Weekly Papers on Quantum Foundations (17)

Authors: Pisin ChenDong-han Yeom

We investigate the entanglement entropy and the information flow of two-dimensional moving mirrors. Here we point out that various mirror trajectories can help to mimic different candidate resolutions to the information loss paradox following the semi-classical quantum field theory: (i) a suddenly stopping mirror corresponds to the assertion that all information is attached to the last burst, (ii) a slowly stopping mirror corresponds to the assertion that thermal Hawking radiation carries information, and (iii) a long propagating mirror corresponds to the remnant scenario. Based on such analogy, we find that the last burst of a black hole cannot contain enough information, while slowly emitting radiation can restore unitarity. For all cases, there is an apparent inconsistency between the picture based on quantum entanglements and that based on the semi-classical quantum field theory. Based on the quantum entanglement theory, a stopping mirror will generate a firewall-like violent emission which is in conflict with notions based on the semi-classical quantum field theory.

Authors: A. M. AloisiP. F. Nali

Around year 2000 the centenary of Planck’s thermal radiation formula awakened interest in the origins of quantum theory, traditionally traced back to the Planck’s conference on 14 December 1900 at the Berlin Academy of Sciences. A lot of more accurate historical reconstructions, conducted under the stimulus of that recurrence, placed the birth date of quantum theory in March 1905 when Einstein advanced his light quantum hypothesis. Both interpretations are yet controversial, but science historians agree on one point: the emergence of quantum theory from a presumed “crisis” of classical physics is a myth with scarce adherence to the historical truth. This article, written in Italian language, was originally presented in connection with the celebration of the World Year of Phyics 2005 with the aim of bringing these scholarly theses to a wider audience.

Tradizionalmente la nascita della teoria quantistica viene fatta risalire al 14 dicembre 1900, quando Planck present\`o all’Accademia delle Scienze di Berlino la dimostrazione della formula della radiazione termica. Numerose ricostruzioni storiche pi\`u accurate, effettuate nel periodo intorno al 2000 sotto lo stimolo dell’interesse per il centenario di quell’avvenimento, collocano invece la nascita della teoria quantistica nel marzo del 1905, quando Einstein avanz\`o l’ipotesi dei quanti di luce. Entrambe le interpretazioni sono tuttora controverse, ma gli storici della scienza concordano su un punto: l’emergere della teoria quantistica da una presunta “crisi” della fisica classica \`e un mito con scarsa aderenza alla verit\`a storica. Con questo articolo in italiano, presentato originariamente in occasione delle celebrazioni per il World Year of Phyics 2005, si \`e inteso portare a un pi\`u largo pubblico queste tesi gi\`a ben note agli specialisti.

Authors: John van de Wetering

There is a long history of representing a quantum state using a quasi-probability distribution: a distribution allowing negative values. In this paper we extend such representations to deal with quantum channels. The result is a convex, strongly monoidal, functorial embedding of the category of trace preserving completely positive maps into the category of quasi-stochastic matrices. This establishes quantum theory as a subcategory of quasi-stochastic processes. Such an embedding is induced by a choice of minimal informationally complete POVM’s. We show that any two such embeddings are naturally isomorphic. The embedding preserves the dagger structure of the categories if and only if the POVM’s are symmetric, giving a new use of SIC-POVM’s. We also study general convex embeddings of quantum theory and prove a dichotomy that such an embedding is either trivial or faithful. The results of this paper allow a clear explanation of the characteristic features of quantum mechanics coming from being epistemically restricted (no-cloning, teleportation) and having negative probabilities (Bell inequalities, computational speed-up).

Authors: Zhong Chao Wu

Using the synchronous coordinates, the creation of a Schwarzschild black hole immersed in a de Sitter spacetime can be viewed as a coherent creation of a collection of timelike geodesics. The previously supposed conical singularities do not exist at the horizons of the constrained instan- ton. Instead, the unavoidable irregularity is presented as a non-vanishing second fundamental form elsewhere at the quantum transition 3-surface. The same arguments can be applied to charged, topological or higher dimensional black hole cases.

Authors: Andrew E ChubykaloAugusto EspinozaB P Kosyakov

The interplay between the action-reaction principle and the energy-momentum conservation law is revealed by the examples of the Maxwell-Lorentz and Yang-Mills-Wong theories, and general relativity. These two statements are shown to be equivalent in the sense that both hold or fail together. Their mutual agreement is demonstrated most clearly in the self-interaction problem by taking account of the rearrangement of degrees of freedom appearing in the action of the Maxwell-Lorentz and Yang-Mills-Wong theories. The failure of energy-momentum conservation in general relativity is attributed to the fact that this theory allows solutions having nontrivial topologies. The total energy and momentum of a system with nontrivial topological content is found to be ambiguous, coordintization-dependent quantities. For example, the energy of a Schwarzschild black hole may take any positive value greater than, or equal to, the mass of the body whose collapse is responsible for arising this black hole. We draw the analogy to the paradoxial Banach-Tarski theorem; the measure becomes a poorly defined concept if initial three-dimensional bounded sets are rearranged in topologically nontrivial ways through the action of free non-Abelian isometry groups.

Authors: C. Wetterich

Graviton fluctuations induce strong non-perturbative infrared renormalization effects for the cosmological constant. In flat space the functional renormalization flow drives a positive cosmological constant to zero. We propose a simple computation of the graviton contribution to the flow of the effective potential for scalar fields. Within variable gravity we find that the potential increases asymptotically at most quadratically with the scalar field. With effective Planck mass proportional to the scalar field, the solutions of the derived cosmological equations lead to an asymptotically vanishing cosmological “constant” in the infinite future, providing for dynamical dark energy in the present cosmological epoch. Beyond a solution of the cosmological constant problem, our simplified computation also entails a sizeable positive graviton-induced anomalous dimension for the quartic Higgs coupling in the ultraviolet regime, as required for the successful prediction of the Higgs boson mass within the asymptotic safety scenario for quantum gravity.

Authors: Tamás Geszti

A minimally nonlinear von Neumann equation for a Stern-Gerlach or Bell-type measuring apparatus, containing coordinate and momentum in a skew-symmetric, split scalar product structure over the configuration space, is shown to display pumping of weights between setup-defined basis states, with a single winner randomly selected in accordance with Born’s rule, and the rest collapsing to zero, following Pearle’s “gambler’s ruin” scheme. Randomness emerges from deterministic irregular dynamics of the detectors, their microscopic states acting as a nonlocal set of hidden parameters, controlling individual outcomes. Statistical predictions defining quantum behavior are fully reproduced, which warrants that the scheme is non-signaling.

Authors: Pasquale BossoSaurya DasRobert B. Mann

The Generalized Uncertainty Principle (GUP) is a modification of Heisenberg’s Principle predicted by several theories of Quantum Gravity. It consists of a modified commutator between position and momentum. In this work we compute potentially observable effects that GUP implies for the harmonic oscillator, coherent and squeezed states in Quantum Mechanics. In particular, we rigorously analyze the GUP-perturbed harmonic oscillator Hamiltonian, defining new operators that act as ladder operators on the perturbed states. We use these operators to define the new coherent and squeezed states. We comment on potential applications.

Authors: Robert Street

The physical constructs underlying the properties of quantum mechanics are explored. Arguments are given that the particle wave function as well as photon and phonon quanta must derive from a more fundamental physical construct that has not yet been identified. An approach to identifying the construct is discussed and a specific construct is proposed and explained.

Authors: Roderich Tumulka

Bohmian mechanics, also known as pilot-wave theory or de Broglie-Bohm theory, is a formulation of quantum mechanics whose fundamental axioms are not about what observers will see if they perform an experiment but about what happens in reality. It is therefore called a “quantum theory without observers.” It follows from these axioms that in a universe governed by Bohmian mechanics, observers will see outcomes with exactly the probabilities specified by the usual rules of quantum mechanics for empirical predictions. Specifically, Bohmian mechanics asserts that electrons and other elementary particles have a definite position at every time and move according to an equation of motion that is one of the fundamental laws of the theory and involves a wave function that evolves according to the usual Schr\”odinger equation. Bohmian mechanics is named after David Bohm (1917-1992), who was, although not the first to consider this theory, the first to realize (in 1952) that it actually makes correct predictions.

Authors: Giorgio Papini

In the study of covariant wave equations, linear gravity manifests itself through the metric deviation $\gamma_{\mu\nu}$ and a two-point vector potential $K_{\lambda}$ itself constructed from $\gamma_{\mu\nu}$ and its derivatives. The simultaneous presence of the two gravitational potentials is non contradictory. Particles also assume the character of quasiparticles and $K_{\lambda}$ carries information about the matter with which it interacts. We consider the influence of $K_{\lambda}$ on the dispersion relations of the particles involved, the particles’ motion, quantum tunneling through a horizon, radiation, energy-momentum dissipation and flux quantization. % No {\it REVTEX} limit to number of lines.

Brown, Harvey R. (2017) Once and for all: the curious role of probability in the Past Hypothesis. [Preprint]
Redhead, Michael (2017) The Relativistic Einstein-Podolsky-Rosen Argument. [Preprint]
Crull, Elise (2017) Translation of: P. Ehrenfest (1925), ‘Energieschwankungen im Strahlungsfeld oder Kristallgitter bei Superposition quantisierter Eigenschwingungen’. [Preprint]
de Swart, Jaco and Bertone, Gianfranco and van Dongen, Jeroen (2017) How dark matter came to matter. Nature Astronomy, 1 (0059). ISSN 2397-3366


Quantum trajectory-based descriptions of interference between two coherent stationary waves in a double-slit experiment are presented, as given by the de Broglie–Bohm (dBB) and modified de Broglie–Bohm (MdBB) formulations of quantum mechanics. In the dBB trajectory representation, interference between two spreading wave packets can be shown also as resulting from motion of particles. But a trajectory explanation for interference between stationary states is so far not available in this scheme. We show that both the dBB and MdBB trajectories are capable of producing the interference pattern for stationary as well as wave packet states. However, the dBB representation is found to provide the ‘which-way’ information that helps to identify the hole through which the particle emanates. On the other hand, the MdBB representation does not provide any which-way information while giving a satisfactory explanation of interference phenomenon in tune with the de Broglie’s wave particle duality. By counting the trajectories reaching the screen, we have numerically evaluated the intensity distribution of the fringes and found very good agreement with the standard results.

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