Related papers: On the non-commutativity of geometric observables …
From general relativity we have learned the principles of general covariance and local Lorentz invariance, which follow from the fact that we consider observables as tensors on a spacetime manifold whose geometry is modeled by a Lorentzian…
We present a new scheme of defining invariant observables for general relativistic systems. The scheme is based on the introduction of an observer which endowes the construction with a straightforward physical interpretation. The…
I analyze the deformation of Lorentz symmetry that holds in certain noncommutative spacetimes and the way in which Lorentz symmetry is broken in other noncommutative spacetimes. I also observe that discretization of areas does not…
It is shown that the joint measurements of some physical variables corresponding to commuting operators performed on pre- and post-selected quantum systems invariably disturb each other. The significance of this result for recent proofs of…
We adapt the axioms of the quantum mechanics to the quantum Minkowski space-time coordinates and their transformations under the quantum Lorentz group to show how we can formulate the noncommutative special relativity and its quantum…
We propose a mathematical structure, based on a noncommutative geometry, which combines essential aspects of general relativity and quantum mechanics, and leads to correct "limiting cases" of both these theories. We quantize a groupoid…
Local observables in (perturbative) quantum gravity are notoriously hard to define, since the gauge symmetry of gravity -- diffeomorphisms -- moves points on the manifold. In particular, this is a problem for backgrounds of high symmetry…
We study metric-compatible Poisson structures in the semi-classical limit of noncommutative emergent gravity. Space-time is realized as quantized symplectic submanifold embedded in R^D, whose effective metric depends on the embedding as…
The time dilation of non-inertial travelers in circular and polygonal closed paths are well known. In both cases observers completing a round trip will age less than an observer at rest with respect to the circle / polygon. This rapid aging…
Considering the simultaneous measurement of non-commuting observables, we define a geometric measure for the degree of non-commuting behavior of quantum measurements coming from the initial and final states of the measurements. The…
We investigate the transformation laws of coordinates in generalizations of special relativity with two observer-independent scales. The request of covariance leads to simple formulas if one assumes noncanonical Poisson brackets,…
We use the vector wedge product in geometric algebra to show that Poisson commutator brackets measure preservation of phase space areas. We also use the vector dot product to define the Poisson anticommutator bracket that measures the…
In a previous Letter, we showed that physical scattering observables for compact spinning objects in general relativity can depend on additional degrees of freedom in the spin tensor beyond those described by the spin vector alone. In this…
We show that at second order, ensemble averages of observables and directional averages do not commute due to gravitational lensing -- observing the same thing in many directions over the sky is not the same as taking an ensemble average.…
We consider pairs of quantum observables (POVMs) and analyze the relation between the notions of non-disturbance, joint measurability and commutativity. We specify conditions under which these properties coincide or differ---depending for…
Although we lack complete understanding of quantum aspects of gravitation, it is usually agreed, using general arguments, that a final quantum gravity theory will endow space and time with some (fundamental or effective) notion of…
After a review of the existing theory of non-inertial frames and mathematical observers in Minkowski space-time we give the explicit expression of a family of such frames obtained from the inertial ones by means of point-dependent Lorentz…
We examine the Wess-Zumino-Novikov-Witten (WZNW) model on a circle and compute the Poisson bracket algebra for left and right moving chiral group elements. Our computations apply for arbitrary groups and boundary conditions, the latter…
Some studies interpret quantum measurement as being explicitly non local. Others assume the preferred frame hypothesis. Unfortunately, these two classes of studies conflict with Minkowski space-time geometry. On the contrary, in Aristotle…
Change and local spatial variation are missing in Hamiltonian General Relativity according to the most common definition of observables (0 Poisson bracket with all first-class constraints). But other definitions have been proposed. Seeking…