Weekly Papers on Quantum Foundations (40)

Palacios, Patricia (2017) Phase Transitions: A Challenge for Reductionism? [Preprint]
Kastner, Ruth and Kauffman, Stuart and Epperson, Michael (2017) Taking Heisenberg's Potentia Seriously. [Preprint]
Ardourel, Vincent and Guay, Alexandre (2017) Why is the transference theory of causation insuffcient? The challenge of the Aharonov-Bohm effect. [Preprint]

Abstract

I examine the relationship between (d+1) -dimensional Poincaré metrics and d-dimensional conformal manifolds, from both mathematical and physical perspectives. The results have a bearing on several conceptual issues relating to asymptotic symmetries in general relativity and in gauge–gravity duality, as follows: (1: Ambient Construction)  I draw from the remarkable work by Fefferman and Graham (Elie Cartan et les Mathématiques d’aujourd’hui, Astérisque, 1985; The Ambient Metric. Annals of Mathematics Studies, Princeton University Press, Princeton, 2012) on conformal geometry, in order to prove two propositions and a theorem that characterise which classes of diffeomorphisms qualify as gravity-invisible. I define natural notions of gravity-invisibility (strong, weak, and simpliciter) that apply to the diffeomorphisms of Poincaré metrics in any dimension. (2: Dualities) I apply the notions of invisibility, developed in (1), to gauge–gravity dualities: which, roughly, relate Poincaré metrics in d+1 dimensions to QFTs in d dimensions. I contrast QFT-visible versus QFT-invisible diffeomorphisms: those gravity diffeomorphisms that can, respectively cannot, be seen from the QFT. The QFT-invisible diffeomorphisms are the ones which are relevant to the hole argument in Einstein spaces. The results on dualities are surprising, because the class of QFT-visible diffeomorphisms is larger than expected, and the class of QFT-invisible ones is smaller than expected, or usually believed, i.e. larger than the PBH diffeomorphisms in Imbimbo et al. (Class Quantum Gravity 17(5):1129, 2000, Eq. 2.6). I also give a general derivation of the asymptotic conformal Killing equation, which has not appeared in the literature before.

Authors: Alan A. Coley

We present a list of open questions in mathematical physics. After a historical introduction, a number of problems in a variety of different fields are discussed, with the intention of giving an overall impression of the current status of mathematical physics, particularly in the topical fields of classical general relativity, cosmology and the quantum realm. This list is motivated by the recent article proposing 42 fundamental questions (in physics) which must be answered on the road to full enlightenment. But paraphrasing a famous quote by the British football manager Bill Shankly, in response to the question of whether mathematics can answer the Ultimate Question of Life, the Universe, and Everything, mathematics is, of course, much more important than that.

Authors: Edward Witten

I discuss gauge and global symmetries in particle physics, condensed matter physics, and quantum gravity. In a modern understanding, global symmetries are approximate and gauge symmetries may be emergent. (Based on a lecture at the April, 2016 meeting of the American Physical Society in Salt Lake City, Utah.)

Authors: K. PiscicchiaA. BassiC. CurceanuR. Del GrandeS. DonadiB.C. HiesmayrA. Pichler

In this paper, new upper limits on the parameters of the Continuous Spontaneous Localization (CSL) collapse model are extracted. To this end, the X-ray emission data collected by the IGEX collaboration are analyzed and compared with the spectrum of the spontaneous photon emission process predicted by collapse models.

This study allows the obtainment of the most stringent limits within a relevant range of the CSL model parameters, with respect to any other method. The collapse rate $\lambda$ and the correlation length $r_C$ are mapped, thus allowing the exclusion of a broad range of the parameter space.

Authors: Mohammad Hossein ZareiAfshin Montakhab

The correspondence between classical spin models and quantum states has attracted much attention in recent years. However, it remains an open problem as to which specific spin model a given (well-known) quantum state maps to. In this Letter, we provide such an explicit correspondence for an important class of quantum states where a duality relation is proved between classical spin models and quantum Calderbank-Shor-Steane (CSS) states. In particular, we employ graph-theoretic methods to prove that the partition function of a classical spin model on a hypergraph $H$ is equal to the inner product of a product state with a quantum CSS state on a dual hypergraph $\tilde{H}$. We next use this dual correspondence to prove that the critical behavior of the classical system corresponds to a relative robustness of the corresponding CSS state to bit-flip (and phase-flip) noise, thus called critical robustness. We finally conjecture that such critical robustness is related to the topological order in quantum CSS states, thus providing a possible practical characterization of such states.

The best atomic clock will only be out of sync 3.5 times in every 10 quintillion ticks. It could help test general relativity and hunt for gravitational waves
Publication date: Available online 3 October 2017
Source:Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics
Author(s): Vladislav Terekhovich
Despite the importance of the variational principles of physics, there have been relatively few attempts to consider them for a realistic framework. In addition to the old teleological question, this paper continues the recent discussion regarding the modal involvement of the principle of least action and its relations with the Humean view of the laws of nature. The reality of possible paths in the principle of least action is examined from the perspectives of the contemporary metaphysics of modality and Leibniz's concept of essences or possibles striving for existence. I elaborate a modal interpretation of the principle of least action that replaces a classical representation of a system's motion along a single history in the actual modality by simultaneous motions along an infinite set of all possible histories in the possible modality. This model is based on an intuition that deep ontological connections exist between the possible paths in the principle of least action and possible quantum histories in the Feynman path integral. I interpret the action as a physical measure of the essence of every possible history. Therefore only one actual history has the highest degree of the essence and minimal action. To address the issue of necessity, I assume that the principle of least action has a general physical necessity and lies between the laws of motion with a limited physical necessity and certain laws with a metaphysical necessity.

Author(s): Clive Emary

Ambiguous measurements do not reveal complete information about the system under test. Their quantum-mechanical counterparts are semiweak (or in the limit, weak) measurements and here we discuss their role in tests of the Leggett-Garg inequalities. We show that, while ambiguous measurements allow on...
[Phys. Rev. A 96, 042102] Published Wed Oct 04, 2017

Abstract

An influential theory has it that metaphysical indeterminacy occurs just when reality can be made completely precise in multiple ways. That characterization is formulated by employing the modal apparatus of ersatz possible worlds. As quantum physics taught us, reality cannot be made completely precise. I meet the challenge by providing an alternative theory which preserves the use of ersatz worlds but rejects the precisificational view of metaphysical indeterminacy. The upshot of the proposed theory is that it is metaphysically indeterminate whether p just in case it is neither true nor false that p, and no terms in ‘p’ are semantically defective. In other words, metaphysical indeterminacy arises when the world cannot be adequately described by a complete set of sentences defined in a semantically nondefective language. Moreover, the present theory provides a reductive analysis of metaphysical indeterminacy, unlike its influential predecessor. Finally, I argue that any adequate logic of a language with an indeterminate subject matter is neither compositional nor bivalent.

Nature Physics 13, 926 (2017). doi:10.1038/nphys4291

Author: Federico Levi

Authors: Saurya DasMatthew P. G. RobbinsElias C. Vagenas

It is believed that classical behavior emerges in a quantum system due to decoherence. It has also been proposed that gravity can be a source of this decoherence. We examine this in detail by studying a number of quantum systems, including ultra-relativistic and non-relativistic particles, at low and high temperatures in an expanding Universe, and show that this proposal is valid for a large class of quantum systems.

Authors: Roberto Longo

Landauer principle provides a link between Shannon information entropy and Clausius thermodynamical entropy. We set up here a basic formula for the incremental free energy of a quantum channel, possibly relative to infinite systems, naturally arising by an Operator Algebraic point of view. By the Tomita-Takesaki modular theory, we can indeed describe a canonical evolution associated with a quantum channel state transfer. Such evolution is implemented both by a modular Hamiltonian and a physical Hamiltonian, the latter being determined by its functoriality properties. This allows us to make an intrinsic analysis, extending our QFT index formula, but without any a priori given dynamics; the associated incremental free energy is related to the logarithm of the Jones index and is thus quantised. This leads to a general lower bound for the incremental free energy of an irreversible quantum channel which is half of the Landauer bound, and to further bounds corresponding to the discrete series of the Jones index. In the finite dimensional context, or in the case of DHR charges in QFT, where the dimension is a positive integer, our lower bound agrees with Landauer bound.

Authors: J. AbajianS. Carlip

We investigate the behavior of small subsets of causal sets that approximate Minkowski space in three, four, and five dimensions, and show that their effective dimension decreases smoothly at small distances. The details of the short distance behavior depend on a choice of dimensional estimator, but for a reasonable version of the Myrheim-Meyer dimension, the minimum dimension is $d \approx 2$, reproducing results that have been seen in other approaches to quantum gravity.

Authors: A. I. Arbab

By expressing the Schr\"{o}dinger wave function in the form $\psi=Re^{iS/\hbar}$, where $R$ and $S$ are real functions, we have shown that the expectation value of $S$ is conserved. The amplitude of the wave ($R$) is found to satisfy the Schr\"{o}dinger equation while the phase ($S$) is related to the energy conservation. Besides the quantum potential that depends on $R$, \emph{viz.}, $V_Q=-\frac{\hbar^2}{2m}\frac{\nabla^2R}{R}$\,, we have obtained a spin potential $V_S=-\frac{S\nabla^2S}{m}$ that depends on $S$ which is attributed to the particle spin. The spin force is found to give rise to dissipative viscous force. The quantum potential may be attributed to the interaction between the two subfields $S$ and $R$ comprising the quantum particle. This results in splitting (creation/annihilation) of these subfields, each having a mass $mc^2$ with an internal frequency of $2mc^2/\hbar$, satisfying the original wave equation and endowing the particle its quantum nature. The mass of one subfield reflects the interaction with the other subfield. If in Bohmian ansatz $R$ satisfies the Klein-Gordon equation, then $S$ must satisfies the wave equation. Conversely, if $R$ satisfies the wave equation, then $S$ yields the Einstein relativistic energy momentum equation.

Authors: Alexey A. Kryukov

Quantum observables can be identified with vector fields on the sphere of normalized states. The resulting vector representation is used in the paper to undertake a simultaneous treatment of macroscopic and microscopic bodies in quantum mechanics. Components of the velocity and acceleration of state under Schr\"odinger evolution are given for a clear physical interpretation. Solutions to Schr\"odinger and Newton equations are shown to be related beyond the Ehrenfest results on the motion of averages. A formula relating the normal probability distribution and the Born rule is found.

Abstract

The growing block view of time holds that the past and present are real whilst the future is unreal; as future events become present and real, they are added on to the growing block of reality. Surprisingly, given the recent interest in this view, there is very little literature on its origins. This paper explores those origins, and advances two theses. First, I show that although C. D. Broads (1923) Scientific Thought provides the first defence of the growing block theory, the theory receives its first articulation in Samuel Alexanders (1920) Space, Time, and Deity. Further, Alexanders account of deity inclines towards the growing block view. Second, I argue that Broad shifted towards the growing block theory as a result of his newfound conviction that time has a direction. By way of tying these theses together, I argue that Broads views on the direction of time and possibly even his growing block theory are sourced in Alexander.

Authors: Marco Roncaglia

According to quantum mechanics, the informational content of isolated systems does not change in time. However, subadditivity of entropy seems to describe an excess of information when we look at single parts of a composite systems and their correlations. Moreover, the balance between the entropic contributions coming from the various parts is not conserved under unitary transformations. Reasoning on the basic concept of quantum mechanics, we find that in such a picture an important term has been overlooked: the intrinsic quantum information encoded in the coherence of pure states. To fill this gap we are led to define a quantity, that we call coherent entropy, which is necessary to account for the "missing" information and for re-establishing its conservation. Interestingly, the coherent entropy is found to be equal to the information conveyed in the future by quantum states. The perspective outlined in this paper may be of some inspiration in several fields, from foundations of quantum mechanics to black-hole physics.

Authors: Rainer Collier

This article examines the consequences of the existence of an upper particle momentum limit in quantum electrodynamics, where this momentum limit is the Planck momentum. The method used is Fourier analysis as developed already by Fermi in his fundamental work on the quantum theory of radiation. After determination of the appropriate Hamiltonian, a Schr\"odinger equation and the associated commutation rules of the field operators are given. At the upper momentum limit mentioned above, the divergent terms occurring in the Hamiltonian (the self-energies of the electrons and the zero-point energy of the electromagnetic field) adopt finite values, which will be stated and compared with each other.

Authors: Ekaterina MorevaMarco GramegnaGiorgio BridaLorenzo MacconeMarco Genovese

In this paper we provide an experimental illustration of Page and Wootters' quantum time mechanism that is able to describe two-time quantum correlation functions. This allows us to test a Leggett-Garg inequality, showing a violation from the "internal" observer point of view. The "external" observer sees a time-independent global state. Indeed, the scheme is implemented using a narrow-band single photon where the clock degree of freedom is encoded in the photon's position. Hence, the internal observer that measures the position can track the flow of time, while the external observer sees a delocalized photon that has no time evolution in the experiment time-scale.

Authors: David Navia

This work is about Bohmian mechanics, a non-relativistic quantum theory about the motion of particles and their trajectories, named after its inventor David Bohm (Bohm,1952). This mechanics resolves all paradoxes associated with the measurement problem in nonrelativistic quantum mechanics. It accounts for quantum randomness, absolute uncertainty, the meaning of the wave function of a system, collapse of the wave function, and familiar (macroscopic) reality. We review the purpose for which Bohmian trajectories were invented: to serve as the foundation of quantum mechanics, i.e., to explain quantum mechanics in terms of a theory that is free of paradoxes and allows an understanding that is as clear as that of classical mechanics. To achieve this we analyse an optical interferometry experiment devised and carried out 2005 by Shahriar Afshar (Afshar,2005). The radical claim of Afshar implies in his own words the 'observation of physical reality in the classical sense' for both 'which path (particle-like)' and 'interference (wave-like)' properties of photons in the same experimental setup through the violation of the Englert-Greenberger duality relation (Englert,1996) that according to Englert can be regarded as quantifying of the 'principle of complementarity'.

Authors: P. Fernandez de CordobaJ.M. Isidro

The holographic principle sets an upper bound on the total entropy content of the Universe. Within the limits of a Newtonian approximation, a quantum-mechanical model is presented to describe the cosmological fluid. Under the assumption that gravitational equipotential surfaces can be identified with isoentropic surfaces, this model allows for a simple computation of the gravitational entropy of the Universe. The results thus obtained no longer saturate the holographic bound, thus representing a considerable improvement on previous theoretical estimates.

Authors: Roman OrusRoger MartinJuan Uriagereka

Matrix syntax is a formal model of syntactic relations in language. The purpose of this paper is to explain its mathematical foundations, for an audience with some formal background. We make an axiomatic presentation, motivating each axiom on linguistic and practical grounds. The resulting mathematical structure resembles some aspects of quantum mechanics. Matrix syntax allows us to describe a number of language phenomena that are otherwise very difficult to explain, such as linguistic chains, and is arguably a more economical theory of language than most of the theories proposed in the context of the minimalist program in linguistics. In particular, sentences are naturally modeled as vectors in a Hilbert space with a tensor product structure, built from 2x2 matrices belonging to some specific group.

Authors: Catarina MoreiraEmmanuel HavenSandro SozzoAndreas Wichert

In this work, we analyse and model a real life financial loan application belonging to a sample bank in the Netherlands. The log is robust in terms of data, containing a total of 262 200 event logs, belonging to 13 087 different credit applications. The dataset is heterogeneous and consists of a mixture of computer generated automatic processes and manual human tasks. The goal is to work out a decision model, which represents the underlying tasks that make up the loan application service, and to assess potential areas of improvement of the institution's internal processes. To this end we study the impact of incomplete event logs for the extraction and analysis of business processes. It is quite common that event logs are incomplete with several amounts of missing information (for instance, workers forget to register their tasks). Absence of data is translated into a drastic decrease of precision and compromises the decision models, leading to biased and unrepresentative results. We investigate how classical probabilistic models are affected by incomplete event logs and we explore quantum-like probabilistic inferences as an alternative mathematical model to classical probability. This work represents a first step towards systematic investigation of the impact of quantum interference in a real life large scale decision scenario. The results obtained in this study indicate that, under high levels of uncertainty, the quantum-like models generate quantum interference terms, which allow an additional non-linear parameterisation of the data. Experimental results attest the efficiency of the quantum-like Bayesian networks, since the application of interference terms is able to reduce the error percentage of inferences performed over quantum-like models when compared to inferences produced by classical models.

Authors: M. C. DiamantiniC. A. Trugenberger

We show that, in discrete models of quantum gravity, emergent geometric space can be viewed as the entanglement pattern in a mixed quantum state of the "universe", characterized by a universal topological network entanglement. As a concrete example we analyze the recently proposed model in which geometry emerges due to the condensation of 4-cycles in random regular bipartite graphs, driven by the combinatorial Ollivier-Ricci curvature. Using this model we show that the emergence of geometric order decreases the entanglement entropy of random configurations. The lowest geometric entanglement entropy is realized in four dimensions.

Author(s): S. P. Kish and T. C. Ralph

We study the problem of estimating the phase shift due to the general relativistic time dilation in the interference of photons using a nonlinear Mach-Zender interferometer setup. By introducing two nonlinear Kerr materials, one in the bottom and one in the top arm, we can measure the nonlinear phas...
[Phys. Rev. A 96, 041801(R)] Published Mon Oct 02, 2017

Authors: Andrei T. Patrascu

The discovery of the Higgs boson by the ATLAS and CMS collaborations allowed us to precisely determine its mass being 125.09 $\pm$ 0.24GeV. This value is intriguing as it lies at the frontier between the regions of stability and meta-stability of the standard model vacuum. It is known that the hierarchy problem can be interpreted in terms of the near criticality between the two phases. The coefficient of the Higgs bilinear in the scalar potential, $m^{2}$, is pushed by quantum corrections away from zero, towards the extremes of the interval $[-M^{2}_{Pl},M^{2}_{Pl}]$ where $M_{Pl}$ is the Planck mass. In this article, I show that demanding topological invariance for the renormalisation group allows us to extend the beta functions such that the particular value of the Higgs mass parameter observed in our universe regains naturalness. In holographic terms, invariance to changes of topology in the bulk is dual to a natural large hierarchy in the boundary quantum field theory. The demand of invariance to topology changes in the bulk appears to be strongly tied to the invariance of string theory to T-duality in the presence of H-fluxes.

Authors: Nicolas GisinEmmanuel Zambrini Cruzeiro

We consider a spin chain extending from Alice to Bob with next neighbors interactions, initially in its ground state. Assuming that Bob measures the last spin of the chain, the energy of the spin chain has to increase, at least on average, due to the measurement disturbance. Presumably, the energy is provided by Bob's measurement apparatus. Assuming now that, simultaneously to Bob's measurement, Alice measures the first spin, we show that either energy is not conserved, - implausible - or the projection postulate doesn't apply, and that there is signalling. An explicit measurement model shows that energy is conserved (as expected), but that the spin chain energy increase is not provided by the measurement apparatus(es), that the projection postulate is not always valid - illustrating the Wigner-Araki-Yanase (WAY) theorem - and that there is signalling, indeed. The signalling is due to the non-local interaction Hamiltonian. This raises the question of a suitable quantum information inspired model of such non-local Hamiltonians.

Bajlo, Darko (2017) The hidden arrow of electromagnetic radiation: unmasking advanced waves. UNSPECIFIED.

Abstract

Mach’s principle asserts that the inertial mass of a body is related to the distribution of other distant bodies. This means that in the absence of other bodies, a single body has no mass. In this case, talking about motion is not possible, because the detection of motion is possible only relative to other bodies. But in physics we are faced with situations that are not fully Machian. As in the case of general theory of relativity where geodesics exist in the absence of any matter, the motion has meaning. Another example which is the main topic of our discussion, refers to Bohmian quantum mechanics, where the inertial mass of a single particle does not vanish, but is modified. We can call such situations in which motion or mass of a single particle has meaning, pseudo-Machian situations. In this paper, we use the Machian or pseudo-Machian considerations to clarify under what circumstances and how a Machian effect leads us to Bohmian quantum mechanics. Then, we shall get the Bohmian quantum potential and its higher order terms for the Klein-Gordon particle through Machian considerations, without using any quantum mechanical postulate or operator formalism.

Tsementzis, Dimitris and Halvorson, Hans (2016) Foundations and Philosophy. [Preprint]

Volume 3, Issue 4, pages 119-125

Andreas Schlatter [Show Biography]

 

Born in Zurich, Switzerland, Andreas Schlatter was educated at the Swiss Federal Institute of Technology in Zurich, where he studied mathematics. He got his PhD in 1994 with work in partial differential equations. He subsequently held a research position at Princeton University, where he did further work mainly on the Yang-Mills heat equation. In 1997 Andreas joined the Asset Management industry and pursued a distinguished career over twenty years, which brought him into the Executive Committee of one of the world’s large Asset Management firms. Today Andreas does consulting work and holds a number of independent board seats. Andreas has been doing research and published during his professional life, mainly in the area of Quantum Foundations and Relativity but also in Finance.

We assign to the radiation vacuum the role of a universal observer with a corresponding universal clock. By demanding that the thermal clock of a gravitationally accelerated observer in its local rest frame marches in step with the universal one, we derive relations between energy content and geometry of space-time.

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Volume 3, Issue 4, pages 100-118

Leonardo Chiatti [Show Biography]

 

Graduated in physics at Rome University “La Sapienza” in 1985, discussing a thesis on spin in stochastic mechanics under the guide of Marcello Cini. His interest focus on the conceptual foundations of quantum mechanics and their relation to areas as quantum dissipative phenomena, quantum cosmology and the spectrum of elementary particles. During ‘90s, he was involved in MQC Project aiming to produce superpositions of quantum states in mesoscopic systems (rf-SQUIDs). Successively, his interest enlarged to medical physics and currently he serves as physicist in chief at ASL Medical Physics Laboratory in Viterbo, Italy. Along the past decade he has been, in collaboration with Ignazio Licata, a proponent of de Sitter quantum cosmology. Together, they have proposed an "objective" view of quantum discontinuity as an "a-dynamic" aspect of interaction. This approach identifies the reduction of wave function with the physical phenomenon of the "quantum leap".

The customary description of radiation processes provided by Quantum Electrodynamics (QED) allows the quantitative derivation of many physical observables, in line with experiments. This extraordinary empirical success, however, leaves open the problem of the ontology of these processes. We identify these with the discontinuities of the evolution of the quantum state of the source, the so-called quantum jumps (QJ). Adopting a time-symmetrical view of the QJ borrowed from the transactional approach, the phenomena of radiation emission and absorption by an electron acquire an adynamic aspect, associated with their emergence from an atemporal background. The QJ activates the progressive generation of the electron timeline, along which its asymptotic state evolves. This causation process is of the formal type, and its dynamic “shadow” on the time domain is constituted by an interval during which the electron is self-interacting. Instead, in the absence of further interaction with external fields the asymptotic state is “on shell” i.e. not self-interacting. These ideas are used to constraint the value of the fine structure constant and of the cosmological constant, and to illustrate some less-known properties of electroweak decays.

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