Related papers: Space-time events and relativistic particle locali…
A definition is proposed to give precise meaning to the counterfactual statements that often appear in discussions of the implications of quantum mechanics. Of particular interest are counterfactual statements which involve events occurring…
We construct a theory of particles moving in curved both momentum space and spacetime, being a generalization of Relative Locality. We find that in order to construct such theory, with desired symmetries, including the general coordinate…
The treatment of time in relativity does not conform to that in quantum theory. In the context of quantum gravity this is called "the problem of time". A crucial difference is that time $t$ may be seen as an observable in relativity theory,…
It is well known that nonrelativistic quantum mechanics presents a clear asymmetry between space and time. Much of this asymmetry is attributed to the lack of Lorentz invariance of the theory. Nonetheless, a recent work [Phys. Rev. A…
We discuss relations between several relativistic spin observables and derive a Lorentz-invariant characteristic of a reduced spin density matrix.A relativistic position operator that satisfies all the properties of its nonrelativistic…
Two different versions of relativistic Langevin equation in curved spacetime background are constructed, both are manifestly general covariant. It is argued that, from the observer's point of view, the version which takes the proper time of…
We use the light-front machinery to study the behavior of a relativistic free particle and obtain the quantum commutation relations from the classical Poisson brackets. We argue that the usual projection onto the light-front coordinates for…
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…
All covariant time operators with normalized probability distribution are derived. Symmetry criteria are invoked to arrive at a unique expression for a given Hamiltonian. As an application, a well known result for the arrival time…
A deformation of special relativistic kinematics (possible signal of a theory of quantum gravity at low energies) leads to a modification of the notion of spacetime. At the classical level, this modification is required when one considers a…
In classical relativistic mechanics, a "preferred" proper direction in spacetime for each particle is determined by the direction of its 4-momentum. Analogously, for each quantum particle we find a local direction uniquely determined by the…
We introduce a covariant canonical quantization for a particle in curved spacetime that tracks operator-ordering ambiguities. Parameterizing spatial and temporal ordering, we derive a Hermitian Hamiltonian with leading quantum-relativistic…
Cosmic observations strongly support a time varying scenario for matter/space. On the other hand, so far, observations at solar system scale failed to identify any time variation on matter/space characteristics. To explain both results it…
The notions of events and their localisation fundamentally differ between quantum theory and general relativity, reconciling them becomes even more important and challenging in the context of quantum gravity where a classical spacetime…
Although time is one of our most intuitive physical concepts, its understanding at the fundamental level is still an open question in physics. For instance, time in quantum mechanics and general relativity are two distinct and incompatible…
The combination of quantum theory and special relativity leads to structures that differ in several respects from non-relativistic quantum mechanics of particles. These differences are quite familiar to practitioners of Algebraic Quantum…
We propose that space-time results from collapse of the wave function of macroscopic objects, in quantum dynamics. We first argue that there ought to exist a formulation of quantum theory which does not refer to classical time. We then…
The hilbert-space structure of quantum mechanics is related to the causal structure of space-time. The usual measurement hypotheses apparently preclude nonlinear or stochastic quantum evolution. By admitting a difference in the calculus of…
We consider the nonrelativistic particle moving on noncommutative space-time in the presence of constant force $\vec{F}$. Further, following the paper M. Daszkiewicz, C.J. Walczyk, Phys. Rev. D 77, 105008 (2008); arXiv: 0802.3575 [math-ph],…
Localization of relativistic particles and their position-momentum uncertainty relations are not yet fully understood. We discuss two schemes of photon localization that are based on the energy density. One scheme produces a positive…