arXiv subjects

Folkert Kuipers

Publications and source records attributed to Folkert Kuipers.

At least 19 recordsLinked to original sources

arXiv2025

Quantum Theory, Gravity and Higher Order Geometry

The fact that quantum theory is non-differentiable, while general relativity is built on the assumption of differentiability sources an incompatibility between quantum theory and gravity. Higher order geometry addresses this issue directly by extending differential geometry, such that it can be applied to theories that are non-differentiable, but have a certain degree of H\"older regularity. As this includes the path integral formulation of quantum theory, it provides a natural mathematical framework for describing the interplay between gravity and quantum theory. In this article, we review the motivation for and the basic features of this framework and point towards future developments.

gr-qc↗

arXiv2024

Quantum Gravitational Hair in Gravastars and Observational Tests

Using the effective field theory of quantum gravity at second order in curvature, we calculate quantum corrections to the metric of gravastars and the closely related dark energy stars. We find that the quantum corrections in the exterior region depend on the equation of state of the gravastar, thus providing an example of quantum gravitational hair. We continue by calculating the induced quantum corrections to the photon sphere and the bending of light rays in the weak field regime. These corrections, albeit Planck scale suppressed, allow in principle to distinguish these objects from black holes observationally.

gr-qc↗

arXiv2024

Quantum Theory, Gravity and Second Order Geometry

We argue that a consistent coupling of a quantum theory to gravity requires an extension of ordinary `first order' Riemannian geometry to second order Riemannian geometry, which incorporates both a line element and an area element. This extension results in a misalignment between the dimension of the manifold and the dimension of the tangent spaces. In particular, we find that for a 4-dimensional spacetime, tangent spaces become 18-dimensional. We then discuss the construction of physical theories within this framework, which involves the introduction of terms that are quadratic in derivatives in the action. On a flat spacetime, the quadratic sector is perpendicular to the first order sector and only affects the normalization of the path integral, whereas in a curved spacetime the quadratic sector couples to the first order sector. Moreover, we show that, despite the introduction of higher order derivatives, the Ostragradski instability can be avoided, due to an order mixing of the two sectors. Finally, we comment on extensions to higher order geometry and on relations with non-commutative and generalized geometry.

hep-th↗

arXiv2024

A Stochastic Origin of Spacetime Non-Commutativity

We propose a stochastic interpretation of spacetime non-commutativity starting from the path integral formulation of quantum mechanical commutation relations. We discuss how the (non-)commutativity of spacetime is inherently related to the continuity or discontinuity of paths in the path integral formulation. Utilizing Wiener processes, we demonstrate that continuous paths lead to commutative spacetime, whereas discontinuous paths correspond to non-commutative spacetime structures. As an example we introduce discontinuous paths from which the $\kappa$-Minkowski spacetime commutators can be obtained. Moreover we focus on modifications of the Leibniz rule for differentials acting on discontinuous trajectories. We show how these can be related to the deformed action of translation generators focusing, as a working example, on the $\kappa$-Poincar\'e algebra. Our findings suggest that spacetime non-commutativity can be understood as a result of fundamental discreteness in temporal and/or spatial evolution.

hep-th↗

arXiv2024

Matching the Vilkovisky-DeWitt Effective Action of Quantum Gravity to String Theory

In this work, we discuss the matching of the Vilkovisky-DeWitt effective action of quantum gravity to an example of an ultra-violet complete theory of quantum gravity. We show how this matching enables a calculation of the local Wilson coefficients of the effective action. We provide several examples in string theory. Moreover, we discuss the matching conditions within the context of the swampland program.

hep-th↗

arXiv2023

Quantum Mechanics from Stochastic Processes

We construct an explicit one-to-one correspondence between non-relativistic stochastic processes and solutions of the Schrodinger equation and between relativistic stochastic processes and solutions of the Klein-Gordon equation. The existence of this equivalence suggests that the Lorentzian path integral can be defined as an Ito integral, similar to the definition of the Euclidean path integral in terms of the Wiener integral. Moreover, the result implies a stochastic interpretation of quantum theories.

quant-ph↗

arXiv2023

Stochastic Mechanics and the Unification of Quantum Mechanics with Brownian Motion

We unify Brownian motion and quantum mechanics in a single mathematical framework. In particular, we show that non-relativistic quantum mechanics of a single spinless particle on a flat space can be described by a Wiener process that is rotated in the complex plane. We then extend this theory to relativistic stochastic theories on manifolds using the framework of second order geometry. As a byproduct, our results suggest that a consistent path integral based formulation of a quantum theory on a Lorentzian (Riemannian) manifold requires an Ito deformation of the Poincare (Galilean) symmetry, arising due to the coupling of the quadratic variation to the affine connection.

quant-ph↗

arXiv2023

Quantum Hair During Gravitational Collapse

We consider quantum gravitational corrections to the Oppenheimer-Snyder metric describing time-dependent dust ball collapse. The interior metric also describes Friedmann-Lemaitre-Robertson-Walker cosmology and our results are interpreted in that context. The exterior corrections are an example of quantum hair, and are shown to persist throughout the collapse. Our results show the quantum hair survives throughout the horizon formation and that the internal state of the resulting black hole is accessible to outside observers.

hep-th↗

arXiv2022

Quantum Hair from Gravity

We explore the relationship between the quantum state of a compact matter source and of its asymptotic graviton field. For a matter source in an energy eigenstate, the graviton state is determined at leading order by the energy eigenvalue. Insofar as there are no accidental energy degeneracies there is a one to one map between graviton states on the boundary of spacetime and the matter source states. A typical semiclassical matter source results in an entangled asymptotic graviton state. We exhibit a purely quantum gravitational effect which causes the subleading asymptotic behavior of the graviton state to depend on the internal structure of the source. These observations establish the existence of ubiquitous quantum hair due to gravitational effects.

hep-th↗

arXiv2022

Spacetime Stochasticity and Second Order Geometry

We discuss the Schwartz-Meyer second order geometry framework and its relevance to theories of quantum gravity that incorporate a notion of spacetime stochasticity or quantum foam. We illustrate the framework in the context of Nelson's stochastic quantization.

gr-qc↗

arXiv2022

Analytic Continuation of Stochastic Mechanics

We study a (relativistic) Wiener process on a complexified (pseudo-)Riemannian manifold. Using Nelson's stochastic quantization procedure, we derive three equivalent descriptions for this problem. If the process has a purely real quadratic variation, we obtain the one-sided Wiener process that is encountered in the theory of Brownian motion. In this case, the result coincides with the Feyman-Kac formula. On the other hand, for a purely imaginary quadratic variation, we obtain the two-sided Wiener process that is encountered in stochastic mechanics, which provides a stochastic description of a quantum particle on a curved spacetime.

math-ph↗

arXiv2022

Black Holes in Quantum Gravity

We review some recent results obtained for black holes using effective field theory methods applied to quantum gravity, in particular the unique effective action. Black holes are complex thermodynamical objects that not only have a temperature but also have a pressure. Furthermore, they have quantum hair which provides a solution to the black hole information paradox.

hep-th↗

arXiv2021

Stochastic Quantization of Relativistic Theories

It was shown recently that stochastic quantization can be made into a well defined quantization scheme on (pseudo-)Riemannian manifolds using second order differential geometry, which is an extension of the commonly used first order differential geometry. In this letter, we show that restrictions to relativistic theories can be obtained from this theory by imposing a stochastic energy-momentum relation. In the process, we derive non-perturbative quantum corrections to the line element as measured by scalar particles. Furthermore, we extend the framework of stochastic quantization to massless scalar particles.

gr-qc↗

arXiv2021

Quantum Gravitational Corrections to the Entropy of a Schwarzschild Black Hole

We calculate quantum gravitational corrections to the entropy of black holes using the Wald entropy formula within an effective field theory approach to quantum gravity. The corrections to the entropy are calculated to second order in curvature and we calculate a subset of those at third order. We show that, at third order in curvature, interesting issues appear that had not been considered previously in the literature. The fact that the Schwarzschild metric receives corrections at this order in the curvature expansion has important implications for the entropy calculation. Indeed, the horizon radius and the temperature receive corrections. These corrections need to be carefully considered when calculating the Wald entropy.

hep-th↗

arXiv2021

Implications of Quantum Gravity for Dark Matter

In this essay we show that quantum gravity and the spin-statistics theorem have very interesting consequences for dark matter candidates. Quantum gravity can lead to fifth force type interactions that lead to a lower bound on the masses of bosonic candidates. In the case of fermions, the spin-statistics theorem leads to a lower bound on fermion masses. For both bosonic and fermionic dark matter candidates, quantum gravity leads to a decay of dark matter particles. A comparison of their lifetime with the age of the universe leads to an upper bound on their masses. For singlet scalar dark matter fields, we find $10^{-3}{\rm eV} \lesssim m\lesssim 10^{7}{\rm eV}$.

hep-ph↗

arXiv2021

Stochastic Quantization on Lorentzian Manifolds

We embed Nelson's stochastic quantization in the Schwartz-Meyer second order geometry framework. The result is a non-perturbative theory of quantum mechanics on (pseudo)-Riemannian manifolds. Within this approach, we derive stochastic differential equations for massive spin-0 test particles charged under scalar potentials, vector potentials and gravity. Furthermore, we derive the associated Schrödinger equation. The resulting equations show that massive scalar particles must be conformally coupled to gravity in a theory of quantum gravity. We conclude with a discussion of some prospects of the stochastic framework.

hep-th↗

arXiv2021

Theoretical bounds on dark matter masses

In this letter, we show that quantum gravity leads to lower and upper bounds on the masses of dark matter candidates. These bounds depend on the spins of the dark matter candidates and the nature of interactions in the dark matter sector. For example, for singlet scalar dark matter, we find a mass range $10^{-3}{\rm eV} \lesssim m_ϕ\lesssim 10^{7}{\rm eV}$. The lower bound comes from limits on fifth force type interactions and the upper bound from the lifetime of the dark matter candidate.

hep-ph↗

arXiv2020

Bounds on Very Weakly Interacting Ultra Light Scalar and Pseudoscalar Dark Matter from Quantum Gravity

In this paper we consider very weakly interacting and ultra light scalar and pseudoscalar dark matter candidates. We show that quantum gravity has important implications for such models and that the masses of the singlet scalar and pseudoscalar fields must be heavier than $3\times 10^{-3}$ eV. However, if they are gauged, their masses could be much lighter and as light as $10^{-22}\, {\rm eV}$. The existence of new gauge forces in the dark matter sector can thus be probed by atomic clocks or quantum sensors experiments.

hep-ph↗