local time-slices.

I discuss these in greater detail in Section 3.

2.2. Why Explaining Non-Markovianism Matters

As Builes and Impagnatiello note for the Markovian case, whether a temporal property is primitive or explained is a point of theoretical virtue. Indeed, if non-Markovianism is a fundamental feature of temporal evolution, a satisfactory theory of time should tell us why.

A theory that accounts for this feature, by deriving it from its ontology and dynamics, thereby reduces the number of brute temporal facts. All else equal, such a theory is to be preferred over a rival that stipulates non-Markovianism without explanation. This is the same virtue appealed to in P1 of the Markovian argument: the direction of the property (Markovian or not) is irrelevant to the meta-point that its explanation is theoretically valuable.

Of course, the justification may also lie in a broader epistemological commitment to explanatory realism, the view that explanatory features of physical theories track genuine modal structure in the world [9,10]. In this view, explanation is not solely pragmatic or instrumental, but an indicator of ontological structure. When a metaphysical theory renders structural features like non-Markovianism intelligible, it earns epistemic credence by reducing brute facts 3.

It is important to stress, as B&I do, that endorsing P1′ does not presuppose Eternalism. One might accept P1′ while holding any number of views about the ontology of time. Our aim in this section is only to establish that if non-Markovianism is in fact a feature of the world, then it is a feature worth explaining. It is just as important to stress that, just as one might question whether Markovianity requires metaphysical explanation rather than being taken as brute, one could raise the same question about non-Markovianity. I clarify that my aim in this paper is not to definitively establish that temporal features must be explained, but rather to show that if one accepts B&I’s premise that explaining Markovianity favors Presentism, then explaining non-Markovianity may, at first glance, favor Eternalism. As I discuss throughout the exposition of the two views, the explanatory burden goes both ways. The force of this conditional argument then depends on empirical questions about whether fundamental physics is truly non-Markovian, but I take it to be a worthwhile endeavor. I offer a survey of the non-Markovian literature in the following section.

3. Non-Markovian Quantum Systems

Consider P1’: A theory of time that explains why time is non-Markovian at the foundational level of quantum mechanics is preferable to one that does not.

In this section I discuss the prospects for this proposition. While many familiar models in statistical mechanics and stochastic dynamics idealize time evolution as Markovian, several speculative lines of work in the foundations of quantum theory challenge the universality of this assumption. As a starting note, whether the universe is a closed or open system is debated. As such, it is useful to consider both outcomes.

3.1. Closed Systems

For closed systems governed by the Schrödinger equation, the dynamics are typically said to be unitary and reversible; the complete wavefunction at t₁ is taken to determine both past and future. However, two examples are particularly salient to challenge this assumption.

Firstly, the question of whether temporal evolution is Markovian touches directly on the longstanding problem of time in theoretical physics. In classical mechanics, time is treated as an external parameter, and dynamical laws are typically cast in a Markovian form: the present state, together with deterministic equations of motion, suffices to generate both past and future trajectories. However, in the transition to quantum theory and especially quantum gravity, this picture has been repeatedly challenged. Canonical approaches to quantum gravity confront the Wheeler–DeWitt equation [13], which lacks an external time parameter altogether, leading to the so-called frozen formalism and the problem of time [14]. Attempts to recover dynamics reveal that temporal evolution may be inherently state-dependent and non-Markovian. The clock ambiguity further underscores that different internal choices of time can yield inequivalent dynamical descriptions, some of which manifest genuine memory effects. With these challenges, the assumption that the fundamental laws are cleanly Markovian appears increasingly like an artifact of limited classical idealizations rather than a universal feature of physics.

An approach to address the problem of time depends on the Tomita–Takesaki framework. To make a long story short, starting with an algebraic structure, it was proven that we may retrieve an automorphism group that resembles the role of the usual external time parameter. In it, this new modular automorphism group ${{\sigma }_t}^{\omega }$ depends explicitly on the global state ω of the algebra of observables. The Thermal Time Hypothesis interprets this group as a collection of operations that represent physical time, though this interpretation remains debated [4,5,15]. This suggests that the temporal ordering of events is a feature emergent from entangled global correlations.4 The state ω encodes correlations stretching over arbitrarily large temporal intervals, and the modular “time” evolution inherits these dependencies. In such cases, prima facie, the present algebraic state does not screen off the rest of the history.5 Proponents of this view may argue in favor of a sense of non-markovianity in that we may have explicit ties between the past and future.

On the other hand, in continuous measurement models and in collapse theories with colored noise, the correlation functions of the noise introduce explicit dependence on earlier states. This breaks the standard divisibility property of Markovian dynamics and shows that memory effects can be built directly into the formal structure of quantum evolution [18]. A more recent development is Barandes’s [6] proposal of a quantum stochastic correspondence. His work continues the long line of attempts to relate quantum theory to stochastic processes, but departs from earlier efforts by treating quantum mechanics itself as an indivisible stochastic process.

Barandes begins with a classical stochastic framework. A system is defined by a time-dependent probability distribution over discrete configurations. The evolution of this distribution is governed by a transition matrix $\Gamma$, where

$$p_i\left(t\right)={\Sigma }_j{\Gamma }_{ij}\left(t\right)p_j\left(0\right)$$

In a Markovian and divisible process, $\Gamma \left(t\right)$ satisfies the composition property $\Gamma \left(t\right) =\Gamma (t\leftarrow t^{\prime })\Gamma \left(t^{\prime }\right)$ for all t > t′ > 0.

However, this composition is absent in Barandes’s model of quantum dynamics.6 Indeed, the transition matrix is not generally factorizable and must instead be constructed from a complex-valued amplitude matrix ${\Theta }_{ij}\left(t\right)$ such that

$${\Gamma }_{ij}(t)=|{{\Theta }_{ij}\left(t\right)|}^2$$

The amplitudes encode interference directly at the level of evolution. Attempting to apply the Markovian composition law, i.e., factoring $\Gamma \left(t\right)$ as $\Gamma (t\leftarrow t^{\prime })\Gamma \left(t^{\prime }\right)$, introduces cross terms due to the underlying amplitude structure and leads to a failure of divisibility. This broadly means that having only the current state’s information is not sufficient in determining future events. Contributions from distinct histories do not add probabilistically, but combine coherently through complex phase relations. This feature distinguishes quantum systems from classical stochastic processes: it introduces a form of dynamical non-decomposability that precludes assigning conditional probabilities between time-indexed configurations. On this view, the non-Markovian character is simply a foundational feature of the theory.

These proposals about closed systems remain highly speculative. More established cases of non-Markovianity arise in open quantum systems, where memory effects are well-documented and experimentally verified. I now present such studies.

3.2. Open Systems and Subsystems

Various experiments and theoretical studies show support for non-Markovian properties in quantum systems that allow for the influx or outflux of energy as an open system. For example, quantum open systems are frequently studied to assess the degree to which they are open [7,19,20,21,22,23]. The view that the universe is indeed open has historical precedent and has attracted sympathizers. Lindley [24], for example, develops a speculation in cosmology that argues for the universe being an open system.

Even if we have proponents of a closed universe, it is nevertheless both interesting and necessary to consider subsystems. As Wallace [25] argues, our best physical theories do not begin with the whole universe. Indeed, our explanatory practices in physics operate at the level of autonomous subsystems. They instead begin with autonomous subsystems whose dynamics are typically non-unitary and, often, non-Markovian. I also note that many ambitions in the foundations of physics indeed only concern themselves with subsystems (take for example Carroll [26], who considers the subsystem of our observable universe as opposed to the Hilbert space of the entire universe in formulating his Everettian interpretation). I take it that such efforts demand that the philosophy of science treats these premises seriously, and we have good reason to think about such subsystems in isolation. That is, these subsystems are where explanatory work gets done, and where temporal metaphysics might have to earn its keep. We, as conscious observers embedded in a larger environment, are precisely such subsystems. If the temporal evolution we experience and must explain is non-Markovian, this constrains viable metaphysics regardless of whether some inaccessible ‘view from nowhere’ would reveal underlying Markovianity. Thus I contend that P1’ has force even if foundational non-Markovianism remains speculative.

B&I [3] affirm to have offered an empirical basis for their argument, in particular for the defense of P1, through various perspectives within physics. On the other hand, this section discussed the perspectives for a non-Markovian time, in a similar spirit of empirical backing. These models arise naturally in the foundations of quantum mechanics, quantum field theory on curved spacetime, and in the study of quantum gravity and thermal time. As with any program within quantum foundations and quantum gravity, there are various concerns regarding their speculative nature—while Markovian physics is well-established in macroscopic scales and in our best-tested theories, we do not yet have a clear consensus on the dynamical nature of fundamental physics. This means P1’ has conditional force: if fundamental physics is non-Markovian (as some research programs suggest), then metaphysical theories should explain this feature. The argument’s ultimate persuasiveness thus depends on how these programs in quantum foundations develop. Nevertheless, the growing technical literature on non-Markovian quantum dynamics warrants philosophical examination now, before empirical questions are settled.

4. Eternalism and Non-Markovian Time

Having discussed the prospects for P1′, I now turn to P2’:

P2′: Particular versions of Eternalism explain why time is non-Markovian.

This section will discuss the prospects of Eternalism in accommodating non-Markovian physics.

In Eternalism, all events in the past, present, and future equally exist. The temporal structure of reality is four-dimensional; the universe is represented as a spacetime manifold populated with events, all of which are equally real [27,28]. Eternalists typically deny any objective ontological “flow” of time; instead, temporal becoming is regarded as an aspect of our phenomenology rather than an ontological feature.

This four-dimensionalist picture affords Eternalists several distinct explanatory strategies for accommodating non-Markovian time. Unlike Presentism, which restricts ontology to the present, Eternalism permits temporally non-local relations to be fully grounded in the structure of spacetime itself. Specifically, there is no metaphysical barrier to correlations obtaining between non-adjacent temporal slices, whether those correlations are due to physical laws, global constraints, or initial conditions.

On the Humean view, laws of nature are descriptive summaries of the Humean mosaic, the total distribution of local matters of particular fact across spacetime [29,30]. While Humean Eternalists typically regard temporally extended correlations as brute features of the mosaic, the block-universe ontology ensures that all such correlations, even those between widely separated times, are part of the actual arrangement of events. Non-Markovian processes, such as those arising from the TTH or non-divisible completely positive trace-preserving (CPTP) maps, can thus be explained in the minimal Humean sense: they are simply among the most informative and simplest regularities of the mosaic. Although this is a relatively deflationary form of explanation, it is straightforwardly compatible with foundational non-Markovianism.

Non-Humean Eternalists who adopt a universals-based view can attempt to explain non-Markovianism by allowing necessitation relations between temporally non-adjacent universals [31,32,33]. For example, a universal property F instantiated at t₀ could necessitate a universal G instantiated at t₂, without mediation by the properties instantiated at t₁. In the block-universe ontology, such cross-temporal necessitation is seemingly unproblematic, since all the relevant instantiations are equally real and embedded in the spacetime manifold.

On primitivist accounts [34,35], laws are fundamental facts that directly govern the entire spacetime history. Here, non-Markovianism can be explained by positing primitive laws whose temporal scope includes relations between non-adjacent times. A fundamental law might, for instance, stipulate that the state at t₂ is a function of both t₁ and t₀, thereby encoding genuine memory effects. Eternalism allows these laws to be understood as governing the whole 4-D history at once, rather than updating a “present” slice.

Neo-Aristotelian causal-powers theorists can likewise explain non-Markovianism by allowing that certain powers are temporally extended in their manifestation [36,37,38]. For example, an entangled quantum field state might have the power to produce correlations that span arbitrary temporal intervals; in a block-universe framework, these temporally extended powers can be directly grounded in the spacetime distribution of the relevant fields.

These strategies fit naturally with the physics surveyed in §2. In the Tomita–Takesaki framework, the modular automorphisms of an algebra A with respect to a state ω depend on global correlations in ω. In an Eternalist picture, these correlations are just relations holding between parts of the total spacetime state; their existence and explanatory role are unproblematic. Similarly, Barandes’s [6] proposal of a quantum–stochastic correspondence can be understood as encoding structural patterns in the entire spacetime history. In his view, quantum theory itself is an indivisible stochastic process, so that non-Markovian correlations are built-in features of the block universe.

Across Humean and Non-Humean varieties, Eternalism offers multiple ways to accommodate non-Markovianism without resorting to brute stipulation. Because the ontology includes the full temporal extent of reality, temporally extended correlations may be seen as natural features of the block universe. However, this may also come with various objections.

While Eternalism appears to provide a natural metaphysical backdrop for temporally extended correlations, this does not mean its explanatory advantages are unqualified. First, many Eternalist strategies rely on global features of the block universe without further grounding. This raises the question of whether such correlations are genuinely explained or merely absorbed into an abundant ontology. Second, the dependence of the state in modular time, i.e., where the flow of time depends on the quantum state, may require Eternalists to revise static conceptions of temporal structure within the block universe. If time arises not from fixed spacetime geometry but from entangled global states, then the explanatory burden may shift from ontology to informational structure, complicating the Eternalist picture. While these do not undermine Eternalism’s ability to accommodate non-Markovianism, they suggest that explanatory elegance is not automatic and may require further metaphysical refinement.

This multiplicity of explanatory routes is a major advantage over Presentism, which must either compress these correlations into present-time surrogates or treat them as unexplained primitives. However, there are various avenues of objections that may arise for both parties during an explicit treatment of non-Markovian physics.

5. Presentism and the Challenge of Non-Markovianism

I now discuss the prospects for Presentism, with regard to P3’.

P3′: No versions of Presentism (plus non-Humeanism) explain why time is non-Markovian.

In Presentism, roughly speaking, only present events exist. The past no longer exists; the future does not yet exist. The present is all there is, and any truths about the past or future must be grounded in facts about the present [39,40]. Explaining non-Markovianism in this framework is no easy task. By definition, non-Markovian dynamics entail that the present state does not screen off the past from the future. Some features of earlier states remain causally or explanatorily relevant. For the Presentist, those earlier states do not exist, so their relevance cannot be grounded in them directly.

One might attempt to bridge this gap by appealing to present traces or records of the past: these are memories, fossils, or more generally, physical configurations encoding information about prior states. However, this strategy has room for failure for the paradigmatic cases in §2. For example, in TTH, the relevant correlations can involve global degrees of freedom that are not locally accessible to the subsystem in question. In indivisible stochastic dynamics, the environmental variables that carry memory effects may be physically inaccessible or distributed across spacelike-separated regions.

In such cases, the “records” required for prediction would have to be encoded in presently existing entities in an extraordinarily non-local and physically opaque way. This pushes Presentists toward one of two options:

• Build non-Markovianism into the laws as a brute feature, abandoning the explanatory ambition of P1′.
• Postulate unobservable present-time structures whose sole role is to mimic the influence of non-existent past states, introducing ontological excess baggage with no independent motivation.

To see this more clearly, it helps to consider how the familiar metaphysical subtypes of Presentism interact with the explanatory challenge. Firstly, for Humean Presentists, there is no built-in temporal structure extending beyond the present. This amounts to saying that there is no reason to expect the patterns in the Humean mosaic to encode the detailed long-range correlations required by non-Markovian physics. If they do, it may be a contingent coincidence that the Humean can record but not explain in the richer, ontologically-grounded sense. This makes Humean Presentism, as-is, particularly ill-suited to satisfying P1′.

A universals-based Presentist might try to ground non-Markovian dependencies in necessitation relations between universals instantiated in the present. But genuine non-Markovianity requires that earlier-time universals (e.g., “having spin configuration X at t₀”) play a direct role in determining future states. If those earlier-time universals no longer exist, the Presentist must either (i) treat them as still in some sense existent, which contradicts Presentism, or (ii) encode their causal role in purely present universals. The latter reduces to the “hidden traces” strategy, which has the potential to become implausible when the relevant correlations involve global or inaccessible degrees of freedom.

A distinct approach available to the Presentist is primitivism about laws. Unlike the universals-based and powers-based views, primitivism does not attempt to ground the laws of nature in anything more fundamental. That is to say, it does not locate lawhood in regularities across the Humean mosaic, in second-order necessitation relations between universals, or in the dispositional essences of natural kinds. Rather, laws are taken to be irreducible features of reality that govern temporal evolution without themselves requiring further ontological support [34]. The appeal of this view lies in its explanatory directness: laws explain why systems evolve as they do precisely because governing is what laws fundamentally do. For the Markovian case, this directness is relatively unproblematic, since a primitive law can simply dictate that the present state generates the next state. However, when the dynamics are non-Markovian, the primitivist faces a distinctive version of the explanatory challenge, since the laws must now reach beyond the present moment to states that, on the Presentist’s own ontology, do not exist.

With this in mind, consider what a primitivist Presentist account of non-Markovian dynamics would require. Such laws could stipulate, for example, that the state at t₂ depends on the actual state at t₀ in a way that bypasses t₁. However, to make this intelligible under Presentism, the law must refer to past states that do not exist. If those references are taken literally, the spirit of Presentism is violated; if they are reinterpreted as referring to present surrogates, the law’s content collapses into a brute stipulation about highly contrived present structures. Either way, the view lacks the explanatory grounding that P1′ demands.

Neo-Aristotelian Presentists could attempt to explain non-Markovianism by positing present-time powers whose manifestations depend on “what was” in addition to “what is” [36,37]. But if “what was” does not exist, these powers can only be sensitive to traces encoded in the present. This invokes the hidden-traces problem. In cases like modular flow or environment-induced memory, the required traces may be so widely distributed or inaccessible that their inclusion in the present ontology looks ad hoc.

The challenge, then, is whether Presentism has the resources to ground temporally extended correlations without appealing to the existence of non-present states. This is not a straightforward question, and Presentists have developed a range of strategies that may serve to be promising. In the following subsection, I examine several of these approaches and assess whether they can accommodate the non-Markovian phenomena surveyed in Section 3.

5.1. Possible Presentist Responses

A more charitable assessment of Presentism’s prospects should acknowledge several sophisticated strategies that go beyond the “hidden traces” approach criticized above. I discuss various approaches that Presentists may consider in thinking about non-Markovian Time.

Firstly, dynamic Presentists who take temporal becoming seriously might argue that non-Markovian correlations reflect genuine causal powers that span temporal boundaries rather than being encoded in present states [41,42]. In this view, the field itself possesses irreducibly diachronic causal powers that manifest across multiple time slices as they successively become present, going beyond mere "traces" at t₁ and t₂. The Presentist can thus maintain that while only present events exist, some present entities have essentially temporal causal profiles that naturally generate memory effects without requiring past states to exist simultaneously. This approach, in part, draws inspiration from neo-Aristotelian accounts of causal powers [43,44] while extending them to accommodate genuinely cross-temporal manifestations.

As with any handling of Presentism, this dynamic approach deserves careful consideration. Unlike the ‘hidden traces’ model where past information is statically encoded in present configurations, dynamic Presentism posits that temporal properties are irreducibly processual. Consider a quantum field in a superposition state. Rather than the present containing encoded information about past measurement contexts, the field itself possesses what we might call ‘temporal dispositions,’ which can be thought of as causal powers whose manifestation patterns inherently span multiple moments. In other words, when such a field becomes entangled at t₀, it does not merely leave informational residue at t₀; instead, it acquires a dispositional profile that will manifest differently at t₂ depending on the specific history through which it evolved. I note that this is not memory in the sense of stored information, but rather a kind of temporal momentum built into the causal structure of reality itself. Further work is to be done in this stance, yet it is a promising vision for Presentism.

Consider how this approach handles Barandes’s interference effects. When a quantum system at t₀ enters superposition, the dynamic Presentist does not claim the present at t₁ contains encoded information about t₀. Instead, the quantum field itself acquires temporally extended powers at the moment of superposition. Evidently, these powers function as forward-directed causal dispositions rather than as memories or records. The interference pattern observed at t₂ arises not from consulting records of t₀, but from the field’s irreducibly diachronic causal profile activating as each moment becomes present.

This differs from the hidden traces model criticized earlier. The field carries forward-directed causal powers that were shaped by past interactions yet exist entirely in the present. When the field was entangled at t₀ (when t₀ was present), it acquired a complex dispositional profile that determines how it will manifest at each future present moment. In this account, the non-Markovian behavior emerges because these dispositions have complex temporal structures, taking the form of extended patterns of potential manifestation..

As another example, consider an electron that passes through a double-slit apparatus. On the dynamic powers view, passing through the slits does not leave “information” in the electron about which slit it traversed. Instead, the interaction with the apparatus confers upon the electron a temporally structured disposition to manifest in particular patterns when it later encounters the detection screen. This disposition exists fully in the present electron as a forward-looking causal power with a complex temporal profile, without relying on encoded historical data.

Additionally, sophisticated Presentists might appeal to grounding relations that connect present truths to modal facts about what was the case, without requiring past events to exist [45]. Drawing on recent work in the grounding literature [46,47], one could argue that present quantum states are partially grounded in modal facts about previous measurement outcomes or field configurations: which are facts that are obtained without requiring past events in the ontology. Consider the modular flow case where temporal evolution depends on global quantum correlations. The sophisticated Presentist might argue that the present quantum state is partially grounded in modal facts of the form “it was the case that the system had correlation C at t₀.” These modal facts obtain in virtue of present reality—perhaps grounded in present records, laws of nature, or primitive temporal operators—without requiring t₀ to exist. The non-Markovian evolution then follows from laws that relate present states to these modal facts about the past.

This approach gains plausibility when we consider that quantum mechanics is already trafficking in modal concepts through probability amplitudes and potentiality. The Presentist might argue that extending modality to cover temporal facts is a natural move within an already modal framework. The correlation functions that generate non-Markovian behavior could be understood as modal structures instantiated in the present, determining evolution based on what was possible or necessary given past configurations, without those configurations needing to exist.

Similarly, some Presentists might embrace a “thick” conception of the present moment that includes not just instantaneous states but also rate-of-change information, derivatives, and other temporally-local but dynamically-rich structures [48,49]. If the present is understood to include velocity, acceleration, and higher-order temporal derivatives as primitive features, then some non-Markovian dependencies might be accommodated without appealing to non-present states. While these strategies face their own challenges in explaining how modal grounding works without existing grounds (cf. Bennett [50]), or how to demarcate the “thickness” of the present in a principled way, they suggest that Presentists have more theoretical resources than the simple hidden-traces picture allows.

For quantum systems, this might mean the present includes not just the wavefunction ψ(t) but also its time derivatives ∂ψ/∂t, ∂²ψ/∂t², and so on, as primitive features of reality. These derivatives could encode information about the system’s temporal trajectory without requiring past states to exist. Non-Markovian behavior would then arise from laws that relate future evolution to these present derivatives rather than to past states directly.

This approach is particularly promising for cases where non-Markovian effects involve only short temporal correlations. If memory effects decay over characteristic timescales, the relevant information might be captured by a finite number of temporal derivatives in a suitably thick present. The challenge is to explain longer-range correlations and to provide an account of how thick the present must be.

It should be emphasized that the strategies discussed in this section, particularly dynamic Presentism and the thick-present approach, are live research programs with philosophical momentum. Dynamic Presentism’s appeal to irreducibly diachronic causal powers offers a potentially fruitful framework, and the thick-present strategy has the resources to accommodate at least short-range non-Markovian correlations in a principled way. Whether these programs can be extended to handle the full range of non-Markovian phenomena surveyed in Section 3 remains an open question. However, the dialectic may shift if either program is developed in explicit engagement with the formal structures of non-Markovian quantum theory. If our fundamental physics is indeed non-Markovian, this may spark various developments and responses on the presentist side.

Having now outlined the various explanatory strategies available to both Eternalism and Presentism, we are in a position to compare them. In what follows, I identify a general dilemma for Presentist explanations of non-Markovianism, regardless of metaphysical subtype.

5.2. Non-Humean Presentism and a Dilemma

B&I devote significant attention to “Non-Humean Presentism,” which allows that the laws of nature are grounded in modal facts that can constrain reality beyond the Humean mosaic of local matters of particular fact. One might hope such a view could explain non-Markovianism by positing laws that involve temporally non-local dependencies. But doing so under Presentism faces a dilemma that applies to all the above subtypes:

• Literal past-reference: If the laws refer to past states as they actually were, those states must in some sense exist.
• Present surrogates: If the laws refer only to past-like structures in the present, we face the same “hidden traces” problem, forcing the present to contain highly contrived encodings of information about past non-existents.

In either horn of the dilemma, the explanatory project collapses into stipulation: non-Markovianism is taken as a primitive feature of the present or of the laws, not as something derived from the ontology. This is precisely the situation P1′ was meant to avoid. This problem has three components that together create a disadvantage.

First, we have what I will deem the encoding problem: non-Markovian dynamics require that past states remain directly relevant to future evolution. Of course, the present alone does not determine what happens next. For the Presentist, this information must somehow be encoded in present entities. In modular flow, the temporal evolution depends on quantum correlations that extend across the entire history of the system. These correlations involve quantum properties that resist compression into any present-moment summary, unlike classical information that can be written down or stored. The famous no-cloning theorem, for example, forbids perfect duplication of unknown quantum states [51]. If all relevant quantum correlations could be encoded in present classical structures, this would constitute a form of cloning via classical intermediaries. This risks violating this fundamental constraint. Any attempted encoding would need to preserve not just information about past values but also their complex phase relationships and entanglement patterns.7

It may be unintuitive what ‘encoding’ means in this context. There are two distinct senses that must be separated. First, informational encoding: whether the present state contains sufficient information (in the Shannon or von Neumann entropy sense) to reconstruct or predict future evolution. Second, metaphysical grounding: whether present entities provide the ontological basis for past-dependent correlations. The Presentist might succeed at the first task, ensuring the present contains all relevant information, while still failing at the second. After all, even if present structures informationally encode past quantum correlations, this does not explain why those correlations obtain or what grounds their continued relevance. The no-cloning concern targets the first sense: quantum information cannot be perfectly duplicated into classical form. But even if we granted that quantum information could be preserved in present quantum structures (avoiding no-cloning), the metaphysical problem remains: those present structures would need to ground temporally extended correlations without appeal to the past states that (according to Presentism) no longer exist. The encoding problem is thus not primarily about information capacity but about metaphysical grounding relations.

In principle, a Presentist could attempt to encode all relevant past information into the present by positing highly structured present-time states that carry forward the necessary information. A few examples would be derivative-like properties, hidden variables, or complex global configurations with regard to the wavefunction. This approach, however, may open debates concerning metaphysical cost or explanatory clarity. First, these present structures must mirror nonlocal entanglement patterns and phase relations across arbitrarily distant times, which risks introducing a staggering informational load that lacks independent physical motivation. Unlike ordinary records (e.g., fossils or memories), these encodings must be tuned with near-miraculous precision to reconstruct correlations that, under Eternalism, arise naturally from the existence of the full temporal manifold. Second, these structures must somehow remain physically inert—they cannot causally influence future evolution on their own, lest they serve as proxies for the very past events the Presentist denies. The result is a metaphysical tension: either these encodings are explanatorily idle, or they violate Presentism’s core ontological commitment. Hence, the charge of “baroqueness” can be framed as a diagnosis of a deeper tension between explanatory adequacy and ontological parsimony.

Second, the proliferation problem: Each moment requires increasingly complex present-time structures to encode the cumulative history relevant for future evolution. Unlike Markovian processes where the present screens off the past, non-Markovian evolution means that arbitrarily distant past events remain causally relevant. The Presentist must therefore posit an ever-growing collection of unobservable present structures whose sole purpose is to carry this historical information forward.

Third, the coordination problem: These present-time encodings must be precisely coordinated to generate the correct future evolution. The mathematical constraints from quantum theory determine unique evolution operators, but the Presentist must explain how disconnected present-time surrogates for non-existent past states could conspire to satisfy these constraints. This coordination cannot be explained by the surrogates themselves, since they are supposed to be mere records rather than causally efficacious entities.

It is worth noting that Eternalism, too, must account for the existence and structure of temporally extended correlations. After all, non-Markovian dynamics impose constraints across time, and any metaphysical framework must explain how such constraints are instantiated. However, under Eternalism, the challenge is significantly attenuated. Since all points in time are equally real, the relevant past and future states that contribute to non-Markovian evolution genuinely exist and can stand in dynamical and entanglement relations without recourse to present-time surrogates or metaphysical encoding. The correlations required by modular flow or temporal entanglement do not need to be compressed or encoded into a single moment, because the temporal manifold itself carries the information. Eternalism can thus model temporally nonlocal dependencies as relations within the spacetime manifold rather than as hidden information atop it. While it may still face philosophical questions about how such global structures obtain or are instantiated, these concerns operate within its core ontology rather than in tension with it. By contrast, Presentism must simulate the explanatory work of real but non-existent past states, placing it under pressure to construct increasingly contrived and ontologically overloaded present-time structures. Thus, although both views must grapple with the implications of non-Markovian physics, the explanatory burden is far heavier for Presentism.

Together, these problems suggest that Presentist explanations of non-Markovianity may collapse into brute stipulation. In such cases, the Presentist must either accept non-Markovianity as an unexplained primitive feature of temporal evolution, or postulate increasingly baroque present-time ontology that mimics the explanatory work done rather straightforwardly by past states in Eternalist frameworks. This motivates the development of Presentist frameworks to explicitly handle our non-Markovian physics cases in greater detail.

5.3. Prospects of Intermediate Positions and the Growing Block

One might wonder whether intermediate positions between Presentism and Eternalism fare better with non-Markovianity. The Growing Block view, where past and present exist but the future does not, initially seems promising. Past states that influence future evolution through non-Markovian dynamics would exist on this view, avoiding the Presentist’s encoding problem.

However, the general idea of the Growing Block seems to face its own set of challenges. The non-Markovian dependencies revealed by quantum theory are often symmetric with respect to time-reversal. In Barandes’s framework, the amplitude structure that generates memory effects works equally in both temporal directions. The Growing Block theorist must explain why forward-time non-Markovian evolution is grounded in existing past states, while backward-time dependencies (which the mathematics treats symmetrically) lack similar grounding. This asymmetry appears arbitrary given the time-reversal invariance of the underlying quantum formalism.

Proponents of this account may benefit from engaging with a notion of causation or a sense of directionality within time. Indeed, one strategy may be to appeal to a primitive arrow of causation: forward-time dependencies track causal influence, whereas backward-time ones do not. But this risks circularity, since causation is itself often analyzed in terms of temporal asymmetry. Another option is to link the Growing Block to the thermal time hypothesis, where the arrow of time is supposed to emerge from the modular structure of states. Yet here, more work is needed: it is not enough to say that correlations are “embedded” in a real number line of modular time. In other words, one must explain why this ordering has metaphysical bite, privileging the “growing” direction over its time-reversed counterpart.

Moreover, the Moving Spotlight view, where all times exist but only one is “present,” may not offer any advantage over standard Eternalism for explaining non-Markovianity. The metaphysically privileged present plays no role in grounding the temporal correlations, since these are handled entirely by the block structure shared with standard Eternalism. It is worth investigating the compatibility of this view with the Eternalist picture when it comes to the emergence of time, however.

Eternalism appears promising to offer a clean, ontologically grounded explanation for non-Markovianism: temporally extended correlations are simply part of the spacetime structure, and the physics that produces them can be understood as features of that structure. Presentism, by contrast, can accommodate non-Markovianism only by brute stipulation or by positing obscure present-time surrogates for non-existent past states. Some current hybrid approaches may also show potential in describing non-Markovian physics, though more developments may support its case.

6. Conclusions and the Call for Interdisciplinary Work

Thus, if non-Markovianity is a genuine feature of fundamental physics, metaphysical accounts of time must be able to explain temporally extended correlations without brute stipulation. Prima facie, Eternalism appears to handle this more smoothly than Presentism, though the overall balance of metaphysical virtues remains an open question.

In this paper, I have aimed to offer preliminary considerations for such an accommodation. The first claim is that the structure of Builes & Impagnatiello’s case for Presentism from Markovian time admits a natural mirror image: an argument for Eternalism from non-Markovian time. After motivating the possibility P1′ from contemporary physics (§2), I explored various accounts of both Eternalism and Presentism in their potential to work alongside non-Markovianism (§3). Non-Markovian laws may serve as a significant theoretical constraint on metaphysical accounts of time. If our best physics supports foundational non-Markovianism, this may offer new challenges on both sides of the debate. Eternalists may turn to the mirror argument; however, sophisticated Presentist responses may offer various forms of pushback. Ultimately, as B&I suggest, the success of these arguments is contingent on the empirical evidence for the nature of the fundamental laws.

Several avenues remain for further work. First, the scope of “foundational” non-Markovianism could be sharpened by systematic study of modular flow, quantum gravity, and other relevant formulations of quantum mechanics. Second, the metaphysical landscape could be broadened to include hybrid or deflationary views of time, testing whether they can offer comparable explanations. Furthermore, a more general methodological moral may be drawn: explanatory virtues in the metaphysics of time can sometimes be illuminated not by generic temporal intuitions, but by specific formal properties of our best physical theories. Lastly, with the growing work of emergence in quantum gravity, our debates on the metaphysics of time may experience various shifts in what is ultimately deemed “fundamental.” I leave these for future consideration. If B&I’s original argument motivates renewed attention to Markovianism, the parallel argument here suggests that its converse is equally worthy of philosophical scrutiny. The metaphysics of time, like the physics, may turn out to be more memory-laden than we thought.