Description This work develops a process-based reconstruction of the quantum switch and the notion of indefinite causal order by introducing P-tacts (П-tacts) as the primitive units of quantum dynamics. Within this framework, quantum evolution is not described as a sequence of time-ordered operations but as a composition of discrete process units connected through explicit topological relations. The present article builds directly on the foundational introduction of the P-tact as the primitive unit of quantum theory, where process is taken as ontologically prior to state and time is not assumed as a fundamental parameter(Pavlov, P-Tact (П-такт) as the Primitive Unit of Quantum Theory, Zenodo, 2026, DOI: 10.5281/zenodo.18516711). In earlier work, this process ontology was applied to the quantum switch, demonstrating that its behavior emerges naturally from discrete process connectivity rather than from fundamentally indefinite causal relations(Pavlov, Quantum Switch as an Emergent Process Structure from Discrete Process Tacts (П-такт), Zenodo, 2026, DOI: 10.5281/zenodo.18498181). The connection between quantum switch behavior and quantum teleportation was subsequently clarified, showing that teleportation can be interpreted as a reindexing of process relations within a shared process topology(Pavlov, Quantum Switch and Teleportation, Zenodo, 2026, DOI: 10.5281/zenodo.18509173). Furthermore, the same P-tact framework was shown to give rise to emergent causality, time, gravity, and three-dimensional space as derived properties of discrete process graph dynamics rather than as fundamental background structures(Pavlov, Emergence of Causality, Gravity, Time, and Three-Dimensional Space from Discrete P-Tact Dynamics, Zenodo, 2026, DOI: 10.5281/zenodo.18504244). In the present work, these results are unified and extended through the explicit introduction of superposition of process graphs as a formal object. Using pentagonal and pentagram (pentacle) structures constructed from P-tacts, the quantum switch is reconstructed as a definite process topology. The appearance of indefinite causal order is shown to arise solely from projecting this topology onto a time-indexed formalism. No global temporal parameter is required at the fundamental level. All process relations are explicitly defined through connectivity, and control operations occupy superpositions of topological positions, not temporal slots. As a result, indefinite causal order is reclassified as a methodological placeholder, signaling the breakdown of time-based descriptive language rather than a fundamental indeterminacy of nature. The framework preserves all experimentally verified predictions while restoring conceptual coherence. It aligns naturally with the Everett interpretation of quantum mechanics, maintaining universal unitarity and eliminating collapse or exceptional measurement postulates. Quantum branching is interpreted as divergence in process graphs rather than as stochastic temporal events. This work prepares the conceptual and formal ground for subsequent studies on process-based quantum computation and programming, where local, dynamically entangled process modules replace long, phase-accumulating quantum circuits, offering a new architectural approach to decoherence and scalability.
Description This work develops a process-based reconstruction of the quantum switch and the notion of indefinite causal order by introducing P-tacts (П-tacts) as the primitive units of quantum dynamics. Within this framework, quantum evolution is not described as a sequence of time-ordered operations but as a composition of discrete process units connected through explicit topological relations. The present article builds directly on the foundational introduction of the P-tact as the primitive unit of quantum theory, where process is taken as ontologically prior to state and time is not assumed as a fundamental parameter(Pavlov, P-Tact (П-такт) as the Primitive Unit of Quantum Theory, Zenodo, 2026, DOI: 10.5281/zenodo.18516711). In earlier work, this process ontology was applied to the quantum switch, demonstrating that its behavior emerges naturally from discrete process connectivity rather than from fundamentally indefinite causal relations(Pavlov, Quantum Switch as an Emergent Process Structure from Discrete Process Tacts (П-такт), Zenodo, 2026, DOI: 10.5281/zenodo.18498181). The connection between quantum switch behavior and quantum teleportation was subsequently clarified, showing that teleportation can be interpreted as a reindexing of process relations within a shared process topology(Pavlov, Quantum Switch and Teleportation, Zenodo, 2026, DOI: 10.5281/zenodo.18509173). Furthermore, the same P-tact framework was shown to give rise to emergent causality, time, gravity, and three-dimensional space as derived properties of discrete process graph dynamics rather than as fundamental background structures(Pavlov, Emergence of Causality, Gravity, Time, and Three-Dimensional Space from Discrete P-Tact Dynamics, Zenodo, 2026, DOI: 10.5281/zenodo.18504244). In the present work, these results are unified and extended through the explicit introduction of superposition of process graphs as a formal object. Using pentagonal and pentagram (pentacle) structures constructed from P-tacts, the quantum switch is reconstructed as a definite process topology. The appearance of indefinite causal order is shown to arise solely from projecting this topology onto a time-indexed formalism. No global temporal parameter is required at the fundamental level. All process relations are explicitly defined through connectivity, and control operations occupy superpositions of topological positions, not temporal slots. As a result, indefinite causal order is reclassified as a methodological placeholder, signaling the breakdown of time-based descriptive language rather than a fundamental indeterminacy of nature. The framework preserves all experimentally verified predictions while restoring conceptual coherence. It aligns naturally with the Everett interpretation of quantum mechanics, maintaining universal unitarity and eliminating collapse or exceptional measurement postulates. Quantum branching is interpreted as divergence in process graphs rather than as stochastic temporal events. This work prepares the conceptual and formal ground for subsequent studies on process-based quantum computation and programming, where local, dynamically entangled process modules replace long, phase-accumulating quantum circuits, offering a new architectural approach to decoherence and scalability.
This work develops a graph-theoretic and process-based foundation for indefinite causal order in quantum theory, demonstrating that causal indefiniteness is not an ad hoc or exotic phenomenon but an emergent structural property of quantum dynamics when the primitive unit of evolution is taken to be the П-такт (P-Tact) — a discrete quantum process composed of local unitary superposition and entangling unitary interaction. Building upon a sequence of previously published foundational works, this paper formulates indefinite causal order as a superposition of quantum process graphs, where each graph encodes a definite causal structure, and the quantum state corresponds to a coherent superposition over such graphs. Within this framework, causal order is not fundamental but arises only in coarse-grained or classical limits. We show that: Indefinite causal order naturally emerges from the superposition of process graphs, without invoking external control systems or higher-order operations. The quantum switch is reinterpreted as a special finite realization of a more general graph-superposition principle. Time and causality emerge as effective parameters in the infinite-graph (continuum) limit of discrete П-такт dynamics. The graph-theoretic formulation is fully compatible with — and structurally supports — the Everettian (Many-Worlds) interpretation, where branching corresponds to graph bifurcations rather than wavefunction collapse. Classical spacetime causality appears as a macroscopic ordering imposed on an underlying non-causal quantum substrate. This approach unifies quantum information, indefinite causal order, emergent temporality, and Everettian branching within a single formal framework based on discrete process units and their graph composition. The results close several open conceptual gaps in the interpretation of quantum switches, process matrices, and non-classical causal structures, offering a consistent ontology grounded in quantum dynamics itself. This paper directly builds upon and extends the following foundational works: Pavlov, M. (2026). Quantum Switch as an Emergent Process Structure from Discrete Process Tacts (П-такт). Zenodo.https://doi.org/10.5281/zenodo.18498181 Pavlov, M. (2026). Quantum Switch and Teleportation. Zenodo.https://doi.org/10.5281/zenodo.18509173 Pavlov, M. (2026). Emergence of Causality, Gravity, Time, and Three-Dimensional Space from Discrete P-Tact (П-такт) Dynamics. Zenodo.https://doi.org/10.5281/zenodo.18504244 Pavlov, M. (2026). P-Tact (П-такт) as the Primitive Unit of Quantum Theory. Zenodo.https://doi.org/10.5281/zenodo.18516711 Together, these works establish a coherent program aimed at demonstrating the universality of quantum mechanics, the absence of fundamental collapse, and the emergence of spacetime and causality from discrete quantum process dynamics.
Abstract This work develops a process-based framework for quantum gravity in which physical space is rigorously described as the topology of a dynamically evolving graph of discrete quantum processes called P-tacts. A P-tact is defined as the primitive unit of quantum evolution, unifying local superposition and entangling operations into a single indivisible process step. Within this formalism, spacetime is not assumed as a pre-existing background but emerges from the connectivity structure of entanglement relations between P-tacts. The present study synthesizes and extends a coherent research program published throughout 2026. The foundational definition of the P-tact as the primitive unit of quantum theory was introduced in: Pavlov, M. (2026). P Tact (П-такт) as the Primitive Unit of Quantum Theory. Zenodo.https://doi.org/10.5281/zenodo.18516711 The emergence of the quantum switch as a process structure and the reconstruction of indefinite causal order were developed in: Pavlov, M. (2026). Quantum Switch as an Emergent Process Structure from Discrete Process Tacts (П-такт).https://doi.org/10.5281/zenodo.18498181 Pavlov, M. (2026). Indefinite Causal Order as Superposition of Process Graphs.https://doi.org/10.5281/zenodo.18519010 Pavlov, M. (2026). From Indefinite Causal Order to Definite Process Order: A Topological Reconstruction of the Quantum Switch via Discrete P-Tacts (П-такт).https://doi.org/10.5281/zenodo.18526959 Pavlov, M. (2026). Quantum Switch as a Minimal P Tact (П-такт) Cycle.https://doi.org/10.5281/zenodo.18607385 The connection between P-tacts, teleportation, and non-classical causal structures was presented in: Pavlov, M. (2026). Quantum Switch and Teleportation.https://doi.org/10.5281/zenodo.18509173 The emergence of time, causality, gravity, and three-dimensional space from discrete P-tact dynamics was developed in: Pavlov, M. (2026). Emergence of Causality, Gravity, Time, and Three-Dimensional Space from Discrete P-Tact (П-такт) Dynamics.https://doi.org/10.5281/zenodo.18504244 Pavlov, M. (2026). Emergence of Time from P Tact Entanglement (Происхождение времени).https://doi.org/10.5281/zenodo.18526015 Pavlov, M. (2026). Causality and Arrow of Time.https://doi.org/10.5281/zenodo.18549931 The Everett interpretation was explicitly formalized within the P-tact graph framework in: Pavlov, M. (2026). Everett Interpretation Formalized via P-Tact (П-такт) Path Graphs.https://doi.org/10.5281/zenodo.18524745 The present work integrates these results into a unified topological model in which space is identified with graph connectivity, curvature corresponds to dynamic restructuring of entanglement relations, and gravitational phenomena emerge as large-scale patterns of connectivity evolution. In this framework, geometry is not fundamental but process-derived. The theory is fully compatible with Everettian quantum mechanics and eliminates the need for wavefunction collapse. Branching structures correspond to graph bifurcations in the P-tact network, providing a structural representation of many-world dynamics. Gravity is thus interpreted not as a fundamental interaction but as an emergent property of quantum process topology. This approach proposes a formally consistent, unitary, and experimentally testable pathway toward quantum gravity grounded entirely in discrete quantum processes. Potential experimental implementations include quantum simulators and BQM platforms capable of modeling evolving entanglement graphs.
Description This work develops a process-based theoretical framework for the emergence of time from entangled discrete quantum processes, addressing one of the most fundamental open problems in quantum theory and the foundations of physics. Time is not assumed as a primitive, continuous, or external parameter. Instead, it is shown to arise as an emergent relational property of discrete process units—P-Tacts (П-такты)—and the entanglement structures connecting them. The central methodological shift of this work consists in replacing time-based evolution with process succession and graph structure. Quantum dynamics is described in terms of discrete operational steps, whose relational organization generates effective notions of temporal order, simultaneity, directionality, and causal structure. Within this approach, temporal relations are encoded in process graphs, rather than introduced through background spacetime or external clocks. The framework provides a unified and physically grounded explanation of: the emergence of temporal order without a fundamental time parameter, indefinite causal order as a natural consequence of superposed process graphs, quantum switch phenomena without higher-order causal primitives, and the appearance of classical temporal flow as a coarse-grained limit of dense entangled process networks. Special attention is given to higher-order organizational structures of process graphs. The progression from simple graph configurations to pentagonal, pentagram, and ultimately pentacle topologies illustrates how increasing structural complexity gives rise to rich temporal and causal behavior. These structures are purely processual and topological, not geometric embeddings in spacetime. The approach is fully compatible with unitary quantum mechanics and naturally aligns with the Everett interpretation, where branching corresponds to divergence of process paths rather than wave-function collapse. Temporal structure is therefore observer-relative and emergent, while the global process graph remains fully quantum and coherent. This article is not a standalone result but part of a coherent and cumulative research program devoted to establishing P-Tacts as primitive units of quantum theory and demonstrating how time, causality, spacetime structure, and information flow emerge from discrete quantum processes. For full conceptual and technical context, the present work should be read together with the following foundational publications. Related works (research program) Pavlov, M. (2026). Quantum Switch as an Emergent Process Structure from Discrete Process Tacts (П-такт)https://doi.org/10.5281/zenodo.18498181 Pavlov, M. (2026). Quantum Switch and Teleportationhttps://doi.org/10.5281/zenodo.18509173 Pavlov, M. (2026). Emergence of Causality, Gravity, Time, and Three-Dimensional Space from Discrete P-Tact (П-такт) Dynamicshttps://doi.org/10.5281/zenodo.18504244 Pavlov, M. (2026). P Tact (П-такт) as the Primitive Unit of Quantum TheoryZenodo, 07.02.2026https://doi.org/10.5281/zenodo.18516711 Pavlov, M. (2026). Indefinite Causal Order as Superposition of Process Graphshttps://doi.org/10.5281/zenodo.18519010 Pavlov, M. (2026). Everett Interpretation Formalized via P-Tact (П-такт) Path Graphshttps://doi.org/10.5281/zenodo.18524745 Cited text (for quotation and reference) This work demonstrates that time is not a fundamental parameter of quantum theory but an emergent property arising from the entanglement structure of discrete quantum processes (P-Tacts). Temporal order, simultaneity, and causal relations are encoded in the topology of process graphs rather than imposed through background spacetime or external clocks.
This work introduces the П-Tact (P-Tact) as the primitive unit of quantum theory, providing a formal, mathematical, and experimentally grounded framework for describing quantum processes at both micro and macro scales. A П-Tact represents a discrete process unit, consisting of two combined unitary operations: a local unitary operation that creates superposition and an entangling unitary operation that establishes quantum connections between nodes. The theory rigorously defines how quantum information propagates through graphs of П-Tacts, giving rise to emergent structures, including space, time, and causal order. We demonstrate how this framework unifies multiple aspects of quantum mechanics: indefinite causal order, quantum switch dynamics, quantum teleportation, and Everettian branching of quantum states. The formalism is expressed through precise unitary operations, mathematical derivations, and illustrative diagrams of П-Tact networks, quantum switch cycles, and emergent Everettian subgraphs. By introducing the П-Tact as the fundamental unit, this work offers a new methodology for understanding the discrete structure of quantum processes and provides a bridge between quantum foundations, quantum information theory, and emergent space-time concepts. Key contributions include: Formal definition and mathematical characterization of П-Tact (P-Tact) as the primitive unit of quantum processes. Construction of quantum network graphs representing information flow and entanglement between П-Tacts. Demonstration of indefinite causal order and quantum switch dynamics at both micro- and macro-levels. Illustration of emergent branching structures corresponding to Everettian subgraphs and classical outcomes. Establishment of a discrete framework connecting quantum dynamics with emergent space-time and topological structures. This publication is suitable for researchers in quantum information, quantum computing, quantum communication, quantum foundations, and theoretical physics, providing both theoretical insights and experimental guidance for exploring discrete quantum process units and their applications in emerging quantum technologies. 1. Pavlov, M. (2026 ). Quantum Switch as an Emergent Process Structure from Discrete Process Tacts (П-такт)https://doi.org/10.5281/zenodo.18498181 2. Pavlov, M. (2026 ). Quantum Switch and Teleportationhttps://doi.org/10.5281/zenodo.18509173 3. Pavlov, M. (2026 ). Emergence of Causality, Gravity, Time, and Three-Dimensional Space from Discrete P-Tact (П-такт) Dynamicshttps://doi.org/10.5281/zenodo.18504244
Description / Abstract This work proposes a process-based interpretation of the quantum switch as an emergent structure arising from discrete, packed quantum processes denoted as P. Instead of treating the quantum switch as a primitive resource associated with an indefinite causal order, we demonstrate that it can be understood as a higher-level process configuration constructed from elementary discrete process units. The proposed framework introduces a pentacle-based quantum language, in which quantum operations are organized as process graphs rather than time-ordered circuits. Within this approach, causal order is not assumed a priori but emerges from the structural relations between discrete processes. The quantum switch appears naturally as a stable process pattern enabled by coherent superposition and entanglement of operational pathways. This perspective aligns with process-matrix formulations and is conceptually consistent with the Everett (many-worlds) interpretation of quantum mechanics, avoiding collapse postulates and treating the wave function as universally valid. The framework suggests experimentally testable implications using interferometric and photonic implementations of the quantum switch and provides a conceptual bridge between quantum information processing, quantum foundations, and discrete models of quantum dynamics.
Description Causality and Arrow of Time is a unifying theoretical work within the author’s ongoing research program on discrete quantum process structures. The paper provides a formal, process-level derivation of causality and the arrow of time as emergent properties of branching quantum dynamics, rather than as fundamental primitives. The central methodological contribution of this work is the use of P-Tacts (П-такты) as primitive units of quantum evolution. Each P-Tact is defined as an irreducible process consisting of a local unitary operation and an entangling unitary operation. From sequences and superpositions of such P-Tacts, directed process graphs naturally arise. Within these graphs, causal relations and temporal ordering are shown to emerge from topology and branching structure, without invoking an external or background time parameter. This article synthesizes and extends the results developed across the author’s previous works, to which it is explicitly self-referential. In particular, it unifies earlier analyses of quantum switch, indefinite causal order, teleportation, emergent time, and Everettian branching into a single causal framework. The present work directly builds upon and integrates the following publications: Pavlov, M. (2026). Quantum Switch as an Emergent Process Structure from Discrete Process Tacts (П-такт).Zenodo. https://doi.org/10.5281/zenodo.18498181 Pavlov, M. (2026). Quantum Switch and Teleportation.Zenodo. https://doi.org/10.5281/zenodo.18509173 Pavlov, M. (2026). Emergence of Causality, Gravity, Time, and Three-Dimensional Space from Discrete P-Tact (П-такт) Dynamics.Zenodo. https://doi.org/10.5281/zenodo.18504244 Pavlov, M. (2026). P-Tact (П-такт) as the Primitive Unit of Quantum Theory.Zenodo. https://doi.org/10.5281/zenodo.18516711 Pavlov, M. (2026). Indefinite Causal Order as a Graph-Theoretic Property of P-Tact Networks.Zenodo (companion work within the same research program). Pavlov, M. (2026). Process Graphs and the Topological Origin of Quantum Time.Zenodo (companion work within the same research program). Pavlov, M. (2026). Branching Dynamics and Everettian Memory Structures.Zenodo (companion work within the same research program). Pavlov, M. (2026). Discrete Process Foundations of Quantum Measurement.Zenodo (companion work within the same research program). Together, these works form a coherent research program in which causality, temporal direction, and branching structure are not postulated but constructed from discrete quantum processes. A key conceptual motivation of this paper is the historical observation that foundational insights often precede the formal tools required to express them precisely. In this spirit, the present framework may be read as a formal completion of ideas first articulated by Hugh Everett III. Everett’s conception of universal wavefunction branching, proposed more than seventy years ago, anticipated many structural features of modern quantum information theory, yet lacked an explicit process-level formalization. This work offers such a formalization. Everettian branching is interpreted here as a concrete graph-theoretic phenomenon generated by P-Tact dynamics, with causal order and the arrow of time emerging as derived, observable features of the branching network. In this sense, the paper does not revise Everett’s ideas but renders them mathematically operational, linking early conceptual foundations to contemporary quantum technologies such as quantum switch, teleportation, and indefinite causal order. The article thus stands as both a technical contribution to quantum foundations and quantum information theory, and as a scholarly tribute to Everett’s legacy—demonstrating that ideas once considered purely interpretational can now be expressed within a precise and testable structural framework.