# Weekly Papers on Quantum Foundations (45)

This is a list of this week’s papers on quantum foundations published in the various journals or uploaded to the preprint servers such as arxiv.org and PhilSci Archive.

The large-scale structure of vacuum. (arXiv:1405.3900v2 [gr-qc] UPDATED)

on 2014-11-07 4:50am GMT

The vacuum state in quantum field theory is known to exhibit an important number of fundamental physical features. In this work we explore the possibility that this state could also present a non-trivial space-time structure on large scales. In particular, we will show that by imposing the renormalized vacuum energy-momentum tensor to be conserved and compatible with cosmological observations, the vacuum energy of sufficiently heavy fields behaves at late times as non-relativistic matter rather than as a cosmological constant. In this limit, the vacuum state supports perturbations whose speed of sound is negligible and accordingly allows the growth of structures in the vacuum energy itself. This large-scale structure of vacuum could seed the formation of galaxies and clusters very much in the same way as cold dark matter does.

Time-Dependent Schrodinger Equation for Black Hole Evaporation: no Information Loss. (arXiv:1304.1899v5 [gr-qc] UPDATED)

on 2014-11-07 4:50am GMT

Authors: Christian Corda

In 1976 S. Hawking claimed that “Because part of the information about the state of the system is lost down the hole, the final situation is represented by a density matrix rather than a pure quantum state” (Verbatim from ref. 2). This was the starting point of the popular “black hole (BH) information paradox”. In a series of papers, together with collaborators, we naturally interpreted BH quasi-normal modes (QNMs) in terms of quantum levels discussing a model of excited BH somewhat similar to the historical semi-classical Bohr model of the structure of a hydrogen atom. Here we explicitly write down, for the same model, a time dependent Schr\”odinger equation for the system composed by Hawking radiation and BH QNMs. The physical state and the correspondent wave function are written in terms of an unitary evolution matrix instead of a density matrix. Thus, the final state results to be a pure quantum state instead of a mixed one. Hence, Hawking’s claim is falsified because BHs result to be well defined quantum mechanical systems, having ordered, discrete quantum spectra, which respect ‘t Hooft’s assumption that Schr\”oedinger equations can be used universally for all dynamics in the universe. As a consequence, information comes out in BH evaporation in terms of pure states in an unitary time dependent evolution. In Section 4 of this paper we show that the present approach permits also to solve the entanglement problem connected with the information paradox.

A Grasp of Identity. (arXiv:1411.1631v1 [quant-ph])

on 2014-11-07 4:50am GMT

Authors: Pere SeglarEnric Pérez

We revisit the treatment of identical particles in quantum mechanics. Two kinds of solutions of Schr\”{o}dinger equation are found and analyzed. First, the known symmetrized and antisymmetrized eigenfunctions. We examine how the very concept of particle is blurred whithin this approach. Second, we propose another kind of solution with no symmetries that we identify with Maxwell-Boltzmann statistics. In it, particles do preserve their individuality, as they are provided with individual energy and momenta. However, these properties cannot be univocally ascribed; moreover, particles do not possess distinctive positions. Finally, we explore how these results affect the calculation of canonical partition function, and we show that extensivity arises as a consequence of identity.

Arbitrarily Small Amount of Measurement Independence Is Sufficient to Manifest Quantum Nonlocality

PRL: General Physics: Statistical and Quantum Mechanics, Quantum Information, etc.

on 2014-11-06 3:00pm GMT

Author(s): Gilles Pütz, Denis Rosset, Tomer Jack Barnea, Yeong-Cherng Liang, and Nicolas Gisin

The use of Bell’s theorem in any application or experiment relies on the assumption of free choice or, more precisely, measurement independence, meaning that the measurements can be chosen freely. Here, we prove that even in the simplest Bell test—one involving 2 parties each performing 2 binary-out…

[Phys. Rev. Lett. 113, 190402] Published Thu Nov 06, 2014

Geometry and the Quantum: Basics. (arXiv:1411.0977v1 [hep-th])

on 2014-11-05 3:52am GMT

Motivated by the construction of spectral manifolds in noncommutative geometry, we introduce a higher degree Heisenberg commutation relation involving the Dirac operator and the Feynman slash of scalar fields. This commutation relation appears in two versions, one sided and two sided. It implies the quantization of the volume. In the one-sided case it implies that the manifold decomposes into a disconnected sum of spheres which will represent quanta of geometry. The two sided version in dimension 4 predicts the two algebras M_2(H) and M_4(C) which are the algebraic constituents of the Standard Model of particle physics. This taken together with the non-commutative algebra of functions allows one to reconstruct, using the spectral action, the Lagrangian of gravity coupled with the Standard Model. We show that any connected Riemannian Spin 4-manifold with quantized volume >4 (in suitable units) appears as an irreducible representation of the two-sided commutation relations in dimension 4 and that these representations give a seductive model of the “particle picture” for a theory of quantum gravity in which both the Einstein geometric standpoint and the Standard Model emerge from Quantum Mechanics. Physical applications of this quantization scheme will follow in a separate publication.

Entanglement is not Enough. (arXiv:1411.0690v1 [hep-th])

on 2014-11-05 3:52am GMT

Authors: Leonard Susskind

This is the written version of a lecture given at KITP in Oct 2014 on Black Holes and quantum complexity. I’ve included (in boldface) various questions that came up during the lecture and discussions the following day, as well as the quantitative calculations that form the basis of the arguments.

Understanding the quantum Cheshire Cat experiment of Denkmayr et al. (arXiv:1410.1522v3 [quant-ph] UPDATED)

on 2014-11-05 3:52am GMT

The authors of a July 2014 paper in Nature Communications made the spectacular claim that their interferometer experiment instantiated the spatial separation of neutrons and their spins. This is akin to the Cheshire Cat being in one place while its grin is in another and they call it the quantum Cheshire Cat experiment. Herein we provide the pedagogic calculation and comparison of the intensities used and observed in their experiment. These simple quantum calculations of intensity, which are not provided in their paper, and the resulting comparison of theory to the experimental outcomes render the experiment easy to understand. The amplitude squared at any point in the device gives the neutrons per second (intensity) at that location. When the magnetic field Bz is introduced to the interferometer’s lower (upper) path it turns some of the |Sx + > (|Sx – >) amplitude there into |Sx – > (|Sx + >) amplitude, i.e., it creates (removes) some neutrons per second associated with spin |Sx – > at that location. We explain the so-called “weak values” in this experiment and show the authors were mistaken in their use and interpretation of weak values in this experiment resulting in their spectacular, but erroneous, claim. Thus, while the quantum mechanical theory is in excellent agreement with the experimental outcomes, there is absolutely no reason to conclude that neutrons and their spins are spatially separated in this experiment.

Einstein’s Boxes: Incompleteness of Quantum Mechanics Without a Separation Principle

Latest Results for Foundations of Physics

on 2014-11-05 12:00am GMT

Abstract

Einstein made several attempts to argue for the incompleteness of quantum mechanics (QM), not all of them using a separation principle. One unpublished example, the box parable, has received increased attention in the recent literature. Though the example is tailor-made for applying a separation principle and Einstein indeed applies one, he begins his discussion without it. An analysis of this first part of the parable naturally leads to an argument for incompleteness not involving a separation principle. I discuss the argument and its systematic import. Though it should be kept in mind that the argument is not the one Einstein intends, I show how it suggests itself and leads to a conflict between QM’s completeness and a physical principle more fundamental than the separation principle, i.e. a principle saying that QM should deliver probabilities for physical systems possessing properties at definite times.

Classical, quantum, and phenomenological aspects of dark energy models. (arXiv:1411.0620v1 [gr-qc])

on 2014-11-04 1:24pm GMT

Authors: Houri Ziaeepour

The origin of accelerating expansion of the Universe is one the biggest conundrum of fundamental physics. In this paper we review vacuum energy issues as the origin of accelerating expansion – generally called dark energy – and give an overview of alternatives, which a large number of them can be classified as interacting scalar field models. We review properties of these models both as classical field and as quantum condensates in the framework of non-equilibrium quantum field theory. Finally, we review phenomenology of models with the goal of discriminating between them.

Relativistic Quantum Noninvasive Measurements. (arXiv:1411.0337v1 [quant-ph])

on 2014-11-04 1:24pm GMT

Quantum weak, noninvasive measurements are defined in the framework of relativity. Invariance with respect to reference frame transformations of the results in different models is discussed. Surprisingly, the bare results of noninvasive measurements are invariant for certain class of models, but not the detection error. Consequently, any stationary quantum realism based on noninvasive measurements will break, at least spontaneously, relativistic invariance and correspondence principle at zero temperature.

The metaphysics of laws: dispositionalism vs. primitivism. (arXiv:1411.0605v1 [physics.hist-ph])

on 2014-11-04 1:24pm GMT

Authors: Mauro DoratoMichael Esfeld

The paper compares dispositionalism about laws of nature with primitivism. It argues that while the distinction between these two positions can be drawn in a clear-cut manner in classical mechanics, it is less clear in quantum mechanics, due to quantum non-locality. Nonetheless, the paper points out advantages for dispositionalism in comparison to primitivism also in the area of quantum mechanics, and of contemporary physics in general.

Quantum Uncertainty and Error-Disturbance Tradeoff. (arXiv:1411.0587v1 [quant-ph])

on 2014-11-04 1:24pm GMT

Authors: Yu-Xiang ZhangShengjun WuZeng-Bing Chen

The uncertainty principle is often interpreted by the tradeoff between the error of a measurement and the consequential disturbance to the followed ones, which originated long ago from Heisenberg himself but now falls into reexamination and even heated debate. Here we show that the tradeoff is switched on or off by the quantum uncertainties of two involved non-commuting observables: if one is more certain than the other, there is no tradeoff; otherwise, they do have tradeoff and the Jensen-Shannon divergence gives it a good characterization.

A simple explanation of the quantum limits of genuine $n$-body nonlocality. (arXiv:1411.0153v1 [quant-ph])

on 2014-11-04 1:24pm GMT

Quantum $n$-body correlations violate inequalities for nonlocal theories in which arbitrary correlations are allowed within any strict subset of bodies while only local correlations are allowed between the subsets. Violations of these inequalities have been recently observed up to $n=6$. An important question is why the universe is exactly as genuinely $n$-body nonlocal as predicted by quantum theory, but not more or less. Here we prove that, for any $n>2$, the exclusivity principle and two assumptions (namely, independence of remote experiments and existence of a joint probability distribution for certain measurements), give, for general probabilistic theories, the same genuinely $n$-body nonlocality found in quantum theory.

A Proposed Experimental Test of Quantum Theory using the Techniques of Atom Optics. (arXiv:1411.0464v1 [quant-ph])

on 2014-11-04 1:24pm GMT

Authors: Peter J. Riggs

It may be possible to empirically discriminate between the predictions of Orthodox Quantum Theory and the deBroglie-Bohm Theory of Quantum Mechanics. An experiment using the measurement methods of Atom Optics is suggested in which an atom trap having evanescent light mirrors in front of each of its walls is used to determine whether trapped atoms are in motion inside the trap. An absence of detected motion would be contrary to the prediction of Orthodox Quantum Theory and would support the deBroglie-Bohm Theory.

On Tracks in a Cloud Chamber

Latest Results for Foundations of Physics

on 2014-11-04 12:00am GMT

Abstract

It is an experimental fact that $$\alpha$$ -decays produce in a cloud chamber at most one track (sequence of liquid droplets) and that this track points in a random direction. This seems to contradict the description of decay in Quantum Mechanics: according to Gamow a spherical wave is produced and moves radially according to Schrödinger’s equation. It is as if the interaction with the supersaturated vapor turned the wave into a particle. The aim of this note is to place this effect in the context of Schrödinger’s Quantum Mechanics. We shall see that the properties of the initial wave function suggest the introduction of a semiclassical formalism in which the $$\alpha$$ -wave can be described as a collection of semiclassical (probability) wavelets; each of them interacts with an atom and forms an entangled state. The interaction can be regarded as a semiclassical inelastic scattering event. The measurement (of the position of the first droplet of the track) selects the wave function of one of the ions, with a probability given by Born’s rule. This ion interacts with the atoms nearby leading to the formation of a droplet. One can reasonably assume that also the wavelet entangled with the selected ion has probability one to remain as part of the description of the system. The measurement process is therefore represented by a (non local) unitary operator. The (semiclassical) wavelet remains sharply localized on a classical path $$\gamma _{class} .$$ It is still a probability wave: it determines the probability that another atom be ionized. This probability is essentially zero unless the atom lies on $$\gamma _{class}$$ . This gives the visible track.

The exclusivity principle singles out the quantum violation of the Bell inequality. (arXiv:1406.5656v2 [quant-ph] UPDATED)

on 2014-11-03 8:28am GMT

We show that, for general probabilistic theories admitting sharp measurements, the exclusivity principle together with two assumptions exactly singles out the Tsirelson bound of the Clauser-Horne-Shimony-Holt Bell inequality.

Pure Qubit Work Extraction Revisited. (arXiv:1406.3937v2 [quant-ph] UPDATED)

on 2014-11-03 8:28am GMT

Many work extraction or information erasure processes in the literature involve the raising and lowering of energy levels via external fields. But even if the actual system is treated quantum mechanically, the field is assumed to be classical and of infinite strength, hence not developing any correlations with the system or experiencing back-actions. We extend these considerations to a fully quantum mechanical treatment, by studying a spin-1/2 particle coupled to a finite-sized directional quantum reference frame, a spin-l system, which models an external field. With this concrete model together with a bosonic thermal bath, we analyse the back-action a finite-size field suffers during a quantum-mechanical work extraction process, the effect this has on the extractable work, and highlight a range of assumptions commonly made when considering such processes. The well-known semi-classical treatment of work extraction from a pure qubit predicts a maximum extractable work W = kT log 2 for a quasi-static process, which holds as a strict upper bound in the fully quantum mechanical case, and is only attained in the classical limit. We also address the problem of emergent local time-dependence in a joint system with globally fixed Hamiltonian.

Non-reflexive Logical Foundation for Quantum Mechanics

Latest Results for Foundations of Physics

on 2014-11-02 12:00am GMT

Abstract

On the one hand, non-reflexive logics are logics in which the principle of identity does not hold in general. On the other hand, quantum mechanics has difficulties regarding the interpretation of ‘particles’ and their identity, also known in the literature as ‘the problem of indistinguishable particles’. In this article, we will argue that non-reflexive logics can be a useful tool to account for such quantum indistinguishability. In particular, we will provide a particular non-reflexive logic that can help us to analyze and discuss this problem. From a more general physical perspective, we will also analyze the limits imposed by the orthodox quantum formalism to consider the existence of indistinguishable particles in the first place, and argue that non-reflexive logics can also help us to think beyond the limits of classical identity.
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