Weekly Papers on Quantum Foundations (21)

Authors: Steven B. GiddingsSeth KorenGabriel Treviño

Two new observational windows have been opened to strong gravitational physics: gravitational waves, and very long baseline interferometry. This suggests observational searches for new phenomena in this regime, and in particular for those necessary to make black hole evolution consistent with quantum mechanics. We describe possible features of “compact quantum objects” that replace classical black holes in a consistent quantum theory, and approaches to observational tests for these using gravitational waves. This is an example of a more general problem of finding consistent descriptions of deviations from general relativity, which can be tested via gravitational wave detection. Simple models for compact modifications to classical black holes are described via an effective stress tensor, possibly with an effective equation of state. A general discussion is given of possible observational signatures, and of their dependence on properties of the colliding objects. The possibility that departures from classical behavior are restricted to the near-horizon regime raises the question of whether these will be obscured in gravitational wave signals, due to their mutual interaction in a binary coalescence being deep in the mutual gravitational well. Numerical simulation with such simple models will be useful to clarify the sensitivity of gravitational wave observation to such highly compact departures from classical black holes.

Authors: Peter Holland

We develop a trajectory construction of solutions to the massless wave equation in n+1 dimensions and hence show that the quantum state of a massive relativistic system in 3+1 dimensions may be represented by a stand-alone four-dimensional congruence comprising a continuum of 3-trajectories coupled to an internal scalar time coordinate. A real Klein-Gordon amplitude is the current density generated by the temporal gradient of the internal time. Complex amplitudes are generated by a two-phase flow. The Lorentz covariance of the trajectory model is established.

Authors: Andreas Aste

This paper addresses the question why quantum mechanics is formulated in a unitary Hilbert space, i.e. in a manifestly complex setting. Investigating the linear dynamics of real quantum theory in a finite-dimensional Euclidean Hilbert space hints at the emergence of a complex structure. A widespread misconception concerning the measurement process in quantum mechanics and the hermiticity of observables is briefly discussed.

Authors: Michael K.-H. Kiessling

This contribution inquires into Clausius’ proposal that “the entropy of the world tends to a maximum.'” The question is raised whether the entropy of `the world’ actually does have a maximum; and if the answer is “Yes!,” what such states of maximum entropy look like, and if the answer is “No!,” what this could entail for the fate of the universe. Following R. Penrose, `the world’ is modelled by a closed Friedman–Lemaitre type universe, in which a three-dimensional spherical `space’ is filled with `matter’ consisting of $N$ point particles, their large-scale distribution being influenced by their own gravity. As `entropy of matter’ the Boltzmann entropy for a (semi-)classical macrostate, and Boltzmann’s ergodic ensemble formulation of it for an isolated thermal equilibrium state, are studied. Since the notion of a Boltzmann entropy is not restricted to classical non-relativistic physics, the inquiry will take into account quantum theory as well as relativity theory; we also consider black hole entropy. Model universes having a maximum entropy state and those which don’t will be encountered. It is found that the answer to our maximum entropy question is not at all straightforward at the general-relativistic level. In particular, it is shown that the increase in Bekenstein–Hawking entropy of general-relativistic black holes does not always compensate for the Boltzmann entropy of a piece of matter swallowed by a black hole.

Hetzroni, Guy (2019) Gauge and Ghosts. The British Journal for the Philosophy of Science. ISSN 1464-3537
Rivat, Sébastien (2019) Renormalization Scrutinized. Studies in History and Philosophy of Modern Physics. ISSN 1355-2198
Rédei, Miklós (2019) On the tension between physics and mathematics. [Preprint]
Cambbell, Douglas Ian and Yang, Yi (2019) Does the Solar System Compute the Laws of Motion? [Preprint]

Authors: Steven B. Giddings

The impressive images from the Event Horizon Telescope sharpen the conflict between our observations of gravitational phenomena and the principles of quantum mechanics. Two related scenarios for reconciling quantum mechanics with the existence of black hole-like objects, with “minimal” departure from general relativity and local quantum field theory, have been explored; one of these could produce signatures visible to EHT observations. A specific target is temporal variability of images, with a characteristic time scale determined by the classical black hole radius. The absence of evidence for such variability in the initial observational span of seven days is not expected to strongly constrain such variability. Theoretical and observational next steps towards investigating such scenarios are outlined.

Authors: Florio M. CiagliaAlberto IbortGiuseppe Marmo

A new picture of Quantum Mechanics based on the theory of groupoids is presented. This picture provides the mathematical background for Schwinger’s algebra of selective measurements and helps to understand its scope and eventual applications. In this first paper, the kinematical background is described using elementary notions from category theory, in particular the notion of 2-groupoids as well as their representations. Some basic results are presented, and the relation with the standard Dirac-Schr\”odinger and Born-Jordan-Heisenberg pictures are succinctly discussed.

Authors: Samir D. Mathur

The vacuum must contain virtual fluctuations of black hole microstates for each mass $M$. We observe that the expected suppression for $M\gg m_p$ is counteracted by the large number $Exp[S_{bek}]$ of such states. From string theory we learn that these microstates are extended objects that are resistant to compression. We argue that recognizing this `virtual extended compression-resistant’ component of the gravitational vacuum is crucial for understanding gravitational physics. Remarkably, such virtual excitations have no significant effect for observable systems like stars, but they resolve two important problems: (a) gravitational collapse is halted outside the horizon radius, removing the information paradox; (b) spacetime acquires a `stiffness’ against the curving effects of vacuum energy; this ameliorates the cosmological constant problem posed by the existence of a planck scale $\Lambda$.

Authors: Klaus RenziehausenIngo Barth

Bohm developed the Bohmian mechanics (BM), in which the Schr\”odinger equation is transformed into two differential equations: A continuity equation and an equation of motion similar to the Newtonian equation of motion. This transformation can be executed both for single-particle systems and for many-particle systems. Later, Kuzmenkov and Maksimov used basic quantum mechanics for the derivation of many-particle quantum hydrodynamics (MPQHD) including one differential equation for the mass balance and two differential equations for the momentum balance, and we extended their analysis in a prework [K. Renziehausen, I. Barth, Prog. Theor. Exp. Phys. 2018, 013A05 (2018)] for the case that the particle ensemble consists of different particle sorts. The purpose of this paper is to show how the differential equations of MPQHD can be derived for such a particle ensemble with the differential equations of BM as a starting point. Moreover, our discussion clarifies that the differential equations of MPQHD are more suitable for an analysis of many-particle systems than the differential equations of BM because the differential equations of MPQHD depend on a single position vector only while the differential equations of BM depend on the complete set of all particle coordinates.

Authors: F. Laloë

We discuss a model where a spontaneous quantum collapse is induced by the gravitational interaction, treated classically. Its dynamics couples the standard wave function of a system with the Bohmian positions of its particles, which are considered as the only source of the gravitational attraction. The collapse is obtained by adding a small imaginary component to the gravitational coupling. It predicts extremely small perturbations of microscopic systems, but very fast collapse of QSMDS (quantum superpositions of macroscopically distinct quantum states) of a solid object, varying as the fifth power of its size. The model does not require adding any dimensional constant to those of standard physics.

Gao, Shan (2019) Are there many worlds? [Preprint]
Halvorson, Hans (2019) There is no invariant, four-dimensional stuff. [Preprint]
Esfeld, Michael (2019) From the measurement problem to the primitive ontology programme. [Preprint]

Author(s): Lev Vaidman

Counterfactual communication, i.e., a communication without particles traveling in the transmission channel, is a bizarre quantum effect. Starting from interaction-free measurements many protocols achieving various tasks from counterfactual cryptography to counterfactual transfer of quantum states w…

[Phys. Rev. A 99, 052127] Published Wed May 29, 2019

Author(s): Andrew Lucas

There may be a universal bound on the dissipative timescale in a many-body quantum system for the decay of a small operator into a combination of large operators.

[Phys. Rev. Lett. 122, 216601] Published Wed May 29, 2019

Nature, Published online: 29 May 2019; doi:10.1038/d41586-019-01592-x

It is extremely difficult to observe the radiation that is thought to be emitted by black holes. The properties of this radiation have now been analysed using an analogue black hole comprising a system of ultracold atoms.

Author(s): Siddhant Das, Markus Nöth, and Detlef Dürr

It is well known that orthodox quantum mechanics does not make unambiguous predictions for the statistics in arrival time (or time-of-flight) experiments. Bohmian mechanics (or de Broglie–Bohm theory) offers a distinct conceptual advantage in this regard, owing to the well-defined concepts of point …

[Phys. Rev. A 99, 052124] Published Tue May 28, 2019

Author(s): Paul Boes, Jens Eisert, Rodrigo Gallego, Markus P. Müller, and Henrik Wilming

The von Neumann entropy is a key quantity in quantum information theory and, roughly speaking, quantifies the amount of quantum information contained in a state when many identical and independent (i.i.d.) copies of the state are available, in a regime that is often referred to as being asymptotic. …

[Phys. Rev. Lett. 122, 210402] Published Tue May 28, 2019

Authors: Valentina BaccettiSebastian MurkDaniel R. Terno

In case of spherical symmetry the assumptions of finite-time formation of a trapped region and regularity of its boundary — the apparent horizon — are sufficient to identify the limiting form of the metric and the energy-momentum tensor in its vicinity. By comparison with the known results for quasi-static evaporation of black holes we complete the identification of their parameters. Consistency of the Einstein equations determines two possible types of higher-order terms in the energy-momentum tensor, and by using its local conservation we provide a method of their identification, explicitly determining the leading order regular corrections. Contraction of a spherically symmetric thin dust shell is the simplest model of gravitational collapse. Nevertheless, the inclusion of a collapse-triggered radiation in different extensions of this model inevitably leads to apparent contradictions. Using our results we resolve these contradictions and demonstrate how gravitational collapse may be completed in finite time according to a distant observer.

Authors: Mariano BauerCesar Augusto AguillonGustavo Garcia

The perspective is advanced that the time parameter in quantum mechanics corresponds to the time coordinate in a Minkowski flat spacetime local approximation to the actual dynamical curved spacetime of General Relativity, rather than to an external Newtonian reference frame. There is no incompatibility, as generally assumed in the extensively discussed “problem of time” in Quantum Gravity.

Nature Physics, Published online: 27 May 2019; doi:10.1038/s41567-019-0533-5

Strong quantum correlations in an ultracoherent optomechanical system are used to demonstrate a displacement sensitivity that is below the standard quantum limit.

Nature Physics, Published online: 27 May 2019; doi:10.1038/s41567-019-0537-1

According to the Unruh effect, for an accelerating observer the vacuum is filled with thermal radiation. Experiments now simulate this effect, recreating the statistics of Unruh radiation in the matter-wave field of a Bose–Einstein condensate.

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