Algebraic properties of quantum reference frames: Does time fluctuate?
arXiv:2211.04520 · doi:10.3390/quantum5010003
Abstract
Quantum reference frames are expected to differ from classical reference frames because they have to implement typical quantum features such as fluctuations and correlations. Here, we show that fluctuations and correlations of reference variables, in particular of time, are restricted by their very nature of being used for reference. Mathematically, this property is implemented by imposing constraints on the system to make sure that reference variables are not physical degrees of freedom. These constraints not only relate physical degrees of freedom to reference variables in order to describe their behavior, they also restrict quantum fluctuations of reference variables and their correlations with system degrees of freedom. We introduce the notion of "almost-positive" states as a suitable mathematical method. An explicit application of their properties to examples of recent interest in quantum reference frames reveals previously unrecognized restrictions on possible frame-system interactions. While currently discussed clock models rely on assumptions that, as shown here, make them consistent as quantum reference frames, relaxing these assumptions will expose the models to new restrictions that appear to be rather strong. Almost-positive states also shed some light on a recent debate about the consistency of relational quantum mechanics.
arXiv comment20 pages
References in corpus (23)
- Relational Quantum Mechanics
- Quantum mechanics and the covariance of physical laws in quantum reference frames
- The Trinity of Relational Quantum Dynamics
- A change of perspective: switching quantum reference frames via a perspective-neutral framework
- An effective approach to the problem of time
- Effective approach to the problem of time: general features and examples
- Quantum clocks and the temporal localisability of events in the presence of gravitating quantum systems
- A quintet of quandaries: five no-go theorems for Relational Quantum Mechanics
- Switching internal times and a new perspective on the 'wave function of the universe'
- Relational Quantum Mechanics is about Facts, not States: A reply to Pienaar and Brukner
- Equivalence of approaches to relational quantum dynamics in relativistic settings
- Relativistic quantum reference frames: the operational meaning of spin
- Entanglement of quantum clocks through gravity
- Spacetime Quantum Reference Frames and superpositions of proper times
- Effective relational dynamics of a nonintegrable cosmological model
- How to switch between relational quantum clocks
- Can chaos be observed in quantum gravity?
- Qubits are not observers -- a no-go theorem
- Second-quantized Unruh-DeWitt detectors and their quantum reference frame transformations
- Relative Facts of Relational Quantum Mechanics are Incompatible with Quantum Mechanics
- Quantization of dynamical symplectic reduction
- An algebraic approach to the "frozen formalism" problem of time
- Is Relational Quantum Mechanics about Facts? If So, Whose? A Reply to Di Biagio and Rovelli's Comment on Brukner and Pienaar