Related papers: An Information-Theoretic Link Between Spacetime Sy…
Information-theoretic arguments are used to obtain a link between the accurate linearity of Schrodinger's equation and Lorentz invariance: A possible violation of the latter at short distances would imply the appearance of nonlinear…
If there exists a formulation of quantum mechanics which does not refer to a background classical spacetime manifold, it then follows as a consequence, (upon making one plausible assumption), that a quantum description of gravity should be…
A nonlinear Schrodinger equation, that had been obtained within the context of the maximum uncertainty principle, has the form of a difference-differential equation and exhibits some interesting properties. Here we discuss that equation in…
Using perturbative methods, we analyse a nonlinear generalisation of Schrodinger's equation that had previously been obtained through information-theoretic arguments. We obtain analytical expressions for the leading correction, in terms of…
In this note, we generalize the nonlinearity-recovery result in [7] for classical cubic nonlinear Schr\"odinger equations to higher-order Schr\"odinger equations with a more general nonlinearity. More precisely, we consider a…
Based on the observation that the exterior space-times of Schwarzschild-type solutions allow two symmetric slicings, a static spherically symmetric one and a timelike homogeneous one, modifications of gravitational dynamics suggested by…
Generalizations of the three main equations of quantum physics, namely, the Schr\"odinger, Klein-Gordon, and Dirac equations, are proposed. Nonlinear terms, characterized by exponents depending on an index $q$, are considered in such a way…
Quantum mechanics in its presently known formulation requires an external classical time for its description. A classical spacetime manifold and a classical spacetime metric are produced by classical matter fields. In the absence of such…
There are four reasons why our present knowledge and understanding of quantum mechanics could be regarded as incomplete. Firstly, the principle of linear superposition has not been experimentally tested for position eigenstates of objects…
The theory of scale relativity provides a new insight into the origin of fundamental laws in physics. Its application to microphysics allows us to recover quantum mechanics as mechanics on a non-differentiable (fractal) spacetime. The…
Information measures for relativistic quantum spinors are constructed to satisfy various postulated properties such as normalisation invariance and positivity. Those measures are then used to motivate generalised Lagrangians meant to probe…
There are fundamental reasons as to why there should exist a reformulation of quantum mechanics which does not refer to a classical spacetime manifold. It follows as a consequence that quantum mechanics as we know it is a limiting case of a…
We introduce a smooth mapping of some discrete space-time symmetries into quasi-continuous ones. Such transformations are related with q-deformations of the dilations of the Euclidean space and with the non-commutative space. We work out…
Starting from a generic generally covariant classical theory we introduce the logarithmic correction to the quantum wave equation. We demonstrate the emergence of the evolution time from the group of automorphisms of the von Neumann algebra…
The introduction of nonlinearities in the Schr\"odinger equation has been considered in the literature as an effective manner to describe the action of external environments or mean fields. Here, in particular, we explore the nonlinear…
It is is explained why physical consistency requires substituting linear observables by nonlinear ones for quantum systems with nonlinear time evolution of pure states. The exact meaning and the concrete physical interpretation are…
A nonlocal nonlinear Schr\"odinger (NLS) equation was recently found by the authors and shown to be an integrable infinite dimensional Hamiltonian equation. Unlike the classical (local) case, here the nonlinearly induced "potential" is $PT$…
The physical origin of spacetime discreteness remains a central open problem in quantum gravity, with most existing approaches relying on specific microscopic structures or model-dependent assumptions. In this letter, spacetime discreteness…
One of the fundamental questions in physics concerns the relation between spacetime and quantum entanglement. The spacetime is usually considered as a fixed background physical space, and the quantum entanglement is usually manifested as a…
Quantum non-local correlations and the acausal, spooky action at a distance suggest a discord between quantum theory and special relativity. We propose a resolution for this discord by first observing that there is a problem of time in…