Yes, there is. – A new kind of gauge theory is introduced, where the minimal coupling and corresponding covariant derivatives are defined in the space of functions pertaining to the functional Schrödinger picture of a given field theory. While, for simplicity, we study the example of a (1) symmetry, this kind of gauge theory can accommodate other symmetries as well. We consider the resulting relativistic nonlinear extension of quantum mechanics and show that it incorporates gravity in the (0+1)-dimensional limit, where it leads to the Schrödinger-Newton equations. Gravity is encoded here into a universal nonlinear extension of quantum theory. The probabilistic interpretation, i.e. Born's rule, holds provided the underlying model has only dimensionless parameters.Yes, there is. – A new kind of gauge theory is introduced, where the minimal coupling and corresponding covariant derivatives are defined in the space of functions pertaining to the functional Schrödinger picture of a given field theory. While, for simplicity, we study the example of a (1) symmetry, this kind of gauge theory can accommodate other symmetries as well. We consider the resulting relativistic nonlinear extension of quantum mechanics and show that it incorporates gravity in the (0+1)-dimensional limit, where it leads to the Schrödinger-Newton equations. Gravity is encoded here into a universal nonlinear extension of quantum theory. The probabilistic interpretation, i.e. Born's rule, holds provided the underlying model has only dimensionless parameters.

arXiv:0704.2559Journal of Physics Conference SeriesMay 1, 200715 citations

In Favor of a Newtonian Quantum Gravity

Lajos Diósi, B. Lukács

Abstract We list arguments for creating a unified theory of Newtonian Gravity and Quantum Mechanics. This nonrelativistic level has been historically bypassed, however even here one is confronted with conceptional problems anticipating some features of Relativistic Quantum Gravity. Bearing in mind Wigner's famous analysis on measurabilitity in the relativistic case here a genuine uncertainty of the Newton potential is verified, leading to the breakdown of the Schrödinger equation when leaving microscopic regions.Abstract We list arguments for creating a unified theory of Newtonian Gravity and Quantum Mechanics. This nonrelativistic level has been historically bypassed, however even here one is confronted with conceptional problems anticipating some features of Relativistic Quantum Gravity. Bearing in mind Wigner's famous analysis on measurabilitity in the relativistic case here a genuine uncertainty of the Newton potential is verified, leading to the breakdown of the Schrödinger equation when leaving microscopic regions.

Annalen der PhysikJan 1, 198746 citations

Relativistic models of nonlinear quantum mechanics

T. W. B. Kibble

Communications in Mathematical PhysicsDec 1, 1978139 citations

Post-Newtonian effects of gravity on quantum interferometry

Shigeru Wajima, Masumi Kasai, Toshifumi Futamase

The effects of general relativistic gravity on quantum mechanics are thoroughly investigated. The Schr\"odinger equation is derived for a nonrelativistic spinless particle and for a spin- $1/2$ particle, with the general relativistic corrections of Earth's gravity up to the first post-Newtonian order, ${O(1/c}^{2})$ . The phase differences due to the post-Newtonian corrections in quantum interferometer experiments are also calculated.The effects of general relativistic gravity on quantum mechanics are thoroughly investigated. The Schr\"odinger equation is derived for a nonrelativistic spinless particle and for a spin-$1/2$ particle, with the general relativistic corrections of Earth's gravity up to the first post-Newtonian order, ${O(1/c}^{2})$. The phase differences due to the post-Newtonian corrections in quantum interferometer experiments are also calculated.

Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fieldsFeb 15, 199732 citations

Generalized Quantum Mechanics and Nonlinear Gauge Transformations

P. Nattermann

Springer eBooksJan 1, 19976 citations

The effects of general relativistic gravity on quantum mechanics are thoroughly investigated. The Schr\"odinger equation is derived for a nonrelativistic spinless particle and for a spin-

1/2

particle, with the general relativistic corrections of Earth's gravity up to the first post-Newtonian order,

{O(1/c}^{2})

. The phase differences due to the post-Newtonian corrections in quantum interferometer experiments are also calculated.