Related papers: Discrete Scale Relativity
Some conceptual issues concerning general invariant theories, with special emphasis on general relativity, are analyzed. The common assertion that observables must be required to be gauge invariant is examined in the light of the role…
We briefly review the various contexts within which one might address the issue of ``why'' the dimensionless constants of Nature have the particular values that they are observed to have. Both the general historical trend, in physics, of…
Rotational invariance of physical laws is a generally accepted principle. We show that it leads to an additional external constraint on local realistic models of physical phenomena involving measurements of multiparticle spin 1/2…
Higher-dimensional theories of the kind which may unify gravitation with particle physics can lead to significant modifications of general relativity. In five dimensions, the vacuum becomes non-standard, and the Weak Equivalence Principle…
Cosmology contributes a good deal to the investigation of variation of fundamental physical constants. High resolution data is available and allows for detailed analysis over cosmological distances and a multitude of methods were developed.…
Motivated by generalized uncertainty principle, we derive a discrete picture of the space that respects Lorentz symmetry as well as gauge symmetry through setting an equivalency between linear GUP correction term and electromagnetic…
We discuss the fate of diffeomorphism symmetry in discrete gravity. Diffeomorphism symmetry is typically broken by the discretization. This has repercussions for the observable content and the canonical formulation of the theory. It might…
In this review article, we discuss the distinction and possible equivalence between scale invariance and conformal invariance in relativistic quantum field theories. Under some technical assumptions, we can prove that scale invariant…
Testing the independence between random vectors is a fundamental problem in statistics. Distance correlation, a recently popular dependence measure, is universally consistent for testing independence against all distributions with finite…
We apply the ``consistent discretization'' approach to general relativity leaving the spatial slices continuous. The resulting theory is free of the diffeomorphism and Hamiltonian constraints, but one can impose the diffeomorphism…
Discrete scale invariance, which corresponds to a partial breaking of the scaling symmetry, is reflected in the existence of a hierarchy of characteristic scales l0, c l0, c^2 l0,... where c is a preferred scaling ratio and l0 a microscopic…
The variational principle for a thin dust shell in General Relativity is constructed. The principle is compatible with the boundary-value problem of the corresponding Euler-Lagrange equations, and leads to ``natural boundary conditions'' on…
We argue that, when a theory of gravity and matter is endowed with (classical) conformal symmetry, the fine tuning required to obtain the cosmological constant at its observed value can be significantly reduced. Once tuned, the cosmological…
Contrary to what is often stated, a fundamental spacetime discreteness need not contradict Lorentz invariance. A causal set's discreteness is in fact locally Lorentz invariant, and we recall the reasons why. For illustration, we introduce a…
The theory of regularity is a philosophical perspective in which laws of nature are just descriptions, that is to say, laws of nature do not govern the world. Moreover, according to the theory of regularity, the number of laws of nature…
Cosmological models that are locally consistent with general relativity and the standard model in which an object transported around the universe undergoes P, C and CP transformations, are constructed. This leads to generalization of the…
We point out that, if one accepts the view that the standard second on an atomic clock is dilated at low gravitational potential (ordinary gravitational time dilation), then the standard meter must also be dilated at low gravitational…
The possibility of mass in the context of scale-invariant, generally covariant theories, is discussed. The realizations of scale invariance which are considered, are in the context of a gravitational theory where the action, in the first…
We study the extent to which diffeomorphism invariance restricts the properties of the primordial perturbations in single scalar field models. We derive a set of identities that constrain the connected correlators of the cosmological…
In this paper a mathematically precise global (i.e. not the usual local) approach is presented to the variational principles of general relativistic classical field theories. Problems of the classic (usual) approaches are also discussed in…