Comment l'espace-temps statique et mathématiquement continu de la relativité générale peut-il être formellement réconcilié avec les mises à jour d'états discrètes et probabilistes définissant le « maintenant » en mécanique quantique et en physique numérique ?

problem of time quantum gravity Wheeler DeWitt canonical quantization general relativity review

### The Problem of Time in Canonical Quantum Gravity In modern fundamental physics, the “Problem of Time” arises from a structural contradiction between general relativity and standard quantum mechanics. Standard quantum mechanics treats time as an external, fixed classical parameter $t$ governing unitary evolution through the Schrödinger equation ($i\hbar \partial_t \Psi = \hat{H}\Psi$). Conversely, Einstein’s general relativity posits spacetime as dynamic and generally covariant: temporal coordinates carry no intrinsic physical meaning, functioning solely as arbitrary labels. When applying Paul Dirac’s canonical quantization to general relativity—foliating 4-dimensional spacetime into 3-dimensional spacelike geometries—the Hamiltonian is not an energy generator producing temporal change, but a constraint enforcing gauge invariance. In their landmark formulation, Bryce DeWitt (1967) and John Wheeler showed that the quantum state functional of the universe $\Psi$ satisfies the Wheeler–DeWitt equation: $$\hat{\mathcal{H}}\Psi = 0$$ Because the equation contains no external time derivative, the universe appears statically “frozen”. As DeWitt famously stated, the coordinate label *“itself is irrelevant, and ‘time’ must be determined intrinsically”*. In canonical review papers, Karel Kuchař (1992) and Chris Isham (1993) classified the primary strategies and ongoing disputes among theoretical physicists: 1. **Time before quantization:** Attempting to isolate an "internal time" coordinate (from geometric variables or reference matter fields) prior to quantizing. 2. **Time after quantization (Emergent Time):** Deriving an approximate, semiclassical time parameter via WKB approximations and quantum decoherence, where classical time emerges only at low-energy macroscopic scales. 3. **Timeless / Relational formulations:** Accepting fundamental timelessness (e.g., Carlo Rovelli’s "evolving constants of motion" and partial observables, or Julian Barbour’s shape dynamics), where dynamics consist strictly of correlations between co-existing quantum degrees of freedom. ### Epistemic Status The mathematical origin of the problem of time is a consensus result of combining canonical quantization with diffeomorphism invariance. However, **no consensus resolution exists**. All proposed solutions—whether relational clocks, emergent semiclassical time, or string-theoretic/holographic reformulations—remain theoretical hypotheses devoid of direct empirical test.

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block universe vs presentism special relativity quantum state reduction philosophy of physics

In analytic philosophy of physics, philosophical naturalists hold that metaphysics must be answerable to fundamental physics. Consequently, the dominant consensus strongly favors **eternalism** (the **block universe**)—wherein past, present, and future events are equally real across a four-dimensional manifold—over **presentism**, the intuitive view that only the transient "now" physically exists. Naturalists generally treat the experience of temporal flow as an artifact of human cognitive architecture and thermodynamic entropy rather than an objective feature of fundamental reality. ### The Relativistic Challenge to Presentism This consensus is grounded in the **relativity of simultaneity** from Einstein’s Special Relativity (SR). Because the speed of light is constant for all inertial observers, observers moving relative to one another slice spacetime along different planes of simultaneity. C. Wim Rietdijk (1966) and Hilary Putnam (1967) codified this into the **Rietdijk–Putnam argument**: an event situated in one observer’s undetermined future can reside in another’s determinate present. Putnam famously concluded: > *“I conclude that the problem of the reality and the determinateness of future events is now solved... future things (or events) are already real.”* Howard Stein (1968) refined this critique, demonstrating that in Minkowski spacetime, temporal becoming cannot be defined globally; it can only be localized relative to an event’s past light cone, precluding any objective, global "present." ### Quantum State Reduction: Tensions and Hypotheses A persistent tension within naturalism arises when reconciling SR with quantum mechanics. Under standard interpretations, **quantum state reduction** (wave-function collapse) upon measurement occurs instantaneously across spatially separated, entangled particles. As Tim Maudlin details in *Quantum Non-Locality and Relativity* (1994), real non-local collapses (demonstrated via Bell’s theorem) seem to demand a **preferred foliation**—a privileged global slicing of spacetime into absolute time steps—to define which collapse precedes another. A speculative minority (e.g., Nicholas Maxwell; Bradley Monton) hypothesizes that this quantum non-locality might rehabilitate an objective present or a "growing block" universe governed by genuine, indeterministic becoming. ### Epistemic Grounding Mainstream philosophy of physics emphasizes that using quantum collapse to resurrect presentism remains a minority, non-consensus view. Standard relativistic Quantum Field Theory maintains strict Lorentz covariance without a preferred foliation. Furthermore, leading unitary formulations like the Everett (Many-Worlds) interpretation eliminate wave-function collapse altogether, leaving the tenseless, four-dimensional block universe as the most parsimonious naturalist account of spacetime.

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divine eternity timelessness vs open theism relational time God relativity quantum mechanics

### Theological Divergence: Timelessness vs. Temporal Relationality Mainstream Christian orthodoxy across Roman Catholicism, Eastern Orthodoxy, and classical Protestantism historically affirms divine timelessness (*atemporality*). Drawing on Augustine’s insight that time was created *with* the world (*Confessions* XI), classical theism holds that God transcends temporal succession. Boethius codified this standard view, defining eternity as “the complete possession all at once of illimitable life” (*interminabilis vitae tota simul et perfecta possessio*, *The Consolation of Philosophy* V.pr.6), a doctrine systematized by Thomas Aquinas (*Summa Theologiae* I, q. 10). In lived practice, classical timelessness underpins divine immutability, impassibility, and exhaustive foreknowledge, assuring believers of God’s absolute sovereignty and unshakeable fidelity. By contrast, late-twentieth-century Open Theism (e.g., Clark Pinnock, John Sanders, Gregory Boyd in *The Openness of God*) and temporalist philosophers (such as Nicholas Wolterstorff) argue that God experiences sequential, relational time. In their pastoral view, genuine reciprocal love, petitionary prayer, and creaturely libertarian free will require a dynamic, open future that God experiences alongside creation. William Lane Craig articulates an influential mediating position: God exists timelessly sans creation, but temporally with creation. ### Engagement with Modern Physics The debate intersects deeply with modern physics and the philosophy of time: * **Relativity and Spacetime**: Proponents of divine timelessness often align their metaphysics with a tenseless “B-theory” of time (the four-dimensional “block universe” derived from Einstein’s Special and General Relativity), where past, present, and future are equally real and accessible to God’s eternal present (*totum simul*). Conversely, temporalists and Open Theists favor a dynamic, tensed “A-theory” (presentism). They point out that cosmic time (derived from the Friedmann-Lemaître-Robertson-Walker metric in cosmology) or Neo-Lorentzian interpretations of relativity preserve a preferred reference frame and an objective cosmic “now”. * **Quantum Indeterminacy**: Physicist-theologians such as John Polkinghorne (*Faith, Science and Understanding*) argue that ontological interpretations of quantum mechanics reveal an inherently flexible, becoming universe. Open theists embrace this indeterminism as physical evidence that the future is unwritten, viewing quantum contingency as the arena for divine persuasion rather than total predetermination. ### Epistemic Honesty The dialogue between Christian theology and physics must distinguish physical consensus from metaphysical interpretation. While the mathematical formalisms of Special/General Relativity and quantum mechanics are scientifically verified, interpreting relativity as a static block universe, or quantum mechanics as proving metaphysical open-endedness (versus deterministic alternatives like Bohmian mechanics or the Many-Worlds interpretation), represents unresolved philosophical extrapolation rather than established empirical consensus.

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1 source from the original research is no longer reachable

Ash'arite atomism continuous time occasionalism kalam cosmology contemporary physics

### Cosmological Position and Distinctive Concepts Classical Ashʿarite *kalām* (the historically dominant school of Sunni speculative theology, systematized by figures such as Abū al-Ḥasan al-Ashʿarī and Abū Bakr al-Bāqillānī in his *Kitāb al-Tamhīd*) developed an atomistic ontology to defend absolute divine omnipotence and *creatio ex nihilo*. In this framework, physical reality does not consist of self-subsisting substances with intrinsic causal powers. Instead, the universe is composed of indivisible, dimensionless atoms (*jawāhir*, singular *jawhar fard*) bearing ephemeral qualities or accidents (*aʿrāḍ*). Because accidents cannot endure across two consecutive instants, God continuously recreates both the atoms and their properties from nothingness at every moment (*tajaddud al-amthāl*, or continuous creation). What humans perceive as natural cause and effect is merely God’s observed habit or regular sequence (*ʿādah*), rather than intrinsic physical necessity. As Abū Ḥāmid al-Ghazālī formulated in *The Incoherence of the Philosophers* (*Tahāfut al-Falāsifa*, Discussion 17): > *"The connection between what is habitually believed to be a cause and what is believed to be an effect is not necessary, according to us."* ### Internal Branches, Tensions, and Lived Experience This occasionalist model contrasts sharply with other Islamic traditions: * **Māturīdism and Muʿtazilism:** Māturīdī theologians allowed greater room for secondary causality and intrinsic natures (*ṭabāʾiʿ*), while Muʿtazilites defended natural causal dispositions and genuine human agency. * **Imāmī Shīʿa Theology:** Systematized by Naṣīr al-Dīn al-Ṭūsī and al-ʿAllāma al-Ḥillī, mainstream Shīʿa theology largely rejected Ashʿarite atomism, adopting Avicennian philosophical frameworks that affirm real secondary causality (*al-asbāb wa-l-musabbabāt*) governed by divine wisdom. * **Sufism and Lived Practice:** Mystics like Ibn ʿArabī internalised continuous recreation as *tajallī* (ceaseless divine self-manifestation), grounding the practitioner’s daily reality in radical, momentary dependence on God (echoing Qurʾān 55:29: *"Every day He is bringing about a matter"*). ### Contemporary Physics and Epistemic Demarcation Modern Muslim thinkers often draw parallels between Ashʿarite discrete spacetime and contemporary physics, noting conceptual affinities between *kalām* occasionalism and quantum indeterminacy, Planck-scale spacetime quantization, or quantum vacuum fluctuations. However, from the standpoint of the philosophy of science, such parallels remain **speculative philosophical interpretations**, not established scientific consensus. Mainstream physics operates via mathematical formalisms and empirical observation without committing to occasionalist metaphysics, and *kalām* atomism was formulated as a metaphysical framework for divine sovereignty rather than an empirical hypothesis testable by modern science.

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kshanikavada momentariness Pratityasamutpada temporal ontology discrete time quantum mechanics

### Buddhist Temporal Ontology: *Pratītyasamutpāda* and *Kṣaṇikavāda* In early Buddhism, the doctrine of dependent origination (*pratītyasamutpāda*) established that all phenomena exist interdependently without enduring essences (*anātman*). In the Abhidharma traditions, this foundational impermanence (*anicca*) was radicalized into **kṣaṇikavāda** (the doctrine of momentariness). Rather than unfolding across a static temporal container, physical and mental phenomena (*dharmas*) exist as a rapid sequence of discrete, momentary events that vanish immediately upon arising. #### Internal Branches and Textual Debates - **Theravāda and Sautrāntika:** In the *Visuddhimagga* (XIV), Buddhaghosa analyzes experience into *citta-kkhaṇa* (consciousness-moments), each comprising three sub-moments: genesis (*uppāda*), presence (*ṭhiti*), and dissolution (*bhaṅga*). In the *Abhidharmakośabhāṣya* (IV.2–3), Vasubandhu defends momentariness by arguing that destruction occurs without an external cause (*akasmiko vināśaḥ*): a dharma perishes simply by virtue of having originated. Dharmakīrti (*Pramāṇavārttika*) further linked momentariness to causal efficacy (*arthakriyāsāmarthya*), arguing that permanent entities cannot exert effects; reality is therefore inherently dynamic and discrete. - **Madhyamaka Dialectic:** Nāgārjuna (*Mūlamadhyamakakārikā*, Ch. 19) challenged this atomization of time. If a moment has intrinsic nature (*svabhāva*), it cannot interact with past or future moments. For Nāgārjuna, time possesses no self-standing ontology; it is empty (*śūnya*) and relative to conditioned events. - **Zen (Chan):** In the *Shōbōgenzō* fascicle *Uji* ("Being-Time"), Dōgen dissolved the dualism between entities and duration: “Time itself is being, and all being is time.” Practitioners live this ontology through *vipaśyanā* (insight meditation), deconstructing coarse perception into flashing micro-events to dismantle reified attachments and the illusion of an enduring self. --- ### Dialogue with Modern Physics and Epistemic Honesty Philosophers frequently compare *kṣaṇikavāda* and *pratītyasamutpāda* to process physics and relational quantum mechanics (e.g., Carlo Rovelli’s relational framework, where physical quantities are defined solely in interactions rather than absolute states). However, a strict epistemic distinction is essential: - **Mainstream Physics Consensus:** Standard quantum mechanics treats time ($t$) as a continuous, external classical parameter in the Schrödinger equation, not as a quantized observable or discrete operator. - **Speculative Hypotheses:** Notions of "discrete time" or a temporal quantum (such as the chronon or Planck-time spacetime foam) remain speculative theoretical proposals within candidate theories of quantum gravity (e.g., loop quantum gravity, causal set theory), lacking decisive empirical confirmation. Parallels between Abhidharma event-ontologies and quantum discreteness represent conceptual analogies rather than verified physical equivalence.

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causal set theory discrete spacetime quantum state transition digital physics Wolfram

### Mainstream Consensus vs. Discrete and Digital Paradigms Mainstream general relativity and quantum field theory model the universe on a continuous, smooth differentiable manifold. In contrast, discrete spacetime and "digital physics" constitute minority or speculative programs proposing that space, time, and physical states are fundamentally granular, relational, or computational. ### Causal Set Theory (Minority Quantum Gravity) The most mathematically rigorous minority program is **Causal Set Theory**, introduced by Luca Bombelli, Joohan Lee, David Meyer, and Rafael Sorkin in their foundational 1987 *Physical Review Letters* paper, *“Space-time as a Causal Set”*. Sorkin’s group proposed that: > *“space-time at the smallest scales is in reality a causal set: a locally finite set of elements endowed with a partial order corresponding to the macroscopic relation that defines past and future”*. In this framework, continuous geometry disappears at the Planck scale. Spacetime is reduced to a discrete partially ordered set (a *causet*): causal connections dictate conformal structure, while element counting provides spacetime volume—succinctly summarized by practitioners as *“order plus number equals geometry.”* Quantum state transitions are understood as stochastic sequential growth, where new spacetime “atoms” are dynamically generated. ### Digital Physics and the Wolfram Model (Speculative Computational Extremes) A more radical departure abandons conventional spacetime entirely in favor of information processing. John Archibald Wheeler seeded this trajectory in *Information, Physics, Quantum: The Search for Links* (1989), asserting: > *“all things physical are information-theoretic in origin and this is a participatory universe”*. Building on early cellular-automaton cosmologies (Konrad Zuse, Edward Fredkin), Stephen Wolfram introduced a discrete hypergraph rewriting model in *A New Kind of Science* (2002) and the **Wolfram Physics Project** (2020). In Wolfram’s model, space is an abstract network of relations (a hypergraph) updating via simple algorithmic substitution rules. Quantum state transitions are represented by **multiway systems**—branching paths of all possible rule applications, yielding an emergent "branchial space" where quantum superposition and entanglement correspond to geometric proximity. ### Epistemic Status & Internal Tensions Practitioners operate across stark methodological divides: - **Causal Set Theory** is an active, peer-reviewed subfield of theoretical quantum gravity, yet struggles to demonstrate how four-dimensional classical spacetime naturally emerges from quantum causets without fine-tuning. - **Digital Physics and the Wolfram Model** remain highly speculative outsiders. Mainstream academic consensus regards them as unverified heuristic models that circumvent standard peer review and currently lack predictive, falsifiable contact with empirical particle physics. Continuous spacetime remains the empirically supported standard at all experimentally accessible scales.

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cognitive neuroscience subjective present perceptual temporal binding continuous physical time

### Mainstream Consensus and Core Position In mainstream cognitive neuroscience and psychophysics, the subjective "present" is understood not as an unmediated window onto continuous physical time, but as a retroactive, active neural construction. Physical events unfold continuously, yet their biological signals arrive at disparate speeds: light travels faster than sound, but visual retinal transduction (~50 ms) is far slower than auditory hair-cell activation (~1 ms), and peripheral neural conduction latencies vary by distance. To produce a coherent sensorimotor experience, the brain buffers, cross-calibrates, and stitches these asynchronous inputs into unified moments. ### Key Concepts and Empirical Milestones * **Temporal Binding Window (TBW):** The epoch (typically 100–300 ms) in which sensory inputs are bound and perceived as simultaneous (e.g., lip movements and vocal sounds). As David Eagleman demonstrated, the brain actively delays the fastest sensory inputs to align them with the slowest before conscious perceptual threshold is breached. * **Postdiction:** Empirical work reveals that conscious awareness is edited retrospectively. Later stimuli influence how preceding stimuli are perceived (observed in visual backward masking, the flash-lag effect, and the flash-beep illusion). As Michael Herzog observed regarding postdictive paradigms: *"Change cannot be perceived immediately. It can only be perceived after it has happened"*. * **The Specious Present:** Ernst Pöppel and Marc Wittmann formalized the hierarchical organization of subjective time: micro-windows of elementary integration (~30–50 ms) scaffold into an operative "subjective present" lasting roughly 2–3 seconds, after which processed events transition into working and episodic memory. ### Internal Debates and Clinical Applications * **Continuous vs. Discrete Perception:** While everyday intuition suggests time flows continuously, a central debate divides researchers. Proponents of discrete perception, such as Rufin VanRullen (linking perceptual snapshots to occipital alpha rhythms) and Herzog (a "two-stage model" where continuous unconscious processing yields discrete conscious updates), argue experience is sampled periodically. Proponents of continuous dynamical systems argue that discrete models confuse experimental artifacts with underlying neural trajectories. * **Clinical Implications:** In clinical psychiatry, dysregulated temporal binding windows are a hallmark of pathology. Individuals with schizophrenia exhibit an abnormally widened TBW, which degrades temporal order judgments and "intentional binding" (the subjective compression between an intended motor act and its outcome). This temporal degradation directly impairs the sense of agency, contributing to auditory hallucinations and delusions of external control. ### Epistemic Boundaries These conclusions rest on robust, replicable psychophysics, EEG temporal decoding, and lesion studies. Mainstream cognitive neuroscience treats temporal binding as a computational property of distributed corticostriatal and cerebellar networks, strictly distinguishing these empirical models from speculative fringe hypotheses such as quantum micro-tubule collapse (Orch-OR) or panpsychism.

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