Related papers: Problems with the Newton-Schr\"odinger Equations
The late time accelerated expansion of the Universe demands that even in local galactic-scales it is desirable to study astrophysical phenomena, particularly relativistic accretion related phenomena in massive galaxies or in galaxy mergers…
We study the quantum gravity corrected decoherence of quantum superpositions in the near-extremal Reissner-Nordstr\"om black holes. By employing the effective field theory approach, we model the black hole as a quantum system coupled to an…
There is renewed interest in the question of whether the Navier-Stokes equations (NSE), one of the fundamental models of classical physics and widely used in engineering applications, are actually self-consistent. After recalling the…
Gravitation, according to General Relativity, is an attribute of space-time's geometry and hence not a force in the Newtonian sense. This is a consequence of Einstein's equivalence principle, which so far passed all experimental tests with…
The Schr\"odinger--Newton model is a semi-classical theory in which, in addition to mutual attraction, massive quantum particles interact with their own gravitational fields. While there are many studies on the phenomenology of single…
In order to test the quantum nature of gravity, it is essential to explore the construction of classical gravity theories that are as consistent with experiments as possible. In particular, the classical gravity field must receive input…
Within Newton-Schr\"odinger quantum mechanics which allows gravitational self-interaction, it is shown that a no-split no-collapse measurement scenario is possible. A macroscopic pointer moves at low acceleration, controlled by the…
Classical gravity theory predicts a state-dependent gravitational potential for a quantum test mass, leading to nonlinear Schrodinger-Newton (SN) state evolution that contrasts with quantum gravity. Testing the effect of SN evolution can…
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…
We study various aspects of higher-curvature theories of gravity built from contractions of the metric, the Riemann tensor and the covariant derivative, $\mathcal{L}(g^{ab},R_{abcd},\nabla_a)$. We characterise the linearized spectrum of…
We argue that in quantum gravity there is no Born rule. The quantum-gravity regime, described by a non-normalisable Wheeler-DeWitt wave functional $\Psi$, must be in quantum nonequilibrium with a probability distribution $P\neq\left\vert…
A wave function can be written in the form of {\psi} = ReiS/h. We put this form of wave function into quantum mechanics equations and take hydrodynamic limit, i. e., let Planck constant be zero. Then equations of motion (EOM) describing the…
This article is based on the covariant causal set ($c$-causet) approach to discrete quantum gravity. A $c$-causet $x$ is a finite partially ordered set that has a unique labeling of its vertices. A rate of change on $x$ is described by a…
A detailed review is given of the semiclassical approximation to quantum gravity in the canonical framework. This includes in particular the derivation of the functional Schr\"odinger equation and a discussion of semiclassical time as well…
Singularities in Newton's gravitation, in general relativity (GR), in Coulomb's law, and elsewhere in classical physics, stem from two ill conceived assumptions: a) there are point-like entities with finite masses, charges, etc., packed in…
The equations of motion for $N$ non-relativistic particles attracting according to Newton's law are shown to correspond to the equations for null geodesics in a $(3N+2)$-dimensional Lorentzian, Ricci-flat, spacetime with a covariantly…
For the purpose of analyzing observed phenomena, it has been convenient, and thus far sufficient, to regard gravity as subject to the deterministic principles of classical physics, with the gravitational field obeying Newton's law or…
We propose an optomechanics experiment that can search for signatures of a fundamentally classical theory of gravity and in particular of the many-body Schroedinger-Newton (SN) equation, which governs the evolution of a crystal under a…
A novel two-tiered organization of the microworld is presented, in which only the fundamental quantum fields of the standard model of particle physics (electrons, photons, quarks, etc.) are true quantum waves, exhibiting linear…
The nonlinear Schr\"odinger equation (NLSE) is a rich and versatile model, which in one spatial dimension has stationary solutions similar to those of the linear Schr\"odinger equation as well as more exotic solutions such as solitary waves…