This paper introduces the theory of the Quantum Reference-Frame Phase Transition (QRPT), challenging the traditional view that macroscopic reference frames are fixed, classical backgrounds. We propose that reference systems can undergo qualitative phase transitions driven by the competition between internal quantum coherence and environmental decoherence. We define a quantum reference coherence order parameter, denoted as R_Q, which measures the relational superposition and spatial delocalization of the reference frame constituents. When the dimensionless control parameter chi_R exceeds a critical threshold chi_c, the system transitions from a Classical Frame phase—where standard external trajectories and potentials apply—to a Quantum Relational Frame phase characterized by macroscopic quantum superpositions, multi-branched effective dynamics, and modified canonical commutation relations. This framework provides novel insights into quantum foundations, macroscopic quantum mechanics, and the relational nature of spacetime and motion.
This paper introduces the theory of the Quantum Reference-Frame Phase Transition (QRPT), challenging the traditional view that macroscopic reference frames are fixed, classical backgrounds. We propose that reference systems can undergo qualitative phase transitions driven by the competition between internal quantum coherence and environmental decoherence. We define a quantum reference coherence order parameter, denoted as R_Q, which measures the relational superposition and spatial delocalization of the reference frame constituents. When the dimensionless control parameter chi_R exceeds a critical threshold chi_c, the system transitions from a Classical Frame phase—where standard external trajectories and potentials apply—to a Quantum Relational Frame phase characterized by macroscopic quantum superpositions, multi-branched effective dynamics, and modified canonical commutation relations. This framework provides novel insights into quantum foundations, macroscopic quantum mechanics, and the relational nature of spacetime and motion.
In general relativity, the description of spacetime relies on idealised rods and clocks, which identify a reference frame. In any concrete scenario, reference frames are associated to physical systems, which are ultimately quantum in nature. A relativistic description of the laws of physics hence needs to take into account such quantum reference frames (QRFs), through which spacetime can be given an operational meaning. Here, we introduce the notion of a spacetime quantum reference frame, associated to a quantum particle in spacetime. Such formulation has the advantage of treating space and time on equal footing, and of allowing us to describe the dynamical evolution of a set of quantum systems from the perspective of another quantum system, where the parameter in which the rest of the physical systems evolves coincides with the proper time of the particle taken as the QRF. Crucially, the proper times in two different QRFs are not related by a standard transformation, but they might be in a quantum superposition one with respect to the other.Concretely, we consider a system of N relativistic quantum particles in a weak gravitational field, and introduce a timeless formulation in which the global state of the N particles appears "frozen", but the dynamical evolution is recovered in terms of relational quantities. The position and momentum Hilbert space of the particles is used to fix the QRF via a transformation to the local frame of the particle such that the metric is locally inertial at the origin of the QRF. The internal Hilbert space corresponds to the clock space, which keeps the proper time in the local frame of the particle. Thanks to this fully relational construction we show how the remaining particles evolve dynamically in the relational variables from the perspective of the QRF. The construction proposed here includes the Page-Wootters mechanism for non interacting clocks when the external degrees of freedom are neglected. Finally, we find that a quantum superposition of gravitational redshifts and a quantum superposition of special-relativistic time dilations can be observed in the QRF.
When reference frames are treated quantum mechanically, the subsystem structure of quantum systems is no longer absolute, but depends on the choice of the quantum reference frame (QRF). This raises a basic question: which dynamical properties are preserved across QRFs, and which depend on the physical reference used to define the system? We study this question in the general setting of open quantum systems. At the operational level, after a QRF transformation, the old reference frame and environmental degrees of freedom may be inaccessible and must therefore be traced out. This motivates the definition of reduced quantum-reference-frame channels: maps that connect the joint description in one frame to the accessible subsystem in another. We characterize their symmetry-constrained structure and define a regime in which a reduced entropy-coherence conservation law holds. We also identify when the induced reduced action on the open system admits a classical interpretation as random frame misalignment, and when it instead reflects quantum reduced-frame effects. We then apply the framework to pure-dephasing dynamics and derive a necessary and sufficient compatibility condition for population preservation. When the frame symmetry commutes with the open system's free Hamiltonian, coherences acquire a multiplicative frame factor, so that locally inferred decoherence rates split into environmental and reference-induced contributions. Ramsey interferometry gives this split a direct operational meaning. Finally, a gravity-motivated dephasing model illustrates how degradation of a phase reference can mimic signatures usually attributed to intrinsic decoherence mechanisms.
The macroscopic manifestation of quantum coherence in complex many-body systems remains one of the most profound and challenging frontiers in modern physics. While traditional percolation theory successfully describes classical connectivity phase transitions in disordered media, and quantum phase transitions typically focus on zero-temperature Hamiltonian parameter variations, the interplay between network topology and quantum coherence propagation lacks a unifying macroscopic framework. In this paper, we propose the theory of Quantum Coherence Percolation Threshold (QCPT), introducing the concept that quantum coherence can undergo a sudden, non-analytic macroscopic percolation transition across complex networks. We formally define the coherence connection probability, denoted as p_C, and demonstrate that when p_C exceeds a critical threshold p_C*, a global coherent cluster abruptly emerges, characterized by a non-zero macroscopic global coherence measure C_global > 0. By formulating the density matrix evolution, local coherence sharing, and topological constraints over complex graph structures, we establish the analytical foundation for this network-mediated quantum phase transition. This framework bridges quantum information theory, statistical mechanics, and network science, offering a foundational blueprint for understanding macroscopic quantum states in complex environments.
Abstract Fundamental discrepancies exist among the foundational postulates of classical mechanics, relativity and quantum mechanics, leaving long-standing open physical puzzles including the origin of the arrow of time, quantum measurement collapse and the nature of spacetime. This paper proposes a self-consistent unified physical paradigm: the physical essence of a reference frame is the selective filtering of the full degrees of freedom of a system. All classical, relativistic and quantum physical theories constitute effective reduced descriptions of degrees of freedom under specific rules imposed by reference frames. Core phenomena such as temporal irreversibility, wave-function collapse, the constancy of the speed of light and the quantum-classical transition are not fundamental ontological properties of the universe, but emergent effects arising from filtering mappings introduced by finite-bandwidth observers. This work establishes an axiomatic framework for reference frames and degree-of-freedom filtering, defining projection filtering mappings, the principle of vanishing relative degrees of freedom, and the dimensionless filtering ratio. Within this framework, we reconstruct classical mechanics, special and general relativity, quantum decoherence and quantum measurement theory. Three categories of irreversible mechanisms — statistical coarse-graining, environmental partial-trace decoherence and time-domain sampling truncation — are integrated into a single mathematical structure. A universal dimensionless filtering ratio is defined. We clarify that the continuity of the control parameter does not imply that observables must evolve smoothly. Conceptually, the system can exhibit three regimes: quantum superposition, intermediate transition and classical state. Experiments on quantum bits at the Weizmann Institute provide preliminary observational hints, yet further verification is required; no specific form of the response curve is assumed in this paper. Three falsifiable quantitative predictions are put forward, involving attosecond spectroscopy, decoherence of superconducting qubits and cold-atom interferometry. We compare the present paradigm with relational quantum mechanics, QBism and consistent histories, discuss the ontological implications of time, observers and irreversibility, and outline extensions towards quantum gravity and cognitive science.
This paper, authored by Aidan McGill in October 2024, proposes a novel reinterpretation of quantum decoherence by framing it as a physical phase transition in probability distributions. It challenges conventional interpretations, such as the Copenhagen and many-worlds theories, which rely on the concept of wave function "collapse" driven by an external observer or measurement. Key aspects of this framework include: Observer-Independent Decoherence: The model removes the necessity of an observer, proposing that classical behavior is an emergent property of quantum complexity rather than a separate reality. The Phase Transition Mechanism: Decoherence is defined as a transition in the probability distribution of a system's wave function, triggered when interactions with external systems cross a specific threshold of complexity. Information and Energy Dynamics: The shift from quantum to classical behavior is driven by informational exchanges and energy transfers between a system and its environment. Empirical Alignment: The framework is supported by real-world examples, including buckyball double-slit experiments and superconducting qubits, which demonstrate quantum effects in macroscopic systems. Consistency with the Born Rule: This reinterpretation maintains the probabilistic outcomes of standard quantum mechanics and remains fully consistent with the Born rule. By focusing on the intrinsic properties of system interactions, this work offers a unified view where quantum mechanics governs all scales, and classical reality is a byproduct of informational complexity.
Recently, it was shown that when reference frames are associated to quantum systems, the transformation laws between such quantum reference frames need to be modified to take into account the quantum and dynamical features of the reference frames. This led to a relational description of the phase space variables of the quantum system of which the quantum reference frames are part of. While such transformations were shown to be symmetries of the system's Hamiltonian, the question remained unanswered as to whether they enjoy a group structure, similar to that of the Galilei group relating classical reference frames in quantum mechanics. In this work, we identify the canonical transformations on the phase space of the quantum systems comprising the quantum reference frames, and show that these transformations close a group structure defined by a Lie algebra, which is different from the usual Galilei algebra of quantum mechanics. We further find that the elements of this new algebra are in fact the building blocks of the quantum reference frames transformations previously identified, which we recover. Finally, we show how the transformations between classical reference frames described by the standard Galilei group symmetries can be obtained from the group of transformations between quantum reference frames by taking the zero limit of the parameter that governs the additional noncommutativity introduced by the quantum nature of inertial transformations.