Related papers: A Shape Dynamics Tutorial
In general relativity (GR), spacetime geometry is no longer just a background arena but a physical and dynamical entity with its own degrees of freedom. We present an overview of approaches to quantum gravity in which this central feature…
This paper makes a first attempt to bring the Shape from Polarization (SfP) problem to the realm of deep learning. The previous state-of-the-art methods for SfP have been purely physics-based. We see value in these principled models, and…
We propose a step-by-step manual for the construction of alternative theories of gravity, perturbatively as well as nonperturbatively. The construction is guided by no more than two fundamental principles that we impose on the gravitational…
Equivalence principles are a major part of modern relativity theory. Gravitational shifts can already be calculated within the time domain as motion shifts, and we examine the consequences of reversing this argument and describing motion…
Till now, the foundation of quantum physics is still mysterious. To explore the mysteries in the foundation of quantum physics, people always take it for granted that quantum processes must be some types of fields/objects on a rigid space.…
That preferred-frame theory accounts for special relativity and reduces to it if the gravitation field cancels. Starting from an interpretation of gravity as a pressure force, it is based on just one scalar field. This scalar gives the…
The field theoretic action for gravitational interactions in d+2 dimensions is constructed in the formalism of 2T-physics. General Relativity in d dimensions emerges as a shadow of this theory with one less time and one less space…
Modified theories of gravity usually present new degrees of freedom, as well as higher order derivatives, wrong signs in certain terms and complicated couplings already present in the Lagrangian from the beginning or originated by the field…
Pure shape dynamics (PSD) is a novel implementation of the relational framework originally proposed by Julian Barbour and Bruno Bertotti. PSD represents a Leibnizian/Machian approach to physics in that it completely describes the dynamical…
It has long been demonstrated that the vacuum scalar-tensor theory in the Jordan-frame Brans-Dicke parametrization is form-invariant under conformal transformations, provided that a suitable transformation of the coupling parameter $\omega$…
Minimally modified gravity theories are modifications of general relativity with two local gravitational degrees of freedom in four dimensions. Their construction relies on the breaking of 4D diffeomorphism invariance keeping however the…
The mathematical treatment and graphical representation of Special Relativity (SR) are well established, yet carry deep implications that remain hard to visualize. This paper presents a new graphical interpretation of the geometry of SR…
The standard theory of General Relativity (GR) currently provides the most reliable description of all gravitational events in Astrophysics and Cosmology. However, current Astronomy allows measurements that contradict the predictions of GR…
We develop a new perspective on the discretization of the phase space structure of gravity in 2+1 dimensions as a piecewise-flat geometry in 2 spatial dimensions. Starting from a subdivision of the continuum geometric and phase space…
This work reflects on mechanics as an epistemological framework on the state of a physical system to regard dynamics as the distribution of mechanical properties over spacetime coordinates. The resulting distribution is taken to be the…
By studying the notion of a fundamentally minimal length scale in asymptotically safe gravity we find that a specific version of deformed special relativity (DSR) naturally arises in this approach. We then consider two thought experiments…
The configuration space of general relativity is superspace - the space of all Riemannian 3-metrics modulo diffeomorphisms. However, it has been argued that the configuration space for gravity should be conformal superspace - the space of…
Conformally-invariant and pure, scale-invariant theories of gravity are particularly interesting in four or higher dimensions. Yet, in contrast to their four-dimensional counterparts, theories in higher dimensions are significantly more…
In this mostly pedagogical tutorial article a brief introduction to modern geometrical treatment of fluid dynamics and electrodynamics is provided. The main technical tool is standard theory of differential forms. In fluid dynamics, the…
This treatise concerns shapes in the sense of constellations of points with various automorphisms quotiented out: continuous translations, rotations and dilations, and also discrete mirror image identification and labelling…