Related papers: Why the Weyl Tile Argument is Wrong
We propose that the gauge principle of d-dimensional Euclidean quantum gravity is Weyl invariance in its stochastic (d+1)-dimensional bulk. Observables are defined as depending only on conformal classes of d-dimensional metrics. We work…
H. Weyl in 1921 demonstrated that for a connected manifold of dimension greater than $1$, if two Riemannian metrics are conformal and have the same geodesics up to a reparametrization, then one metric is a constant scaling of the other one.…
A consistent quantum theory of gravity has remained elusive ever since the emergence of General Relativity and Quantum Field Theory. Attempts to date have not yielded a candidate that is either free from problematic theoretical…
We determine the leading order fall-off behaviour of the Weyl tensor in higher dimensional Einstein spacetimes (with and without a cosmological constant) as one approaches infinity along a congruence of null geodesics. The null congruence…
A conservative extension of general relativity by integrable Weyl geometry is formulated, and a new class of cosmological models ({\em Weyl universes}) is introduced and studied. A short discussion of how these new models behave in the…
It took two millennia after Euclid and until in the early 1880s, when we went beyond the ancient axiom of parallels, and inaugurated geometries of curved spaces. In less than one more century, General Relativity followed. At present,…
Weyl gravity has been advanced in the recent past as an alternative to General Relativity (GR). The theory has had some success in fitting galactic rotation curves without the need for copious amounts of dark matter. To check the viability…
Contemporary relativity theory is restricted in two points: (1) a use of the Riemannian space-time geometry and (2) a use of inadequate (nonrelativistic) concepts. Reasons of these restrictions are analysed in [1]. Eliminating these…
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…
A method for deriving the asymptotic behaviour of any physical field is presented. This leads to a geometrically meaningful derivation of the peeling properties for arbitrary values of the cosmological constant. Application to the…
For many years now it has become conventional for theorists to argue that "space-time is doomed", with the difficulties in finding a quantum theory of gravity implying the necessity of basing a fundamental theory on something quite…
In this paper, we analyse the well-posedness of the initial value formulation for particular kinds of geometric scalar-tensor theories of gravity, which are based on a Weyl integrable space-time. We will show that, within a frame-invariant…
Quantum walks are accepted as a generic model for quantum transport. The character of the transport crucially depends on the properties of the walk like its geometry and the driving coin. We demonstrate that increasing transport distance…
We introduce a general framework for analysing general probabilistic theories, which emphasises the distinction between the dynamical and probabilistic structures of a system. The dynamical structure is the set of pure states together with…
In this talk notes we expose the possibility to induce the cosmological constant from extra dimensions, in a geometrical framework where our four-dimensional Riemannian space-time is embedded into a five-dimensional Weyl integrable space.…
In a recent paper, algebraic descriptions for all non-relativistic spins were derived by elementary means directly from the Lie algebra $\specialorthogonalliealgebra{3}$, and a connection between spin and the geometry of Euclidean…
The rules of quantum mechanics require a time coordinate for their formulation. However, a notion of time is in general possible only when a classical spacetime geometry exists. Such a geometry is itself produced by classical matter…
The evolution of 4-dimensional and (4+d)-dimensional (d=1,2) cosmological models based on the integrable Weyl geometry are considered numerically both for empty space-time and for scalar field with non minimal coupling with gravity.
We present a simple, systematic and practical method to construct conformally invariant equations in arbitrary Riemann spaces. This method that we call "Weyl-to-Riemann" is based on two features of Weyl geometry. i) A Weyl space is defined…
In this paper we study a random walk on an affine building of type $\tilde{A}_r$, whose radial part, when suitably normalized, converges to the Brownian motion of the Weyl chamber. This gives a new discrete approximation of this process,…