Related papers: Time evolutions in Quantum mechanics and (Lorentzi…
A modification of the Fokker action is proposed, which allows one to formulate the covariant quantum theory of the charge system, in which the proper time of each particle serves as the evolution parameter and the particles themselves…
We formulate quantum mechanics in spacetimes with real-order fractional geometry and more general factorizable measures. In spacetimes where coordinates and momenta span the whole real line, Heisenberg's principle is proven and the…
For a large class of time-dependent non-Hermitain Hamiltonians expressed in terms linear and bilinear combinations of the generators for an Euclidean Lie-algebra respecting different types of PT-symmetries, we find explicit solutions to the…
Hamiltonian mechanics describes the evolution of a system through its Hamiltonian. The Hamiltonian typically also represents the energy observable, a Noether-conserved quantity associated with the time-invariance of the law of evolution. In…
We consider quantum geometrodynamics and parametrized quantum field theories in the framework of the Bohm-de Broglie interpretation. In the first case, and following the lines of our previous work [1], where a hamiltonian formalism for the…
We show that observational limits on the possible time variation of constants of Nature are significantly affected by allowing for both space and time variation. Bekenstein's generalisation of Maxwell's equations to allow for cosmological…
We experience some challenges in general gravitational theory owing to Einstein to explain late time acceleration of universe. To address this issue, geometric components of gravity have been modified in quite a few occasions to have a more…
A century after the advent of Quantum Mechanics and General Relativity, both theories enjoy incredible empirical success, constituting the cornerstones of modern physics. Yet, paradoxically, they suffer from deep-rooted, so-far intractable,…
The turn of the millennium was a time of optimism about an approach to noncommutative geometry inspired by rich mathematical objects called `quantum groups' and its applications to quantum spacetime. This would model quantum gravity effects…
This paper is a serious attempt at reconciling quantum and classical mechanics through the concept of dynamic space and the acceptance of non-zero Ricci tensor for vacuum. Starting with scalar particles, the paper shows that with those two…
We consider defining time as a function of a cyclical field, an abstraction of a clock. The definition of time corresponds to a novel interpretation of the relationship between space-time coordinates of observers at different locations in…
In this letter we discuss the possibility of treating the spacetime by itself as a kind of deformable body for which we can define an fundamental lattice, just like atoms in crystal lattices. We show three signs pointing in that direction.…
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],…
The theories of quantum mechanics and relativity dramatically altered our understanding of the universe ushering in the era of modern physics. Quantum theory deals with objects probabilistically at small scales, whereas relativity deals…
In recent years, a growing momentum has been gained by the emergent gravity framework. Within the latter, the very concepts of geometry and gravitational interaction are not seen as elementary aspects of Nature but rather as collective…
We argue that the Lorentzian path integral is a better starting point for quantum cosmology than the Euclidean version. In particular, we revisit the mini-superspace calculation of the Feynman path integral for quantum gravity with a…
Newtonian gravity arises as the nonrelativistic, static, weak-field limit of some Lorentzian spacetime geometry solving the generally covariant Einstein equations for a given matter field configuration. Spacetime geometry has a local…
The causal spacetimes admitting a covariantly constant null vector provide a connection between relativistic and non-relativistic physics. We explore this relationship in several directions. We start proving a formula which relates the…
The ontology proposed in this paper is aimed at demonstrating that it is possible to understand the counter-intuitive predictions of quantum mechanics while still retaining much of the framework underlying classical physics, the implication…
Along with the construction of non-Lorentz-invariant effective field theories, recent studies which are based on geometric models of Finsler space-time become more and more popular. In this respect, the Finslerian approach to the problem of…