A First-Principles Implementation of Scale Invariance Using Best Matching

We present a first-principles implementation of spatial scale invariance as a local gauge symmetry in geometry dynamics using the method of best matching . In addition to the 3-metric, the proposed scale invariant theory also contains a 3-vector potential $A_k$ as a dynamical variable. Although some of the mathematics is similar to Weyl's ingenious but physically questionable theory, the equations of motion of this new theory are second order in time-derivatives. Thereby we avoid the problems associated with fourth order time derivatives that plague Weyl's original theory. It is tempting to try to interpret the vector potential $A_k$ as the electromagnetic field. We exhibit four independent reasons for not giving into this temptation. A more likely possibility is that it can play the role of "dark matter". Indeed, as noted in scale invariance seems to play a role in the MOND phenomenology. Spatial boundary conditions are derived from the free-endpoint variation method and a preliminary analysis of the constraints and their propagation in the Hamiltonian formulation is presented.Comment: 11 page

An introduction to the physics of Cartan gravity

A distance can be measured by monitoring how much a wheel has rotated when rolled without slipping. This simple idea underlies the mathematics of Cartan geometry. The Cartan-geometric description of gravity consists of a SO(1,4) gauge connection $A^{AB}(x)$ and a symmetry-breaking field $V^A(x)$. The clear similarity with symmetry-broken Yang-Mills theory suggests strongly the existence of a new field in nature: the gravitational Higgs field $V^A$. By treating $V^A$ as a genuine dynamical field we arrive at a natural generalization of General Relativity with a wealth of new phenomenology and with General Relativity reproduced exactly in the limit where $V^2$ tends to a positive constant. We show that in regions wherein $V^2(x)$ varies, but has a definite sign, the Cartan-geometric formulation is a form of a scalar-tensor theory. A specific choice of action yields the Peebles-Ratra quintessence model whilst more general actions are shown to exhibit propagation of torsion. Regions where the sign of $V^2$ changes correspond to a change in signature of the geometry; a simple choice of action with FRW symmetry yields, without any additional ad hoc assumptions, a classical analogue of the Hartle-Hawking no-boundary proposal. Solutions from more general actions are discussed. A gauge prescription for coupling matter to gravity is described and matter actions are presented which reduce to standard ones in the limit $V^2\rightarrow const$. It becomes clear that Cartan geometry may function as a novel platform for inspiring and exploring modified theories of gravity with applications to dark energy, black holes, and early-universe cosmology. We end by listing a set of open problems.Comment: Updated to reflect content of published versio

Spatiotemporal perspectives on urban energy transitions: a comparative study of three cities in China

This paper develops an integrated framework to study the socio-spatial and temporal dimensions of urban energy transitions to investigate the development and spread of solar energy technologies in urban China. A comparative analysis of three case studies of solar energy transitions in the cities of Foshan (in Guangdong), Rizhao (in Shandong), and Wuxi (in Jiangsu) demonstrates the framework’s applicability. The results map each city’s trajectory towards low carbon energy. Transitions result from dynamic interactions among central and local governments, solar manufacturers, solar installers, and residents. Alongside industrial strategies, locally-specific factors have a determining influence on the eventual outcomes

Physical interpretation of the Wigner rotations and its implications for relativistic quantum information

We present a new treatment for the spin of a massive relativistic particle in the context of quantum information based on a physical interpretation of the Wigner rotations, obtaining different results in relation to the previous works. We are lead to the conclusions that it is not possible to define a reduced density matrix for the particle spin and that the Pauli-Lubanski (or similar) spin operators are not suitable to describe measurements where spin couples to an electromagnetic field in the measuring apparatus. These conclusions contradict the assumptions made by most of the previous papers on the subject. We also propose an experimental test of our formulation.Comment: 10 pages, 2 figures. Several changes were made on the text. One extra example was include