Related papers: Why the Weyl Tile Argument is Wrong

We consider logics derived from Euclidean spaces $\mathbb{R}^n$. Each Euclidean space carries relations consisting of those pairs that are, respectively, distance more than 1 apart, distance less than 1 apart, and distance 1 apart. Each…

Weyl geometry is a natural extension of conformal geometry with Weyl covariance mediated by a Weyl connection. We generalize the Fefferman-Graham (FG) ambient construction for conformal manifolds to a corresponding construction for Weyl…

During his whole scientific life Hermann Weyl was fascinated by the interrelation of physical and mathematical theories. From the mid 1920s onward he reflected also on the typical difference between the two epistemic fields and tried to…

The belief that three dimensional space is infinite and flat in the absence of matter is a canon of physics that has been in place since the time of Newton. The assumption that space is flat at infinity has guided several modern physical…

A new space namely the Weyl-Kahler is proposed to the quantum state space. Some of the physical consequences are discussed.

In four space-time dimensions, there are good theoretical reasons for believing that General Relativity is the correct geometrical theory of gravity, at least at the classical level. If one admits the possibility of extra space-time…

In pregeometry a metric arises as a composite object at large distances. We investigate if its signature, which distinguishes between time and space, could be a result of the dynamics rather than being built in already in the formulation of…

I explain in what sense the structure of space and time is probably vague or indefinite, a notion I define. This leads to the mathematical representation of location in space and time by a vague interval. From this, a principle of…

The proper Euclidean geometry is considered to be metric space and described in terms of only metric and finite metric subspaces (sigma-immanent description). Constructing the geometry, one does not use topology and topological properties.…

The usual quantization of a classical space-time field does not touch the non-geometrical character of quantum mechanics. We believe that the deep problems of unification of general relativity and quantum mechanics are rooted in this poor…

There exist two consistent theories of self-interacting gravitons: general relativity and Weyl transverse gravity. The latter has the same classical solutions as general relativity, but different local symmetries. We argue that Weyl…

A new method for the construction of conformally invariant equations in an arbitrary four dimensional (pseudo-) Riemannian space is presented. This method uses the Weyl geometry as a tool and exploits the natural conformal invariance we can…

A purely geometrical relativity theory results from a construction that produces from three-dimensional space a happy unification of Kaluza's five-dimensional theory and Weyl's conformal theory. The theory can provide geometrical…

Of those gauge theories of gravity known to be equivalent to general relativity, only the biconformal gauging introduces new structures - the quotient of the conformal group of any pseudo-Euclidean space by its Weyl subgroup always has…

Effective geometries arising from a hypothetical discrete structure of space-time can play an important role in the understanding of the gravitational physics beyond General Relativity. To discuss this question, we make use of lessons from…

It was argued recently that conformal invariance in flat spacetime implies Weyl invariance in a general curved background for unitary theories and possible anomalies in the Weyl variation of scalar operators are identified. We argue that…

A basic principle of physics is the freedom to locally choose any unit system when describing physical quantities. Its implementation amounts to treating Weyl invariance as a fundamental symmetry of all physical theories. In this thesis, we…

In two papers titled "On the so-called non-Euclidean geometry", I and II, Felix Klein proposed a construction of the spaces of constant curvature -1, 0 and and 1 (that is, hyperbolic, Euclidean and spherical geometry) within the realm of…

The present paper considers if the new proposed conformal geometrodynamics (CGD) can extend the Nature features compared with general theory of relativity (GTR). The answer for this question can be connected with unique phenomenon arising…

We investigate (2+1)-dimensional gravity in a Weyl integrable spacetime (WIST). We show that, unlike general relativity, this scalar-tensor theory has a Newtonian limit for any dimension and that in three dimensions the congruence of world…