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It has long been recognized as a difficult problem to determine whether the observed statistical correlation between two classical variables arise from causality or from common causes. Recent research has shown that in quantum theoretical…
Recently it has been proposed, using the formalism of positive-operator-valued measures, a possible definition of quantum coordinates for events in the context of quantum mechanics. In this short note we analyze this definition from the…
A class of time independent and physically meaningful Hamiltonians leads to evolution of observable quantities whose Ehrenfest times are arbitrarily large. This fact contradicts the popular claim that the true chaos is in quantum mechanics…
Quantum theory is formulated as the uniquely consistent way to manipulate probability amplitudes. The crucial ingredient is a consistency constraint: if the amplitude of a quantum process can be computed in two different ways, the two…
In classical physics the joint probability of a number of individually rare independent events is given by the Poisson distribution. It describes, for example, unidirectional transfer of population between the densely and sparsely populated…
It is shown that the joint measurements of some physical variables corresponding to commuting operators performed on pre- and post-selected quantum systems invariably disturb each other. The significance of this result for recent proofs of…
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…
Lorentz boosts on particles with spin and momentum degrees of freedom induce momentum-dependent rotations. Since, in general, different particles have different momenta, the transformation on the whole state is not a representation of the…
Free-field formalism for quantum groups provides a special choice of coordinates on a quantum group. In these coordinates the construction of associated integrable system is especially simple. This choice also fits into general framework of…
The relativistic free particle system in 1+1 dimensions is formulated as a ``bi-Hamiltonian system''. One Hamiltonian generates ordinary time translations, and another generates (essentially) boosts. Any observer, accelerated or not, sees…
Einstein, in his "Zur Elektrodynamik bewegter Korper", gave a physical (operational) meaning to "time" of a remote event in describing "motion" by introducing the concept of "synchronous stationary clocks located at different places". But…
Within ordinary ---unitary--- quantum mechanics there exist global protocols that allow to verify that no definite event ---an outcome to which a probability can be associated--- occurs. Instead, states that start in a coherent…
We here deduce Lorentz transformation (LT) as a member of a class of time-dependent coordinate transformations, complementary to those already known as spatial translations and rotations. This exercise validates the principle of physical…
The four-dimensional gauge group of general relativity corresponds to arbitrary coordinate transformations on a four-manifold. Theories of gravity with a dynamical structure remarkably like Einstein's theory can be obtained on the basis of…
Our conventional system of physical units is based on local or microscopic {\it dimensional} quantities which are {\it defined}, for convenience or otherwise aesthetic reasons, to be spacetime-independent. A more general choice of units may…
The introduction and quantization of a center-of-mass coordinate is demonstrated for the one-soliton sector of nonlinear field theories in (1+1) dimensions. The present approach strongly emphazises the gauge and BRST-symmetry aspects of…
The definition of physical states is the main technical issue of canonical approaches towards Quantum Gravity. In this work, we outline how those states can be found in Einstein-Cartan theory via a continuum limit and they are given by…
Quantum groups emerged in the latter quarter of the 20th century as, on the one hand, a deep and natural generalisation of symmetry groups for certain integrable systems, and on the other as part of a generalisation of geometry itself…
This paper elaborates on an intrinsically quantum approach to gravity, which begins with a general framework for quantum mechanics and then seeks to identify additional mathematical structure on Hilbert space that is responsible for gravity…
A realist description of our universe requires a twofold concept of locality. On one hand, there are the strictly Einstein-local interactions which generate the time evolution. On the other hand, the quantum state space calls for a…