Related papers: General reference frames and their associated spac…
The definition of a reference frame in General Relativity is achieved through the construction of a congruence of time-like world-lines. In this framework, splitting techniques enable us to express physical phenomena in analogy with Special…
We introduce regular charts as physical reference frames in spacetime, and we show that general spacetimes can always be fully captured by regular charts. Effective quantum field theories (QFTs) can be conveniently defined in regular…
We propose that observables in quantum theory are properly understood as representatives of symmetry-invariant quantities relating one system to another, the latter to be called a reference system. We provide a rigorous mathematical…
We argue that correct account of the quantum properties of macroscopic objects which form reference frames (RF) demand the change of the standard space-time picture accepted in Quantum Mechanics. Galilean or Lorentz space-time…
A global vector field $v$ on a "spacetime" differentiable manifold $\mathrm{V}$, of dimension $N+1$, defines a congruence of world lines: the maximal integral curves of $v$, or orbits. The associated global space $\mathrm{N}\_v$ is the set…
A general formal definition of a theory of space and time compatible with the inertia principle is given. The formal definition of reference frame and inertial equivalence between reference frames are used to construct the class of inertial…
We postulate the applicability of the general form-invariance principle in special relativity. It is shown that this principle holds in classical mechanics. Some examples of transformations between the reference frames which satisfy this…
A reference frame consists of: a reference space, a time scale and a spatial metric. The geometric structure induced by these objects in spacetime is developed. The existence of a class of spatial metrics that are rigid, have free mobility…
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…
Physics is a model of nature able to both describe and predict the results of measurements made with respect to reference systems. These reference systems, in turn, are themselves physical and thus subject to the laws of physics. The…
We study the limitations for defining spatial and temporal intervals when the only available reference frame is a single composite quantum system, whose internal degrees of freedom serve as a temporal reference, a clock, and whose center of…
The study of quantum reference frames (QRFs) is motivated by the idea of taking into account the quantum properties of the reference frames used, explicitly or implicitly, in our description of physical systems. Like classical reference…
It is widely accepted that the fundamental geometrical law of nature should follow from an action principle. The particular subset of transformations of a system's dynamical variables that maintain the form of the action principle comprises…
We provide a possible fully geometric formulation of the core idea of quantum reference frames (QRFs) as it has been applied in the context of gravity, freeing its definition from unnecessary (though convenient) ingredients, such as…
Quantum reference frames have attracted renewed interest recently, as their exploration is relevant and instructive in many areas of quantum theory. Among the different types, position and time reference frames have captivated special…
This article suggests that thinking about the role of reference frames can provide new insight into Extended Wigner's Friend scenarios. This involves appealing to symmetries to make a principled distinction between properties of a system…
Based on a recent relational formulation of quantum reference frame transformations, especially with a case of quantum spatial translations in particular, we analyzed how the `value' of an observable for a fixed state change. That is the…
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…
A transition of focus from state space to frames of reference and their transformations is argued as being the appropriate setup for ensuring the covariance of physical laws. Such an approach can not only simplify and clarify aspects of…
This is an introduction to quantum algebra, from a geometric perspective. The classical spaces $X$, such as the Lie groups, homogeneous spaces, or more general manifolds, are described by various algebras $A$, defined over various fields…