It is mandatory to know how to operationally define and translate a reference frame into mathematics, in order that a physical interpretation of theory calculations in terms of observational data is possible. The situation is particularly challenging for gauge systems such as General Relativity where spacetime coordinates are subject to spacetime diffeomorphisms considered as gauge transformations turning coordinates into non-observables. This motivates the idea of operationally defined (material) reference frames which specify coordinates in terms of matter or geometry reference fields leading to the concept of relational observables, relational reference frames and gauge reduction. Upon quantisation, all fields become operator valued distributions. Now new conceptual and technical questions arise such as: Should one reduce before or after quantisation and how are the reference fields quantised respectively in either route? Is a reference frame itself subject to quantisation and how are different quantum reference frames related? How does the gauge reduction fit into this, i.e. how can it be that a certain reference field is considered a non-observable in one reference frame and an observable in another which upon quantisation even displays fluctuations? How precisely are gauge dependent fields interpreted in terms of the relational observables in a given reference frame? What is the relative dynamics, e.g. how exactly are physical Hamiltonians of two relational reference frames related? The present conceptual work addresses these and related questions in a non-perturbative field theory context of sufficient generality to cover General Relativity coupled to standard matter. A central role is played by the concept of the relational reference frame transformation (RRFT) for which a general formula is derived and its properties are explored.
It is mandatory to know how to operationally define and translate a reference frame into mathematics, in order that a physical interpretation of theory calculations in terms of observational data is possible. The situation is particularly challenging for gauge systems such as General Relativity where spacetime coordinates are subject to spacetime diffeomorphisms considered as gauge transformations turning coordinates into non-observables. This motivates the idea of operationally defined (material) reference frames which specify coordinates in terms of matter or geometry reference fields leading to the concept of relational observables, relational reference frames and gauge reduction. Upon quantisation, all fields become operator valued distributions. Now new conceptual and technical questions arise such as: Should one reduce before or after quantisation and how are the reference fields quantised respectively in either route? Is a reference frame itself subject to quantisation and how are different quantum reference frames related? How does the gauge reduction fit into this, i.e. how can it be that a certain reference field is considered a non-observable in one reference frame and an observable in another which upon quantisation even displays fluctuations? How precisely are gauge dependent fields interpreted in terms of the relational observables in a given reference frame? What is the relative dynamics, e.g. how exactly are physical Hamiltonians of two relational reference frames related? The present conceptual work addresses these and related questions in a non-perturbative field theory context of sufficient generality to cover General Relativity coupled to standard matter. A central role is played by the concept of the relational reference frame transformation (RRFT) for which a general formula is derived and its properties are explored.
Diffeomorphism invariance is a central feature of general relativity. Without external reference structures, matter and geometry must be specified relationally, with respect to internal subsystems serving as reference frames. In quantum gravity, these reference systems must themselves be treated as quantum, motivating the use of quantum reference frames. In this work, we address how such a relational description could be formulated within linearized quantum gravity. To this purpose, we introduce quantum reference fields, i.e.,sets of four dynamical scalar fields whose stress-energy tensors enter the gravitational constraints. These fields extend the notion of quantum reference frames to local field-theoretic reference systems, allowing matter and gravitational degrees of freedom to be described relationally with respect to physical quantum systems whose states cannot be sharply peaked on definite field configurations. By generalizing the perspective-neutral construction of quantum reference frames, we show that relational, gauge invariant observables admit reduced descriptions in the perspective of each quantum reference field, and we derive the unitary transformations relating them. The resulting unitary maps implement local quantum coordinate changes between different internal perspectives, and act on the linearized gravitational field with an analogous structure to a linearized diffeomorphism, but with the classical gauge parameter replaced by a physical quantum field. Finally, we construct a relational von Neumann-type measurement scheme, showing how the corresponding reduced observables can be accessed operationally from the perspective of a quantum reference field.
The quantum reference frames program is based on the idea that reference frames should be treated as quantum physical systems. In this work, we combine these insights with the emphasis on operationality, understood as refraining from introducing into the framework objects not directly related to in principle verifiable probabilities of measurement outcomes, and identifying the setups indistinguishable as such. Based on intuitions from special relativity and gauge theory, we introduce an operational notion of a quantum reference frame -- which is defined as a quantum system equipped with a covariant positive operator-valued measure (POVM) -- and build a framework on the concept of operational equivalence that allows us to enforce operationality by quotienting the quantum state spaces with equivalence relation of indistinguishability by the available effects, assumed to be invariant under gauge transformations, and framed in the sense of respecting the choice of the frame's POVM. Such effects are accessed via the yen construction, which maps effects on the system to those on the composite system, satisfying gauge invariance and framing. They are called relative, and the classes of states indistinguishable by them are referred to as relative states. We show that when the frame is localizable, meaning that it allows for states that give rise to a highly localized probability distribution of the frame's observable, by restricting the relative description upon such localized frame preparation we recover the usual, non-relational formalism of quantum mechanics. We provide a consistent way of translating between different relative descriptions by means of frame-change maps and compare these with the corresponding notions in other approaches to QRF, establishing an operational agreement in the domain of common applicability.
Physical observation is made relative to a reference frame. A reference frame is essentially a quantum system given the universal validity of quantum mechanics. Thus, a quantum system must be described relative to a quantum reference frame (QRF). Further requirements on QRF include using only relational observables and not assuming the existence of external reference frame. To address these requirements, two approaches are proposed in the literature. The first one is an operational approach (F. Giacomini, et al, Nat. Comm. 10:494, 2019) which focuses on the quantization of transformation between QRFs. The second approach attempts to derive the quantum transformation between QRFs from first principles (A. Vanrietvelde, et al, Quantum 4:225, 2020). Such first principle approach describes physical systems as symmetry induced constrained Hamiltonian systems. The Dirac quantization of such systems before removing redundancy is interpreted as perspective-neutral description. Then, a systematic redundancy reduction procedure is introduced to derive description from perspective of a QRF. The first principle approach recovers some of the results from the operational approach, but not yet include an important part of a quantum theory - the measurement theory. This paper is intended to bridge the gap. We show that the von Neumann quantum measurement theory can be embedded into the perspective-neutral framework. This allows us to successfully recover the results found in the operational approach, with the advantage that the transformation operator can be derived from the first principle. In addition, the formulation presented here reveals several interesting conceptual insights. For instance, the projection operation in measurement needs to be performed after redundancy reduction, and the projection operator must be transformed accordingly when switching QRFs. These results represent one step forward in understanding how quantum measurement should be formulated when the reference frame is also a quantum system.
In physics, every observation is made with respect to a frame of reference. Although reference frames are usually not considered as degrees of freedom, in all practical situations it is a physical system which constitutes a reference frame. Can a quantum system be considered as a reference frame and, if so, which description would it give of the world? Here, we introduce a general method to quantise reference frame transformations, which generalises the usual reference frame transformation to a "superposition of coordinate transformations". We describe states, measurement, and dynamical evolution in different quantum reference frames, without appealing to an external, absolute reference frame, and find that entanglement and superposition are frame-dependent features. The transformation also leads to a generalisation of the notion of covariance of dynamical physical laws, to an extension of the weak equivalence principle, and to the possibility of defining the rest frame of a quantum system.
This paper is the thirty-first in a sequence developing an interpretive framework that redescribes physical reality as a causally consistent history of information updates rather than as a collection of independently existing objects. It is the third panel — the capstone — of the eighth grouping, a foundational-physics trilogy. Its subject is spacetime localization: where and when a record or system is — its position, orientation, relative phase, and time. The claim is that localization is real but not authoritatively global. There is no Global Frame: no physically privileged reference system that fixes absolute location and orientation, a privileged global simultaneity, a classical frame standing outside quantum theory, and one physically privileged, globally valid perspectival gauge-fixing. Localization is relational: positions and times are defined relative to a declared quantum reference frame (QRF), itself a quantum system that may be superposed and entangled with what it localizes (Giacomini, Castro-Ruiz, & Brukner, 2019; Loveridge, Miyadera, & Busch, 2018). What keeps this objective rather than subjective is a strict typing of cross-frame comparison: a single gauge-invariant relational (Dirac) observable has one invariant prediction, its perspectival representations intertwined by a frame-change map (case A); distinct relational observables form a relationally consistent web (case B); and where two frames share no common refinement their claims are declared incomparable (case C). "Objective" means invariance of the physical predictions under the declared symmetry group and the frame-change groupoid over the admissible frame family, to a declared tolerance — never frame-independence in an absolute sense. The flagship R-A is a dynamics-independent kinematic existence witness: a finite-dimensional discrete-ring model exhibits one physical state and two admissible ideal QRFs under which the localization profile and the entanglement structure differ — a sharp product relative to one particle; an entangled state with a delocalized, mixed marginal relative to another — while the distribution of the same relational observable is preserved. R-B splits into a domain covariance on shared refinements (ideal QRFs compose and agree on shared Dirac predictions) and a model-dependent global-perspective obstruction: where a globally valid relational gauge-fixing fails, as in known Gribov-type models (Vanrietvelde, Höhn, & Giacomini, 2023), no single perspective covers the whole physical state space — which is neither the same as, nor a consequence of, the absence of a privileged frame, and does not preclude a perspective-neutral description. R-C places Paper 8's relational time as the time-translation special case, with its finite-resolution-clock, conditional-covariance, and record–clock qualifications, separating the retired claim (no global clock) from the deferred one (relativistic foliation with dynamical geometry). R-D identifies and transports the frame-representable localization sector of certain Paper-30 grains, partially discharging that paper's grain-coherence deferral while leaving interaction, fragmentation, redundancy, and history-family structure grain-relative. This completes the trilogy's dismantling of the Global Bookkeeper while keeping geometry fixed: the quantum-mechanics–gravity interface is prepared, not entered. Localization is frame-relative but objective: no absolute frame, no globally gauge-fixed perspective claimed beyond what models establish, and no anarchy. ALAC Paper 31. Third panel (capstone) of the eighth grouping — a foundational-physics trilogy (29 Public Quantum Records -> 30 Classicality Without a Global Classicalizer -> 31 Spacetime Localization Without a Global Frame). Part of the Consistency-Constrained Information History (Akashic Ledger Architecture Cosmology) series. Presents no new quantum mechanics; results are interpretive (L2) on imported physics (L1).
The topic of quantum reference frames (QRFs) has attracted a great deal of attention in the recent literature. Potentially, the correct description of such frames is important for both the technological applications of quantum mechanics and for its foundations, including the search for a future theory of quantum gravity. In this letter, we point out potential inconsistencies in the mainstream approach to this subject and propose an alternative definition that avoids these problems. Crucially, we reject the notion that transformations between QRFs can be represented by unitary operators and explain the clear physical reasons for this. An experimental protocol, capable of empirically distinguishing between competing definitions of the term, is also proposed. The implications of the new model, for uncertainty relations, spacetime symmetries, gauge symmetries, the quantisation of gravity, and other foundational issues are discussed, and possible directions for future work in this field are considered.