Causality and Arrow of Time

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.