This thesis investigates the role of gravitational waves in quantum systems, motivated by advances in our understanding of the quantum–gravity interface and efforts to identify experimental signatures of quantum gravity. It focuses on gravitational decoherence and the interplay between internal energy and centre-of-mass dynamics in composite quantum systems, complemented by a study of internal-energy effects in gravitationally mediated entanglement. First, we develop relativistic Hamiltonian formulations showing that changes in a composite system’s internal energy increase its gravitational mass rather than alter its momentum. This removes earlier ad hoc arguments for eliminating “anomalous friction forces”. We show that gravitational waves act as a dynamical background, inducing curvature-dependent forces that modify total momentum. Second, we revisit a thought experiment in which tensions between causality and complementarity arise. We identify a scenario in which these tensions follow from energy–mass equivalence, making the effect specific to gravitational interactions. In a gravitationally mediated entanglement experiment using Newtonian gravity as mediator, we investigate whether decohering gravitational radiation can resolve the apparent conflict. Finally, we build upon a model of gravitational decoherence consistent with general relativity. This requires deriving a higher-derivative quantum Langevin equation and master equation. The resulting dynamics show that gravitational interactions induce decoherence in the canonical momentum basis of the quadrupole and generate acceleration- and jerk-dependent corrections absent in electrodynamics. Together, these results show that weak-field gravitational interactions leave distinct relativistic imprints on quantum systems, including effects unique to gravitational waves, providing potential signatures that distinguish gravity from other interactions.
One of the biggest unsolved problems in physics is the unification of quantum mechanics and general relativity. The lack of experimental guidance has made the issue extremely evasive, though various attempts have been made to relate the loss of matter wave coherence to quantum spacetime fluctuations. We present a new approach to the gravitational decoherence near the Planck scale, made possible by recently discovered conformal structure of canonical gravity. This leads to a gravitational analogue of the Brownian motion whose correlation length is given by the Planck length up to a scaling factor. With input from recent matter wave experiments, we show that the minimum value of this factor to be well within the expected range for quantum gravity theories. This suggests that the sensitivities of advanced matter wave interferometers may be approaching the fundamental level due to quantum spacetime fluctuations and that investigating Planck scale physics using matter wave interferometry may become a reality in the near future. Physics on the large scale is based on Einstein’s theory of general relativity (GR), which interprets gravity as the curvature of spacetime. Despite its tremendous success as an isolated
Gravitational decoherence and gravitational wave function collapse are presented as two related but conceptually distinct ideas. Gravitational decoherence measures the effect of gravitational perturbations on the evolution of quantum systems, in particular their progressive lack of coherence. Gravitational wave function collapse starts with the assumption that the Schr¨odinger equation is not entirely right, and must be supplemented with extra terms, which cause the (random) collapse of the wave function; the collapse is then linked to gravity. Some of the most popular models are reviewed, with an emphasis on their conceptual status, stage of development, and open questions.
Background:In quantum mechanics energy is an observable, whereas time is a parameter. Pauli's theorem and the problem of time in canonical quantum gravity reflect this asymmetry.Material and methods:We define the time operator
t^=x^/c and form, with the relativistic energy
E^R, Einstein's constant
κ and the time
t^0 in the rest system, operators of gravitational-field and curvature type. Commutation relations, wave equations and spectra are derived in the time and in the energy representation.Results:The commutator
[t^,E^R]=ciℏv^x is bounded with norm
ℏ and is not a multiple of the identity, so Pauli's theorem is not contradicted. The sum
ct^+κE^R is unitarily equivalent to the time operator and has a continuous spectrum with explicit eigenfunctions. A postulated field equation,
G^0+Λ^=κE^R, has the structure of Einstein's equation; the term
Λ^ is an operator with continuous spectrum, the Ricci scalar operator contains the energy, and for small velocities the equation becomes the Schr\"odinger equation of a particle in a homogeneous field.Conclusion:Based on the postulated field equation, a quantization of the gravitational-field and curvature terms is derived: they become operators with explicit commutation relations and spectra. The metric tensor of Einstein's field equation has not been quantized.\par
We examine the origin of the Newton–Schrödinger equations (NSEs) that play an important role in alternative quantum theories (AQT), macroscopic quantum mechanics and gravity-induced decoherence. We show that NSEs for individual particles do not follow from general relativity (GR) plus quantum field theory (QFT). Contrary to what is commonly assumed, the NSEs are not the weak-field (WF), non-relativistic (NR) limit of the semi-classical Einstein equation (SCE) (this nomenclature is preferred over the 'Moller–Rosenfeld equation') based on GR+QFT. The wave-function in the NSEs makes sense only as that for a mean field describing a system of N particles as , not that of a single or finite many particles. From GR+QFT the gravitational self-interaction leads to mass renormalization, not to a non-linear term in the evolution equations of some AQTs. The WF-NR limit of the gravitational interaction in GR+QFT involves no dynamics. To see the contrast, we give a derivation of the equation (i) governing the many-body wave function from GR+QFT and (ii) for the non-relativistic limit of quantum electrodynamics. They have the same structure, being linear, and very different from NSEs. Adding to this our earlier consideration that for gravitational decoherence the master equations based on GR+QFT lead to decoherence in the energy basis and not in the position basis, despite some AQTs desiring it for the 'collapse of the wave function', we conclude that the origins and consequences of NSEs are very different, and should be clearly demarcated from those of the SCE equation, the only legitimate representative of semiclassical gravity, based on GR+QFT.