Related papers: Discrete Quantum Mechanics I: Quantum Covariance
Quantum mechanics rests on the assumption that time is a classical variable. As such, classical time is assumed to be measurable with infinite accuracy. However, all real clocks are subject to quantum fluctuations, which leads to the…
Bohmian mechanics offers a deterministic alternative to conventional quantum theory through well-defined particle trajectories. While successful in nonrelativistic contexts, its extension to curved spacetime-and hence quantum…
The Principle of Relativity has so far been understood as the {\it covariance} of laws of Physics with respect to a general class of reference frame transformations. That relativity, however, has only been expressed with the help of {\it…
Quantum mechanics is usually presented starting from a series of postulates about the mathematical framework. In this work we show that those same postulates can be derived by assuming that measurements are discrete interactions: that is,…
Some of the possible consequences of a generalized uncertainty principle (which emerges in the context of string theory and quantum gravity models as a consequence of fluctuations of the background metric) are analyzed considering the case…
The general formalism of quantum mechanics for the description of statistical experiments is briefly reviewed, introducing in particular position and momentum observables as POVM characterized by their covariance properties with respect to…
Quantum theory does not only predict probabilities, but also relative phases for any experiment, that involves measurements of an ensemble of systems at different moments of time. We argue, that any operational formulation of quantum theory…
In 1926, Dirac stated that quantum mechanics can be obtained from classical theory through a change in the only rule. In his view, classical mechanics is formulated through commutative quantities (c-numbers) while quantum mechanics requires…
We here consider a generalization of the Klein-Gordon scalar wave equation which involves a single arbitrary function. The quantization may be viewed as allowing $\hbar$ to be a function of the momentum or wave vector rather than a…
The Projection Postulate from Standard Quantum Mechanics relies fundamentally on measurements. But measurements implicitly suggest the existence of anthropocentric notions like measuring devices, which should rather emerge from the theory.…
We have performed an experimental test under the conditions of which quantum mechanics predicts a spatially-discontinuous single-particle transport. The transport is beyond the relativistic paradigm of movement in Cartesian space and…
We present a definite formulation of the Principle of General Covariance (GCP) as a Principle of General Relativity with physical content and thus susceptible of verification or contradiction. To that end it is useful to introduce a kind of…
Quantum coherence quantifies the amount of superposition in a quantum system, and is the reason and resource behind several phenomena and technologies. It depends on the natural basis in which the quantum state of the system is expressed,…
The relation between continuous functions and random vectors is revealed in the paper that the main meaning is described as, for any given continuous function, there must be a sequence of probability spaces and a sequence of random vectors…
Quantum measurement is a fundamental concept in the field of quantum mechanics. The action of quantum measurement, leading the superposition state of the measured quantum system into a definite output state, not only reconciles…
Canonical vacuum gravity is expressed in generally-covariant form in order that spacetime diffeomorphisms be represented within its equal-time phase space. In accordance with the principle of general covariance, the time mapping ${\T}:…
We consider the evolution of quantum fields on a classical background space-time, formulated in the language of differential geometry. Time evolution along the worldlines of observers is described by parallel transport operators in an…
If the block universe view is correct, the future and the past have similar status and one would expect physical theories to involve final as well as initial boundary conditions. A plausible consistency condition between the initial and…
A quantum theory of the universe consists of a theory of its quantum dynamics and a theory of its quantum state The theory predicts quantum multiverses in the form of decoherent sets of alternative histories describing the evolution of the…
A consistent classical mechanics formulation is presented in such a way that, under quantization, it gives a noncommutative quantum theory with interesting new features. The Dirac formalism for constrained Hamiltonian systems is strongly…