We extend our proof of mathematical equivalence between quantum and classical mechanics to interacting systems, towards the the complete unification framework. By demonstrating that reference frame integration of classical interacting trajectories yields the exact quantum propagators for multi-particle systems, we show that quantum entanglement emerges naturally from correlated reference frame transformations of classical dynamics. The key insight is that reference frame democracy and interaction dynamics operate on orthogonal degrees of freedom: boosts affect only center-of-mass motion while interactions govern relative coordinates. This factorization explains why quantum mechanics naturally separates into free center-of-mass propagation and interacting relative motion. We provide explicit derivations for two-particle systems with arbitrary interactions V(r), demonstrate the emergence of quantum bound states from classical orbital motion, and prove that the entire mathematical apparatus of non-relativistic quantum mechanics is equivalent to classical mechanics for interacting systems, viewed through the lens of reference frame democracy. The pencil dot insight thus extends further its revolutionary implications: there is no separate quantum world---only classical reality properly accounting for Einstein's relativity.
We extend our proof of mathematical equivalence between quantum and classical mechanics to interacting systems, towards the the complete unification framework. By demonstrating that reference frame integration of classical interacting trajectories yields the exact quantum propagators for multi-particle systems, we show that quantum entanglement emerges naturally from correlated reference frame transformations of classical dynamics. The key insight is that reference frame democracy and interaction dynamics operate on orthogonal degrees of freedom: boosts affect only center-of-mass motion while interactions govern relative coordinates. This factorization explains why quantum mechanics naturally separates into free center-of-mass propagation and interacting relative motion. We provide explicit derivations for two-particle systems with arbitrary interactions V(r), demonstrate the emergence of quantum bound states from classical orbital motion, and prove that the entire mathematical apparatus of non-relativistic quantum mechanics is equivalent to classical mechanics for interacting systems, viewed through the lens of reference frame democracy. The pencil dot insight thus extends further its revolutionary implications: there is no separate quantum world---only classical reality properly accounting for Einstein's relativity.
We present an extension of reference frame democracy to relativistic physics and quantum gravity, exploring how quantum field theory might emerge from classical mechanics through Lorentz frame integration. Starting from the principle that physics should be invariant under arbitrary reference frame transformations, we investigate whether quantum mechanics could emerge as the Fourier transform of classical mechanics over all possible frames. Extending from Galilean to Lorentz transformations appears to yield quantum field theory, with the Klein-Gordon propagator arising from boost integration and QED Feynman rules from frame-democratic path integrals. We explore three fundamental challenges: (1) Whether quantum gravity could emerge as reference frame crystallization at the Planck scale; (2) How fermion statistics might arise from the topology of frame rotations; (3) Whether the measurement problem could resolve through environmental frame pinning. The framework suggests specific experimental predictions including modified uncertainty relations and gravitational phase shifts in quantum interference. This work explores whether all fundamental physics -particles, forces, and spacetime itself- might emerge from the democratic superposition of reference frame perspectives.
In standard quantum mechanics, reference frames are treated as abstract entities. We can think of them as idealized, infinite-mass subsystems which decouple from the rest of the system. In nature, however, all reference frames are realized through finite-mass systems that are subject to the laws of quantum mechanics and must be included in the dynamical evolution. A fundamental physical theory should take this fact seriously. In this paper, we further develop a symmetry-inspired approach to describe physics from the perspective of quantum reference frames. We find a unifying framework allowing us to systematically derive a broad class of perspective dependent descriptions and the transformations between them. Working with a translational-invariant toy model of three free particles, we discover that the introduction of relative coordinates leads to a Hamiltonian structure with two non-commuting constraints. This structure can be said to contain all observer-perspectives at once, while the redundancies prevent an immediate operational interpretation. We show that the operationally meaningful perspective dependent descriptions are given by Darboux coordinates on the constraint surface and that reference frame transformations correspond to reparametrizations of the constraint surface. We conclude by constructing a quantum perspective neutral structure, via which we can derive and change perspective dependent descriptions without referring to the classical theory. In addition to the physical findings, this work illuminates the interrelation of first and second class constrained systems and their respective quantization procedures.
Recently there has been much effort in developing a quantum generalisation of reference frame transformations. Despite important progress, a complete understanding of their principles is still lacking. In particular, we argue that previous proposals could yield reversible transformations between arbitrary quantum reference frames only when applied to the whole universe. In contrast, here we derive quantum reference frame transformations from first principles, using only standard quantum theory. Our framework, naturally based on incoherent rather than coherent group averaging, yields reversible transformations that only depend on the reference frames and system of interest. We find more general transformations than those studied so far, which are valid only in a restricted subspace. Importantly, our framework contains additional degrees of freedom in the form of an "extra particle," which carries information about the quantum features of reference frame states. Our formalism is valid for a broad range of symmetry groups. We study the centrally extended Galilei group specifically, highlighting key differences from previous proposals.
The concept of a reference frame has been a part of the physical formalism since the early days of physics. The reference frame was always understood as a physical system with respect to which states of other physical systems are described. With the adoption of quantum theory, our understanding of physical systems has fundamentally changed, yet we still rely on classical systems for the definition of reference frames. If we acknowledge the fact that all systems are quantum mechanical, including reference frames, then we have to be able to describe quantum systems relative to other quantum systems. \n \nIn this thesis we develop a framework for integrating quantum reference frames into the formalism of quantum mechanics. We show how the description of states and measurements has to be refined in order to account for the quantum nature of the reference frame. Initially, we study the implications of the new description with a quantum reference frame associated with a generic compact group. Then, we apply the same approach to the study of relativistic quantum reference frames associated with the Poincaré group, which is not compact. \n \nOur findings for the generic compact group include an analysis of how well a quantum system defines a frame of reference for other systems. Also in the generic case we analyze the effects of a measurement on a quantum reference frame. In the relativistic case we first find how the massive representations of the Poincaré group decompose into irreducible representations. This is a key problem in the analysis of quantum reference frames. Finally, we analyze a relativistic quantum reference frame that is used for measuring the total momentum. We will show how the relativistic measurements of total momentum should be described with respect to a quantum reference frame. We will also show how these measurements affect the quantum reference frame.
Recently there has been much effort in developing a quantum generalisation of reference frame transformations. Despite important progress, a complete understanding of their principles is still lacking. Here we derive quantum reference frame transformations for a broad range of symmetry groups from first principles, using only standard quantum theory. Our framework, naturally based on incoherent rather than coherent group averaging, yields reversible transformations that only depend on the reference frames and system of interest. We find more general transformations than those studied so far, which are valid only in a restricted subspace. Our framework contains additional degrees of freedom in the form of an "extra particle", which carries information about the quantum features of reference frame states. We study the centrally extended Galilei group specifically, highlighting key differences from previous proposals.
In physical experiments, reference frames are standardly modeled through a specific choice of coordinates used to describe the physical systems, but they themselves are not considered as such. However, any reference frame is a physical system that ultimately behaves according to quantum mechanics. We develop a framework for rotational (i.e., spin) quantum reference frames, with respect to which quantum systems with spin degrees of freedom are described. We give an explicit model for such frames as systems composed of three spin coherent states of angular momentum j and introduce the transformations between them by upgrading the Euler angles occurring in classical SO(3) spin transformations to quantum mechanical operators acting on the states of the reference frames. To ensure that an arbitrary rotation can be applied on the spin we take the limit of infinitely large j, in which case the angle operator possesses a continuous spectrum. We prove that rotationally invariant Hamiltonians (such as that of the Heisenberg model) are invariant under a larger group of quantum reference frame transformations. Our result is a development of the quantum reference frame formalism for a non-Abelian group.