Related papers: Quantum metric for null separated events and space…
It is shown that, with some reasonable assumptions, the theory of general relativity can be made compatible with quantum mechanics by using the field equations of general relativity to construct a Robertson-Walker metric for a quantum…
We introduce two new formulations for the notion of "quantum metric on noncommutative space". For a compact noncommutative space associated to a unital C*-algebra, our quantum metrics are elements of the spatial tensor product of the…
We discuss time measurement in quantum gravity. Using general relativity for large distances and the uncertainty principle we find a minimum time interval of the order of the Planck time, therefore the uncertainty in time measurment is…
A quantum mechanical theory is proposed which abandons an external parameter ``time'' in favor of a self-adjoint operator on a Hilbert space whose elements represent measurement events rather than system states. The standard quantum…
The observable spacetime can be viewed as worldline coincidences (events) between a particle system and the observers of an extended (material) reference frame (ERF). Particle positions are then operationally well defined with respect to…
This paper presents a simple model that mimics quantum mechanics (QM) results in terms of probability fields of free particles subject to self-interference, without using Schroedinger equation or complex wavefunctions. Unlike the standard…
Understanding out-of-equilibrium quantum dynamics is a critical outstanding problem, with key questions regarding characterizing adiabaticity for applications in quantum technologies. We show how the metric-space approach to quantum…
The quantum mechanics description of a physical object stretched in space and stable in time from the relativistic space-time properties point of view, introduced in special theory of relativity, is considered and analysed. The mathematical…
The history based formalism known as Quantum Measure Theory (QMT) generalizes the concept of probability-measure so as to incorporate quantum interference. The resulting \textit{quantum measure} $\mu$ is defined for arbitrary events (sets…
This paper introduces a novel uncertainty quantification framework for regression models where the response takes values in a separable metric space, and the predictors are in a Euclidean space. The proposed algorithms can efficiently…
Non-Euclidean data become more prevalent in practice, necessitating the development of a framework for statistical inference analogous to that for Euclidean data. Quantile is one of the most important concepts in traditional statistical…
Measurement outcomes of a quantum state can be genuinely random (unpredictable) according to the basic laws of quantum mechanics. The Heisenberg-Robertson uncertainty relation puts constrains on the accuracy of two noncommuting observables.…
We investigate the problem of metric fluctuations in the presence of the vacuum fluctuations of matter fields and critically assess the usual assertion that vacuum energy implies a Planckian cosmological constant. A new stochastic classical…
A discussion of the meaning of a physical concept cannot be separated from discussion of the conditions for its ideal measurement. We assert that quantization is no more than the invocation of the quantum of action in the explanation of…
We generate numerically on a lattice an ensemble of stationary metrics, with spherical symmetry, which have Einstein action $S_E \ll \hbar$. This is obtained through a Metropolis algorithm with weight $\exp(-\beta^2 S^2_E)$ and $\beta \gg…
In quantum metrology, one of the major applications of quantum technologies, the ultimate precision of estimating an unknown parameter is often stated in terms of the Cram\'er-Rao bound. Yet, the latter is no longer guaranteed to carry an…
We consider a number of aspects of the problem of defining time observables in quantum theory. Time observables are interesting quantities in quantum theory because they often cannot be associated with self-adjoint operators. Their…
The 4-dimensional space-time is extended to pseudo-complex coordinates. Proposing the standard quantization rules in this extended space, the ones for the 4-dimensional sub-space acquire, as one solution, the commutation relations with…
The scale of quantum mechanical effects in matter is set by Planck's constant, $\hbar$. This represents the quantisation scale for material objects. In this article, we present a simple argument why the quantisation scale for space, and…
We show that quantum measures and integrals appear naturally in any $L_2$-Hilbert space $H$. We begin by defining a decoherence operator $D(A,B)$ and it's associated $q$-measure operator $\mu (A)=D(A,A)$ on $H$. We show that these operators…