A change of perspective: switching quantum reference frames via a perspective-neutral framework

TL;DR

This work develops a perspective-neutral framework for transforming between quantum reference frames by unifying ideas from quantum information and quantum gravity. It combines a gravity-inspired symmetry principle and constrained-system methods to embed all frame perspectives into a single structure, from which frame changes are realized as symmetry transformations. In a concrete 1D toy model, the authors demonstrate how Dirac (perspective-neutral) quantization and reduced (frame-specific) quantizations relate via a quantum symmetry reduction, and provide explicit maps that implement frame changes. The approach clarifies how relational observables, entanglement, and classicality depend on the quantum reference frame, and it connects to notions of quantum general covariance and diffeomorphism symmetry in quantum gravity. The framework promises a systematic path to extend quantum reference-frame transformations to more complex systems and to relational clocks, with potential implications for both quantum foundations and quantum gravity.

Abstract

Treating reference frames fundamentally as quantum systems is inevitable in quantum gravity and also in quantum foundations once considering laboratories as physical systems. Both fields thereby face the question of how to describe physics relative to quantum reference systems and how the descriptions relative to different such choices are related. Here, we exploit a fruitful interplay of ideas from both fields to begin developing a unifying approach to transformations among quantum reference systems that ultimately aims at encompassing both quantum and gravitational physics. In particular, using a gravity inspired symmetry principle, which enforces physical observables to be relational and leads to an inherent redundancy in the description, we develop a perspective-neutral structure, which contains all frame perspectives at once and via which they are changed. We show that taking the perspective of a specific frame amounts to a fixing of the symmetry related redundancies in both the classical and quantum theory and that changing perspective corresponds to a symmetry transformation. We implement this using the language of constrained systems, which naturally encodes symmetries. Within a simple one-dimensional model, we recover some of the quantum frame transformations of arXiv:1712.07207, embedding them in a perspective-neutral framework. Using them, we illustrate how entanglement and classicality of an observed system depend on the quantum frame perspective. Our operational language also inspires a new interpretation of Dirac and reduced quantized theories within our model as perspective-neutral and perspectival quantum theories, respectively, and reveals the explicit link between them. In this light, we suggest a new take on the relation between a `quantum general covariance' and the diffeomorphism symmetry in quantum gravity.

Figures (10)

• Figure 1: Phase space geometry of classical frame perspective switches.
• Figure 2: Diagram of the two quantization methods and their relation for three particles. The horizontal arrows between Hilbert spaces are all isometries. The red diagram is commutative. The quantum symmetry reduction procedure from the perspective-neutral physical Hilbert space $\mathcal{H}^{\rm phys}$ of the Dirac quantization to the reduced Hilbert space, say, in A-perspective $\mathcal{H}_{BC|A}$ involves two steps: 1. a constraint trivialization $\mathcal{T}_{A,BC}$ which transforms the constraint in such a way that it only acts on the reference frame variables; 2. the reference frame variables, having become redundant, are discarded by projecting onto the classical gauge fixing conditions.
• Figure 3: In the perspective-neutral description, the three systems A, B, and C behave like two harmonic oscillators, with springs being attached to system C and A (with spring constanst $k_A$), and to systems C and B (with spring constant $k_B$). From this perspective, the Hamiltonian (both in the classical and quantum case) is $H= \frac{p_A^2}{2m_A} + \frac{p_B^2}{2m_B} + \frac{p_C^2}{2m_C} + \frac{1}{2}k_A (q_C - q_A)^2 + \frac{1}{2}k_B (q_C - q_B)^2$.
• Figure 4: Up: $x_A(t)$ and $x_B(t)$ when $A_0 = B_0 =1$, $\omega_A = 1$, $\omega_B=10$, $\phi_A =0$ and $\phi_B= \pi/2$. Down: the solutions of the equations of motion $q_B(t)$ and $q_C(t)$ in A's reference frame.
• Figure 5: Up: $x_A(t)$ and $x_B(t)$ when $A_0 =0.3$$B_0 =1$, $\omega_A = 10$, $\omega_B=1$, $\phi_A =0$ and $\phi_B= \pi/2$. Down: the solutions of the equations of motion $q_B(t)$ and $q_C(t)$ in A's reference frame.