Definition of the Main General Relativity Terms (Source e-Lecture of General Relativity Initiation of Richard Taillet Teacher-Researcher at Savoie Mont Blanc University)

We report off-shell Noether currents obtained from off-shell Noether potentials for first-order general relativity described by n-dimensional Palatini and Holst Lagrangians including the cosmological constant. These off-shell currents and potentials are achieved by using the corresponding Lagrangian and the off-shell Noether identities satisfied by diffeomorphisms generated by arbitrary vector fields, local SO(n) or SO(n−1,1) transformations, ‘improved diffeomorphisms’, and the ‘generalization of local translations’ of the orthonormal frame and the connection. A remarkable aspect of our approach is that we do not use Noether’s theorem in its direct form. By construction, the currents are off-shell conserved and lead naturally to the definition of off-shell Noether charges. We also study what we call the ‘half off-shell’ case for both Palatini and Holst Lagrangians. In particular, we find that the resulting diffeomorphism and local SO(3,1) or SO(4) off-shell Noether currents and potentials for the Holst Lagrangian generically depend on the Immirzi parameter, which holds even in the ‘half off-shell’ and on-shell cases. We also study Killing vector fields in the ‘half off-shell’ and on-shell cases. The current theoretical framework is illustrated for the ‘half off-shell’ case in static spherically symmetric and Friedmann–Lemaitre–Robertson–Walker spacetimes in four dimensions.

Background With standardization ever squeezing creative curricula in K–1 classrooms, creating time for a play-based multimodal writing curriculum that leverages children's strengths as storytellers is revolutionary. Due in part to accountability policy pressures, print-based writing and verbocentric writing feedback are still often privileged in school curricula. And yet, children are natural whole-body storytellers who will be asked to write and present ideas in all sorts of forms. In order to leverage children's storytelling strengths, we need to teach writing through multiple modes: This means expanding both writing instruction and the types of feedback offered to writers in primary classrooms. Research Questions This study examines two questions: How is feedback being given, and what impact does it have on children's storytelling? How is play/storying being sanctioned? Setting & Participants The study took place in a K–1 classroom in an inquiry-based, project-based school in the U.S. Midwest during a month-long storytelling workshop unit. Participants included two co-teachers and 46 children aged 5 to 7. Research Design This qualitative study used ethnographic methods and participant observation. Data Collection & Analysis Video data were collected during workshop each day for one month, including minilessons, writing time, and share time, which is the focus of this article. Discourse analysis and a multimodality theoretical lens were used to analyze how children gave one another feedback on their stories through embodied demonstration, gesture, acting, out, or copying one another's storytelling devices. Findings Findings indicate that children's acting/embodiment, humor/parody, and copying all worked as effective forms of multimodal feedback, which ultimately functioned as teaching for developing peers’ storytelling strategies and skills. However, teachers inadvertently privileged language alone via narration, or language with demonstration in feedback sessions. Conclusions Teacher/researcher collaborations should explore ways to reimagine forms of writer's feedback that include and account for demonstration, copying, and impromptu performance and that, ultimately, open up the definition of what counts as writing at school. Um, you should work on making your story, like, real. Because, um, you're going all over the place [wiggles entire body to illustrate]—Allen, age 6

We consider rotational motion of an arbitrarily composed and shaped, deformable weakly self-gravitating body being a member of a system of N arbitrarily composed and shaped, deformable weakly self-gravitating bodies in the post-Newtonian approximation of general relativity. Considering importance of the notion of angular velocity of the body (Earth, pulsar) for adequate modelling of modern astronomical observations, we are aimed at introducing a post-Newtonian-accurate definition of angular velocity. Not attempting to introduce a relativistic notion of rigid body (which is well known to be ill-defined even at the first post-Newtonian approximation) we consider bodies to be deformable and introduce the post-Newtonian generalizations of the Tisserand axes and the principal axes of inertia.

Entangled states of light exhibit measurable correlations between light detections at separated locations. These correlations are exploited in entangled-state quantum key distribution. To do so involves setting up and maintaining a rhythm of communication among clocks at separated locations. Here, we try to disentangle our thinking about clocks as used in actual experiments from theories of time, such as special relativity or general relativity, which already differ between each other. Special relativity intertwines the concept of time with a particular definition of the synchronization of clocks, which precludes synchronizing every clock to every other clock. General relativity imposes additional barriers to synchronization, barriers that invite seeking an alternative depending on any global concept of time. To this end, we focus on how clocks are actually used in some experimental situations. We show how working with clocks without worrying about time makes it possible to generalize some designs for quantum key distribution and also clarifies the need for alternatives to the special-relativistic definition of synchronization.

In this paper a set of canonical collective variables is defined for a classical Klein–Gordon field and the problem of the definition of a set of canonical relative variables is discussed. This last point is approached by means of a harmonic analysis in momentum space. This analysis shows that the relative variables can be defined if certain conditions are fulfilled by the field configurations. These conditions are expressed by the vanishing of a set of conserved quantities, referred to as supertranslations since as canonical observables they generate a set of canonical transformations whose algebra is the same as that which arises in the study of the asymptotic behavior of the metric of an isolated system in General Relativity.9