Related papers: Short-Time Propagators and the Born--Jordan Quanti…
In this paper we continue to study so called ``inverse Born's rule problem'': to construct representation of probabilistic data of any origin by a complex probability amplitude which matches Born's rule. The corresponding algorithm --…
Canonical quantization of the Brane-World effective action presented by Kanno and Soda containing higher order curvature invariant terms, has been performed. It requires introduction of an auxiliary variable. As observed in a series of…
We show that quantum probabilities can be derived from statistical mechanics of classical fields. We consider Brownian motion in the space of fields and show that such a random field interacting with threshold type detectors produces clicks…
Despite the fact that it has been known since the time of Heisenberg that quantum operators obey a quantum version of Newton's laws, students are often told that derivations of quantum mechanics must necessarily follow from the Hamiltonian…
Quantum mechanics predicts correlation between spacelike separated events which is widely argued to violate the principle of Local Causality. By contrast, here we shall show that the Schr\"odinger equation with Born's statistical…
The Born-Jordan method for constructing the quantum condition of the Matrix Mechanics is pointed out to be inappropriate in the present work. We modify this method and reconstruct the quantum condition by setting up a new expression for the…
In this work, we show that the quantum mechanical notions of density operator, positive operator-valued measure (POVM), and the Born rule, are all simultaneously encoded in the categorical notion of a natural transformation of functors. In…
Quantum algorithms for electronic-structure simulations are actively being developed, yet many hybrid quantum-classical approaches are bottlenecked by the measurement overhead associated with large molecular Hamiltonians. Here we introduce…
Quantum devices based on Josephson effect in superconductors are usually described by a Hamiltonian obtained by commonly used canonical quantization. However, this recipe has not been yet rigorously justified. We show that this approach is…
We show that the Born's rule is incompatible with Lorentz symmetry of the Square Root Klein-Gordon equation (SRKG equation). It has been demonstrated that the Born rule must be modified in relativistic regime if one wishes to keep the SRKG…
The minimal-length paradigm is a cornerstone of quantum gravity phenomenology. Recently, it has been demonstrated that minimal-length quantum mechanics can alternatively be described as an undeformed theory set on a nontrivial momentum…
Five physical assumptions are proposed that together entail the general qualitative results, including the Born rule, of non-relativistic quantum mechanics by physical and information-theoretic reasoning alone. Two of these assumptions…
We consider how the Born rule, a fundamental principle of quantum mechanics, can be tested for particles created on the shortest timescales ($\sim10^{-25}\,\mathrm{s}$) currently accessible at high-energy colliders. We focus on targeted…
When a conscious observer is part of a quantum mechanical system, rule (4) cuts off solutions to the Schrodinger equation. It is important to show that this interruption of the Hamiltonian dynamics does not effect the statistical…
In this treatise I introduce the time dependent Generalized Born's Rule for the probabilities of quantum events, including conditional and consecutive probabilities, as the unique fundamental time evolution equation of quantum theory. Then…
This paper provides theorems aimed at shedding light on issues in the foundations of quantum mechanics. These theorems can be used to propose new interpretations to the theory, or to better understand, evaluate and improve current…
The very old problem of the statistical content of quantum mechanics (QM) is studied in a novel framework. The Born's rule (one of the basic postulates of QM) is derived from theory of classical random signals. We present a measurement…
The numerical version of the Hamilton-Jacobi quantization method, recently proposed, is applied to the one dimensional quartic oscillator. A suitable quantization condition is formulated and various energy levels and wave functions are…
The central limit theorem has been found to apply to random vectors in complex Hilbert space. This amounts to sufficient reason to study the complex valued Gaussian, looking for relevance to quantum mechanics. Here we show that the…
We propose a complete proof of the Born rule using an additional postulate stating that for a short enough time {\Delta}t between two measurements, a property of a particle will keep its values fixed. This dynamical postulate allows us to…