It has already been suggested that quantum theory needs to be reformulated or modified in order to explain the measurement process and the successive collapse of the wave- function. However, there are also models of another type which keep quantum theory intact and instead modify the classical gravity by introducing stochasticity to it. These models suggest that there is a fluctuation in the background gravitational field which eventually results in the decoherence of the wavefunction. These fluctuations limit the precision with which one can measure the properties of a spacetime geometry with a quantum probe. Two similar models along this line have been suggested by Karolyhazy (K-model) and Diósi(D-model). They are based upon apparently different spacetime bounds. The results obtained for the coherence length are also somewhat different. In this article, we show that, given certain conditions apply, the minimal spacetime bounds in these two models are equivalent. We also derive the two-point correlation for the fluctuation potential in K-model which turns out to be non-white, unlike in D-model, where the corresponding correlation is white noise in time. In our opinion, this is the origin of discrepancy in the predictions of the two models. We argue that the noise correlation cannot be determined uniquely from a given spacetime bound.
It has already been suggested that quantum theory needs to be reformulated or modified in order to explain the measurement process and the successive collapse of the wave- function. However, there are also models of another type which keep quantum theory intact and instead modify the classical gravity by introducing stochasticity to it. These models suggest that there is a fluctuation in the background gravitational field which eventually results in the decoherence of the wavefunction. These fluctuations limit the precision with which one can measure the properties of a spacetime geometry with a quantum probe. Two similar models along this line have been suggested by Karolyhazy (K-model) and Diósi(D-model). They are based upon apparently different spacetime bounds. The results obtained for the coherence length are also somewhat different. In this article, we show that, given certain conditions apply, the minimal spacetime bounds in these two models are equivalent. We also derive the two-point correlation for the fluctuation potential in K-model which turns out to be non-white, unlike in D-model, where the corresponding correlation is white noise in time. In our opinion, this is the origin of discrepancy in the predictions of the two models. We argue that the noise correlation cannot be determined uniquely from a given spacetime bound.
It has been suggested in the literature that spatial coherence of the wave function can be dynamically suppressed by fluctuations in the spacetime geometry. These fluctuations represent the minimal uncertainty that is present when one probes spacetime geometry with a quantum probe. Two similar models have been proposed, one by Diósi [D-model] and one by Karolyhazy and collaborators [K-model], based on apparently unrelated minimal spacetime bounds. The two models arrive at somewhat different expressions for the dependence of the localization coherence length on the mass and size of the quantum object. In the present article we compare and contrast the two models from three aspects: (i) comparison of the spacetime bounds, (ii) method of calculating decoherence time, (iii) comparison of noise correlation. We show that under certain conditions the minimal spacetime bounds in the two models can be derived one from the other. We argue that the methods of calculating the decoherence time are equivalent. We re-derive the two-point correlation for the fluctuation potential in the K-model, and confirm the earlier result of Diósi and Lukács that it is non-white noise, unlike in the D-model, where the corresponding correlation is white noise in time. This seems to be the origin of the different results in the two models. We derive the non-Markovian master equation for the K-model. We argue that the minimal spacetime bound cannot predict the noise correlation uniquely, and additional criteria are necessary to accurately determine the effects of gravitationally induced decoherence.
A consistent theory including gravitational effects in quantum mechanics has not been found. Although many different approaches have been proposed for theory of quantum gravity, several authors have suggested that gravity may be fundamentally classical. As there is no experimental evidence for a fundamentally quantum vs. fundamentally classical theory of gravity, it is hoped that investigating the consequences of semiclassical gravity, one may propose an experiment to distinguish between the quantum or classical nature of gravity. As opto- and electromechanical devices allow quantum limited measurement and control over massive, mechanical degrees of freedom, they are ideal systems to test violations of standard quantum mechanics arising from gravitational effects. After a brief introduction to the background theory and literature review, we begin by introducing a semiclassical model of gravity based on quantum measurement and control. We show under which conditions the theory behaves like a collapse model, and how a Newtonian potential is recovered in the multi particle case.We then go on to analyse our semiclassical model in two scenarios: firstly in a cosmological setting, and secondly by considering quantum clocks on the surface of the earth. In the cosmological description, we show that a violation of energy conservation, resulting from our model, can be reinterpreted as a dark energy fluid in the spacetime, suggesting that perhaps local violations of conservations of energy may be resolved in a cosmological framework. Secondly, we derive a minimum, gravitational dephasing rate for quantum clocks under the semiclassical model, which unsurprisingly, is is well below the resolution of current state of the art clocks. The next chapters diverge from analysing the gravitational model, and instead focus on novel methods of manipulating and measuring micromechanical devices, that may be used to experimentally probe the results of the semi-classical theory. Firstly we show that a sequence of coherently controlled pulses in an optomechanical system can be used to directly probe the momentum of an oscillator - opening up the possibility for direct detection of momentum diffusion, which is a consequence of the semiclassical gravity model. Secondly, we introduce an electro-mechanical device, and sequence of control operations, that may be understood as an interferometer for the wave function of a mechanical oscillator coupled to a qubit. We show how the resulting interference pattern can distinguish between unitary evolution, thermalisation/decoherence, and a purely classical description of the mechanical oscillator. We also show how the qubit-oscillator interaction can be used generate arbitrary wave functions of the mechanical oscillator, using only classical qubit driving.
Abstract We report new experimental constraints on the generalized version of the gravity-induced decoherence model originally proposed by Károlyházy. Using data collected by the VIP Collaboration at the INFN Gran Sasso National Laboratory with a high-purity germanium detector, we derive an improved lower bound on the spatial correlation length R K characterizing metric fluctuations in the model. We obtain a bound R K > 4.64 m (95% C.L.), which exceeds by more than an order of magnitude the previous experimental limit. When combined with the theoretical upper bound R K < 1.98 m derived from macroscopic localization requirements, our result excludes the generalized Károlyházy model. The same conclusion applies to an associated non-Markovian formulation of the continuous spontaneous localization model. Our findings significantly tighten experimental constraints on gravity-related decoherence scenarios and demonstrate the sensitivity of underground low-background experiments to foundational modifications of quantum mechanics.
We report new experimental constraints on the generalized version of the gravity-induced decoherence model originally proposed by Károlyházy. Using data collected by the VIP Collaboration at the INFN Gran Sasso National Laboratory with a high-purity germanium detector, we derive an improved lower bound on the spatial correlation length RK characterizing metric fluctuations in the model. We obtain a bound RK>4.64 m (95\% C.L.), which exceeds by more than an order of magnitude the previous experimental limit. When combined with the theoretical upper bound RK<1.98 m derived from macroscopic localization requirements, our result excludes the generalized Károlyházy model. The same conclusion applies to an associated non-Markovian formulation of the Continuous Spontaneous Localization (CSL) model. Our findings significantly tighten experimental constraints on gravity-related decoherence scenarios and demonstrate the sensitivity of underground low-background experiments to foundational modifications of quantum mechanics.
Several phenomenological approaches to quantum gravity predict the existence of a minimal measurable length and/or a maximum measurable momentum near the Planck scale. When embedded into the framework of quantum mechanics, such constraints induce a modification of the canonical commutation relations and thus a generalization of the Heisenberg uncertainty relations, commonly referred to as generalized uncertainty principle (GUP). Different models of quantum gravity imply different forms of the GUP. For instance, in the framework of string theory the GUP is quadratic in the momentum operator, while in the context of doubly special relativity it includes an additional linear dependence. Among the possible physical consequences, it was recently shown that the quadratic GUP induces a universal decoherence mechanism, provided one assumes a foamy structure of quantum spacetime close to the Planck length. Along this line, in the present work we investigate the gravitational decoherence associated to the linear-quadratic GUP and we compare it with the one associated to the quadratic GUP. We find that, despite their similarities, the two generalizations of the Heisenberg uncertainty principle yield decoherence times that are completely uncorrelated and significantly distinct. Motivated by this result, we introduce a theoretical and experimental scheme based on cavity optomechanics to measure the different time evolution of nonlocal quantum correlations corresponding to the two aforementioned decoherence mechanisms. We find that the deviation between the two predictions occurs on time scales that are macroscopic and thus potentially amenable to experimental verification. This scenario provides a possible setting to discriminate between different forms of the GUP and therefore different models of quantum gravity.
The possibility that the collapse of the wave function in quantum mechanics is real and ultimately connected to (classical) gravity has been debated for decades with main contributions by Diósi and Penrose (DP). In particular, Diósi proposed a noise-based dynamical reduction model, which captures the same order of magnitudes for the collapse time suggested by Penrose based on heuristic arguments. This is known in the literature as the DP model (Diósi–Penrose). A peculiarity of the DP model is the prediction of spontaneous heating of matter, which can be tested without the need for massive quantum superpositions. Notably, a very similar effect is predicted by recent theoretical approaches to gravity as a classical-only information channel. Here, we reconsider the current constraints on the DP model from spontaneous heating by analyzing experimental situations not properly considered before. We argue that the parameter-free version of the DP model is close to be ruled out by standard heat leak measurements at ultralow temperatures with a conclusive exclusion likely within reach with existing technology. This result would strengthen a recent claim of exclusion inferred by spontaneous x-ray emission experiments, which relies on the somewhat stronger assumption that the DP noise field is white up to x-ray frequencies.