Quantum mechanics and the covariance of physical laws in quantum reference frames (1712.07207v2)

Abstract: 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.

• The paper introduces a quantisation of reference frame transformations, revealing that entanglement and superposition are frame-dependent.
• The paper reinterprets the covariance of the Schrödinger equation by extending classical dynamics to include quantum superpositions and boosts.
• The paper extends the weak equivalence principle to superpositions, paving the way for experimental tests in quantum gravity and refined observer-dependent studies.

Overview of Quantum Mechanics and Covariance in Quantum Reference Frames

The paper by Giacomini, Castro-Ruiz, and Brukner proposes a novel methodological framework for treating quantum reference frames (QRFs), incorporating quantum mechanics into discussions of reference frames as physical systems. This approach extends the conventional reliance on abstract, classical reference frames to consider quantum systems themselves acting as frames of reference. The authors develop a mechanism to account for quantum superposition and entanglement by allowing transformations between these quantum frames, thereby revealing the frame-dependence of these quintessentially quantum features.

Key Developments in the Paper

• Quantisation of Reference Frame Transformations: The authors establish a general procedure for quantising transformations between QRFs, suggesting the transformation needs to be understood as a superposition of coordinate adjustments, which include translations and Galilean boosts or even more complex motions.
• Frame-Dependent Quantum Features: Their findings emphasize that both entanglement and superposition are relative constructs, dependent on the chosen reference frame. This observation aligns with the relational aspect of many quantum mechanical interpretations, whereby such properties are not intrinsic to the systems in question but instead inherit meaning only in relation to another system.
• Covariance of Physical Laws: The paper successfully reinterprets the covariance of dynamical physical laws within the QRF context. The transformation formalism proposed respects the covariance of the Schrödinger equation analogous to its classical counterpart in non-relativistic physics but expanded to include quantum state perspectives.
• Weak Equivalence Principle Extension: They propose an innovative extension whereby the weak equivalence principle is generalized to superpositions, suggesting that superpositions of gravitational fields are indistinguishable from superpositions of uniform accelerations, thus potentially offering new windows into understanding quantum gravity.

Implications and Future Perspectives

The research presented offers substantial implications for both theoretical and practical aspects of quantum mechanics and reference frame theory:

• Theoretical Advances: The introduction of QRFs facilitates further exploration of foundational questions in quantum mechanics, particularly those around reference frame dependency, an area where current insights might refine debates around measurement theory or observer-dependent phenomena.
• Experimental Validation: As quantum systems become increasing elements of experimental setups, the authors' work suggests pathways for experimental teams to test the principles governing superpositions of reference frames, potentially requiring high sensitivity apparatus capable of probing relative degrees of freedom with precision.
• Quantum Gravity: These innovations might intersect with burgeoning fields of research, especially concerning how quantum mechanics interacts with general relativity, contributing to discussions leading towards quantum gravity.

The approach of treating reference frames as quantum systems rather than relying on external, abstract constructs could also lead to nuanced understanding and novel experimental designs in areas such as quantum communication and quantum cosmology.

While the paper remains within the field of Galilean relativity, the proposed framework is robust enough that future work could expand it into special and general relativistic contexts. This suggests a broad vista of prospective interdisciplinary research unifying quantum dynamics with relativistic mechanics under common principles and formalisms.

In conclusion, by addressing these dynamics and transformations within QRFs, the authors lay the groundwork for future research that could bridge gaps in current theories, enhance precision in experimental quantum physics, and stimulate new lines of inquiry in the quest to reconcile quantum mechanics with relativity. The potential to extend the fundamental principles of physics into these richly quantum domains illustrates the highly promising nature of Giacomini et al.'s innovative framework.