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We discuss some of the consequences of changing the matter to gravity coupling without affecting the gravitational dynamics. The Einstein tensor is usually assumed to be proportional to the stress tensor due to the divergence free property…
We reformulate Einstein's theory of gravity, isolating the conformal degree of freedom in a covariant way. This is done by introducing a physical metric defined in terms of an auxiliary metric and a scalar field appearing through its first…
The raising of both indices in the components of the Minkowski electromagnetic field strength 2-form to give the components of the electromagnetic excitation bivector field can be regarded as being equivalent to an electromagnetic…
Motivated in part by the bi-gravity approach to massive gravity, we introduce and study the multimetric Finsler geometry. For the case of an arbitrary number of dimensions, we study some general properties of the geometry in terms of its…
We consider inverse problems for the Einstein equation with a time-depending metric on a 4-dimensional globally hyperbolic Lorentzian manifold $(M,g)$. We formulate the concept of active measurements for relativistic models. We do this by…
The nonanalytic property of metric resulting from the presence of gravitomagnetic monopoles is considered. The curvature tensors, dual curvature tensors, dual Einstein tensor (and hence the gravitational field equation of gravitomagnetic…
We consider a system with a discrete configuration space. We show that the geometrical structures associated with such a system provide the tools necessary for a reconstruction of discrete quantum mechanics once dynamics is brought into the…
Local inertial frame invariance is taken as the fundamental principle of physical geometry, where a local inertial frame is represented by a verbein. Invariance of the vierbein with respect to local Lorentz transformations then expresses…
It is known that statistical model selection as well as identification of dynamical equations from available data are both very challenging tasks. Physical systems behave according to their underlying dynamical equations which, in turn, can…
This essay considers a simple model of observers that are influenced by the world around them. Consistent quantification of information about such influences results in a great deal of familiar physics. The end result is a new perspective…
For the past two decades, Einstein's Hole Argument (which deals with the apparent indeterminateness of general relativity due to the general covariance of the field equations) and its resolution in terms of Leibniz equivalence (the…
We illustrate how quantum information theory and free (i.e. noncommutative) semialgebraic geometry often study similar objects from different perspectives. We give examples in the context of positivity and separability, quantum magic…
The usual notion of separability has to be reconsidered when applied to states describing identical particles. A definition of separability not related to any a priori Hilbert space tensor product structure is needed: this can be given in…
Inspired by Bohr's dictum that "physical phenomena are observed relative to different experimental setups", this article investigates the notion of relativity in Bohr's sense, starting from a set of binary elements. The most general form of…
A discussion is given of the conformal Einstein field equations coupled with matter whose energy-momentum tensor is trace-free. These resulting equations are expressed in terms of a generic Weyl connection. The article shows how in the…
The binary model of physical vacuum is considered. This model reveals unified cause-and-effect mechanism of electromagnetic and gravitational interactions. The model of binary vacuum does not identify physical vacuum to a substance as the…
Due to the absence of an external, classical time variable, the probabilistic predictions of covariant quantum theory are ambiguous when multiple measurements are considered. Here, we introduce an information theoretic framework to the…
How do symmetries induce natural and useful quantum structures? This question is investigated in the context of models of three interacting particles in one-dimension. Such models display a wide spectrum of possibilities for dynamical…
This paper develops a geometric model for coupled two-state quantum systems (qubits), which is formulated using geometric (aka Clifford) algebra. It begins by showing how Euclidean spinors can be interpreted as entities in the geometric…
In the standard approach to Finsler geometry the metric is defined as a vertical Hessian and the Chern or Cartan connections appear as just two among many possible natural linear connections on the pullback tangent bundle. Here it is shown…