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We have previously presented a version of the Weak Equivalence Principle for a quantum particle as an exact analog of the classical case, based on the Heisenberg picture analysis of free particle motion. Here, we take that to a full…
Covariant generalizations of well-known wave equations predict the existence of inertial-gravitational effects for a variety of quantum systems that range from Bose-Einstein condensates to particles in accelerators. Additional effects arise…
Familiar textbook quantum mechanics assumes a fixed background spacetime to define states on spacelike surfaces and their unitary evolution between them. Quantum theory has changed as our conceptions of space and time have evolved. But…
General relativity is a covariant theory of two transverse, traceless graviton degrees of freedom. According to a theorem of Hojman, Kuchar, and Teitelboim, modifications of general relativity must either introduce new degrees of freedom or…
The rigorous approach aimed at providing exact analytical results for hybrid classical-quantum models is elaborated on the grounds of generalized algebraic mapping transformations. This conceptually simple method allows one to obtain novel…
For purposes of quantization, classical gravity is normally expressed by canonical variables, namely the metric $g_{ab}(x)$ and the momentum $\pi^{cd}(x)$. Canonical quantization requires a proper promotion of these classical variables to…
This paper presents nine inconsistency theorems for general relativity theory (GRT), and shows that they ultimately originate from the use of Riemannian curvature and the abandonment of universal invariance (which is stronger than the…
That gravitation can be understood as purely metric phenomenon depends crucially on the validity of a number of hypotheses which are summarised by the Einstein Equivalence Principle, the least well tested part of which being the…
We present an exact quantum observable analog of the weak equivalence principle for a `relativistic' quantum particle. The quantum geodesic equations are obtained from Heisenberg equations of motion as an exact analog of a fully covariant…
From general relativity we have learned the principles of general covariance and local Lorentz invariance, which follow from the fact that we consider observables as tensors on a spacetime manifold whose geometry is modeled by a Lorentzian…
We extend the notion of general coordinate invariance to many-body, not necessarily relativistic, systems. As an application, we investigate nonrelativistic general covariance in Galilei-invariant systems. The peculiar transformation rules…
Quantum mechanics marks a radical departure from the classical understanding of Nature, fostering an inherent randomness which forbids a deterministic description; yet the most fundamental departure arises from something different. As shown…
The true dynamical randomness is obtained as a natural fundamental property of deterministic quantum systems. It provides quantum chaos passing to the classical dynamical chaos under the ordinary semiclassical transition, which extends the…
In this paper a didactic approach is described which immediately leads to an understanding of those postulates of quantum mechanics used most frequently in quantum computation. Moreover, an interpretation of quantum mechanics is presented…
Wigner had expressed the opinion that the impossibility of exact measurements of single operators like position operators rendered the notion of geometrical points somewhat dubious in physics. Using Sewell's recent resolution of the…
The equivalence postulate approach to quantum mechanics entails a derivation of quantum mechanics from a fundamental geometrical principle. Underlying the formalism there exists a basic cocycle condition, which is invariant under…
Spherically symmetric models of loop quantum gravity have been studied recently by different methods that aim to deal with structure functions in the usual constraint algebra of gravitational systems. As noticed by Gambini and Pullin, a…
Answers to the question how a classical world emerges from underlying quantum physics are revisited, connected and extended as follows. First, three distinct concepts are compared: decoherence in open quantum systems, consistent/decoherent…
Quantum gravity may modify the fundamental symmetries that govern identical particles. In particular, noncommutative spacetime frameworks predict deformations of Bose and Fermi statistics. Here we develop a relativistic quantum field theory…
We argue that recent developments in discretizations of classical and quantum gravity imply a new paradigm for doing research in these areas. The paradigm consists in discretizing the theory in such a way that the resulting discrete theory…