Related papers: Shape dynamics and Mach's principles: Gravity from…
Classical field theory is considered as a theory of unparametrized surfaces embedded in a configuration space, which accommodates, in a symmetric way, spacetime positions and field values. Dynamics is defined by a (Hamiltonian) constraint…
We consider the Brans-Dicke theory in non-metricity gravity, which belongs to the family of symmetric teleparallel scalar-tensor theories. Our focus lies in exploring the implications of the conformal transformation, as we derive the…
We review recently offered notions of quasi-static evolution of the axial self-gravitating structures at large-scales and the criteria to characterize the corresponding evolutionary aspects under the influence of strong curvature regimes.…
We present a formalism for constructing schematic diagrams to depict chaotic three-body interactions in Newtonian gravity. This is done by decomposing each interaction in to a series of discrete transformations in energy- and angular…
We introduce a new geometric framework for relativistic particle dynamics based on contact geometry and suitable for treating dissipative processes like particle decay. The dynamics is formulated on a nine--dimensional extended phase space…
Shape had been intuitively recognized to play a dominant role in determining the global motion patterns of bio-molecular assemblies. However, it is not clear exactly how shape determines the motion patterns. What about the local…
Kendall's Similarity Shape Theory for constellations of points in the carrier space $\mathbb{R}^n$ was developed for use in Probability and Statistics. It was subsequently shown to reside within (Classical and Quantum) Mechanics'…
We give an alternative description of the physical content of general relativity that does not require a Lorentz invariant spacetime. Instead, we find that gravity admits a dual description in terms of a theory where local size is…
In the statistical analysis of shape a goal beyond the analysis of static shapes lies in the quantification of `same' deformation of different shapes. Typically, shape spaces are modelled as Riemannian manifolds on which parallel transport…
Recently, a unique class of local Higher Spin Gravities with propagating massless fields in $4d$ - Chiral Higher Spin Gravity - was given a covariant formulation both in flat and $(A)dS_4$ spacetimes at the level of equations of motion. We…
The following questions are germane to our understanding of gauge-(in)variant quantities and physical possibility: how are gauge transformations and spacetime diffeomorphisms understood as symmetries, in which ways are they similar, and in…
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…
Modified theories of gravity often introduce geometric structure beyond general relativity in order to address unresolved problems in the gravitational sector without invoking ad hoc matter fields. Mimetic gravity, for example, generates an…
The meaning and significance of Mach's Principle and its dependence on ideas about relativistic rotating frame theory and the celestial sphere is explained and discussed. Two new relativistic rotation transformations are introduced by using…
A suite of relational notions of shape are presented at the level of configuration space geometry, with corresponding new theories of shape mechanics and shape statistics. These further generalize two quite well known examples: --1)…
On the path towards quantum gravity, we find friction between temporal relations in quantum mechanics (QM) (where they are fixed and field-independent), and in general relativity (where they are field-dependent and dynamic). This paper aims…
Mach's principle fits into the wider "relational principle", advocating that not only inertia, but also space and time emerge from the interaction of matter. Concepts of a Machian/relational theory are proposed, where inertia and energy are…
Two different Hamiltonian formulations of the metric gravity are discussed and applied to describe a free gravitational field in the $d$ dimensional Riemann space-time. Theory of canonical transformations, which relate equivalent…
We present here a relativistic theory of gravity in which the spacetime metric is derived from a single scalar field $\Phi$. The field equation, derived from a simple variational principle, is a non-linear flat-space four-dimensional wave…
Recently we have presented a new formulation of the theory of gravity based on an implementation of the Einstein Equivalence Principle distinct from General Relativity. The kinetic part of the theory - that describes how matter is affected…