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It is well known that in a generally covariant gravitational theory the choice of spacetime scalars as coordinates yields phase-space observables (or "invariants"). However their relation to the symmetry group of diffeomorphism…
Classical mechanics, in the Koopman-von Neumann formulation, is described in Hilbert space. It is shown here that classical canonical transformations are generated by Hermitian operators that are in general noncommutative. This naturally…
Uncertainty principle is one of the cornerstones of quantum theory. In the literature, there are two types of uncertainty relations, the operator form concerning the variances of physical observables and the entropy form related to entropic…
We discuss unimodular gravity at a classical level, and in terms of its extension into the UV through an appropriate path integral representation. Classically, unimodular gravity is simply a gauge fixed version of General Relativity (GR),…
A general theory of preparational uncertainty relations for a quantum particle in one spatial dimension is developed. We derive conditions which determine whether a given smooth function of the particle's variances and its covariance is…
The classical uncertainty principle inequalities were imposed over the general relativity geodesic equation as a mathematical constraint. In this way, the uncertainty principle was reformulated in terms of proper space-time length element,…
Quantum Mechanics is revisited as the appropriate theoretical framework for the description of the outcome of experiments that rely on the use of classical devices. In particular, it is emphasized that the limitations on the measurability…
A geometric approach to formulate the uncertainty principle between quantum observables acting on an $N$-dimensional Hilbert space is proposed. We consider the fidelity between a density operator associated with a quantum system and a…
The Generalized Uncertainty Principle and the related minimum length are normally considered in non-relativistic Quantum Mechanics. Extending it to relativistic theories is important for having a Lorentz invariant minimum length and for…
Endeavoring to formulate an exhaustive solution to the measurement problem in view of the theory of decoherence leads to a better understanding of the status of the collapse and of the emergence of classicality, thanks to a precise…
The best mathematical arguments against a realistic interpretation of quantum mechanics - that gives definite but partially unknown values to all observables - are analysed and shown to be based on reasoning that is not compelling. This…
The correspondence principle in physics between quantum mechanics and classical mechanics suggests deep relations between spectral and geometric entities of Riemannian manifolds. We survey---in a way intended to be accessible to a wide…
For any fundamental quantum field theory, unitarity, renormalizability, and relativistic invariance are considered to be essential properties. Unitarity is inevitably connected to the probabilistic interpretation of the quantum theory,…
Quantum theory famously entails the existence of incompatible measurements; pairs of observables which cannot be simultaneously measured to arbitrary precision. Incompatibility is widely regarded to be a uniquely quantum phenomenon, linked…
It is shown explicitly that in the framework of Bohmian quantum gravity, the equations of motion of the space-time metric are Einstein's equations plus some quantum corrections. It is observed that these corrections are not covariant. So…
In this article we propose a solution to the measurement problem in quantum mechanics. We point out that the measurement problem can be traced to an a priori notion of classicality in the formulation of quantum mechanics. If this notion of…
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…
The gap between classical mechanics and quantum mechanics has an important interpretive implication: the Universe must have an irreducible fundamental level, which determines the properties of matter at higher levels of organization. We…
The generalized uncertainty principle has been described as a general consequence of incorporating a minimal length from a theory of quantum gravity. We consider a simple quantum mechanical model where the operator corresponding to position…
When compared to quantum mechanics, classical mechanics is often depicted in a specific metaphysical flavour: spatio-temporal realism or a Newtonian "background" is presented as an intrinsic fundamental classical presumption. However, the…