Weekly Papers on Quantum Foundations (3)

Authors: Tejinder P. Singh

By invoking an asymmetric metric tensor, and borrowing ideas from non-commutative geometry, string theory, and trace dynamics, we propose an action function for quantum gravity. The action is proportional to the four dimensional non-commutative curvature scalar (which is torsion dependent) that is sourced by the Nambu-Goto world-sheet action for a string, plus the Kalb-Ramond string action. This `quantum gravity’ is actually a non-commutative {\it classical} matrix dynamics, and the only two fundamental constants in the theory are the square of Planck length and the speed of light. By treating the entity described by this action as a microstate, one constructs the statistical thermodynamics of a large number of such microstates, in the spirit of trace dynamics. Quantum field theory (and $\hbar$) and quantum general relativity (and $G$) emerge from the underlying matrix dynamics in the thermodynamic limit. The statistical fluctuations that are inevitably present about equilibrium, are the source for spontaneous localisation, which drives macroscopic quantum gravitational systems to the classical general relativistic limit. While the mathematical formalism governing these ideas remains to be developed, we hope here to highlight the deep connection between quantum foundations, and the sought for quantum theory of gravity. In the sense described in this article, ongoing experimental tests of spontaneous collapse theories are in fact also tests of string theory!

Authors: Alessio BelenchiaDionigi M.T. BenincasaFrancesco MarinFrancesco MarinoAntonello OrtolanMauro PaternostroStefano Liberati

Motivated by the development of on-going optomechanical experiments aimed at constraining non-local effects inspired by some quantum gravity scenarios, the Hamiltonian formulation of a non-local harmonic oscillator, and its coupling to a cavity field mode(s), is investigated. In particular, we consider the previously studied model of non-local oscillators obtained as the non-relativistic limit of a class of non-local Klein-Gordon operators, $f(\Box)$, with $f$ an analytical function. The results of previous works, in which the interaction was not included, are recovered and extended by way of standard perturbation theory. At the same time, the perturbed energy spectrum becomes available in this formulation, and we obtain the Langevin’s equations characterizing the interacting system.

Authors: Joy Christian (Oxford)

In the context of EPR-Bohm experiments and spin detections confined to spacelike hypersurfaces, a local, deterministic, and realistic model within a Friedmann-Robertson-Walker spacetime with constant spatial curvature (S^3) is presented which describes simultaneous measurements of the spins of two fermions emerging in a singlet state from the decay of a spinless boson. Exact agreement with the probabilistic predictions of quantum theory is achieved in the model without data rejection, remote contextuality, superdeterminism, or backward causation. A singularity-free Clifford-algebraic representation of S^3 with vanishing spatial curvature and non-vanishing torsion is then employed to transform the model in a more elegant form. Several event-by-event numerical simulations of the model are presented, which confirm our analytical results with the accuracy of 4 parts in 10^4 parts.

Authors: A T M Anishur Rahman

The superposition principle is one of the main tenets of quantum mechanics. In the past, it has been experimentally verified using electrons, photons, atoms, and molecules. However, a similar experimental demonstration using a nano or micro particle is still missing and many proposals have been put forward in the literature for creating such a state. In the existing proposals, the attainable spatial separations between the delocalized states are less than the size of the particles that have been used to create such states. In this article, using a $50~$nm levitated ferromagnetic particle and existing technologies, we show that a spatial separation of $1~$mm between the superposed states is readily achievable. This may lead to the possibility of testing quantum gravity, collapse models and gravity induced state reduction.

Authors: Arthur Jabs

Why microscopic objects exhibit wave properties (are delocalized), but macroscopic do not (are localized)? Traditional quantum mechanics attributes wave properties to all objects. When complemented with a deterministic collapse model (Quantum Stud.: Math. Found. 3, 279 (2016)) quantum mechanics can dissolve the discrepancy. Collapse in this model means contraction and occurs when the object gets in touch with other objects and satisfies a certain criterion. One single collapse usually does not suffice for localization. But the object rapidly gets in touch with other objects in a short time, leading to rapid localization. Decoherence is not involved.

Authors: Lev Vaidman

Counterfactual communication, i.e., communication without particle travelling in the transmission channel, is a bizarre quantum effect. Starting from interaction-free measurements many protocols achieving various tasks from counterfactual cryptogrphy to counterfactual transfer of quantum states were proposed and implemented in experiments. However, the meaning of conterfactuality in various protocols remained a controversial topic. A simple error-free counterfactual protocol is proposed. This protocol and its modification are used as a test bed for analysis of meaning of counterfactuality to clarify the counterfactuality status of various counterfactual proposals.

Authors: Antoine TilloyThomas M. Stace

Collapse models, like the Continuous Spontaneous Localization (CSL) model, aim at solving the measurement problem of quantum mechanics through a stochastic non-linear modification of the Schr\”odinger equation. Such modifications have sometimes been conjectured to be caused by gravity, the most famous example being the Diosi-Penrose (DP) model. In general, collapse models posit an intrinsic (possibly gravitational) noise, which endogenously collapses superpositions of sufficiently macroscopic systems (in a particular basis), while preserving the predictions of quantum mechanics at small scales. One notable consequence of these models is spontaneous heating of massive objects. Neutron stars, which represent a stable state of matter that balances gravitational attraction with the Pauli exclusion principle, are extremely dense, macroscopic quantum-limited objects. As such, they offer a unique system on which to test the predictions of collapse models. Here, we calculate an estimate of the equilibrium temperature of a neutron star radiating heat generated from spontaneous collapse models. We find that the CSL model would result in equilibrium temperatures much higher than those observed in astrophysical neutron stars, ruling out all plausible CSL model parameter values. For the DP model, our calculation yields a bound on the model parameter.

Authors: Berthold-Georg EnglertKelvin HoriaJibo DaiYink Loong LenHui Khoon Ng

We stand by our findings in Phys. Rev A. 96, 022126 (2017). In addition to refuting the invalid objections raised by Peleg and Vaidman, we report a retrocausation problem inherent in Vaidman’s definition of the past of a quantum particle.

Author(s): Yakir Aharonov and Lev Vaidman

The possibility to communicate between spatially separated regions, without even a single photon passing between the two parties, is an amazing quantum phenomenon. The possibility of transmitting one value of a bit in such a way, the interaction-free measurement, has been known for quarter of a cent…

[Phys. Rev. A 99, 010103(R)] Published Fri Jan 18, 2019

Ambitious new theories dreamed up to explain reality have led us nowhere. Meet the hardcore physicists trying to think their way out of this black hole
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Albert, David Z. (2019) How to Teach Quantum Mechanics. [Preprint]

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