# Weekly Papers on Quantum Foundations (50)

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

Demonstrating the contextuality of quantum mechanics with observables in Hilbert spaces of arbitrary dimensions. (arXiv:1512.03334v1 [quant-ph])

quant-ph updates on arXiv.org

on 2015-12-12 8:03am GMT

The contextuality of quantum mechanics can be shown by the violation of inequalities based on measurements of well chosen observables. An important property of such observables is that their expectation value can be expressed in terms of probabilities of obtaining two exclusive outcomes. In order to satisfy this, inequalities have been constructed using either observables with a dichotomic spectrum or using periodic functions obtained from displacement operators in phase space. Here we unify both strategies by introducing general conditions to demonstrate the contextuality of quantum mechanics from measurements of observables of arbitrary dimensions. Among the consequences of our results is the impossibility of having a maximal violation of contextuality in the Peres-Mermin scenario with discrete observables of odd dimensions. In addition, we show how to construct a large class of observables with a continuous spectrum enabling the realization of contextuality tests both in the gaussian and non-gaussian regimes.

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Response to Dr. Pashby: Time operators and POVM observables in quantum mechanics

ScienceDirect Publication: Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics

on 2015-12-12 7:48am GMT

Publication date: November 2015
Source:Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics, Volume 52, Part A
Author(s): Gordon N. Fleming
I argue against a general time observable in quantum mechanics except for quantum gravity theory. Then I argue in support of case specific arrival, dwell and relative time observables with a cautionary note concerning the broad approach to POVM observables because of the wild proliferation available.

Assessing the Montevideo interpretation of quantum mechanics

ScienceDirect Publication: Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics

on 2015-12-12 7:48am GMT

Publication date: November 2015
Source:Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics, Volume 52, Part A
Author(s): Jeremy Butterfield
This paper gives a philosophical assessment of the Montevideo interpretation of quantum theory, advocated by Gambini, Pullin and co-authors. This interpretation has the merit of linking its proposal about how to solve the measurement problem to the search for quantum gravity: namely by suggesting that quantum gravity makes for fundamental limitations on the accuracy of clocks, which imply a type of decoherence that ‘collapses the wave-packet’. I begin (Section 2) by sketching the topics of decoherence, and quantum clocks, on which the interpretation depends. Then I expound the interpretation, from a philosopher׳s perspective (Sections 3–5). Finally, inSection 6, I argue that the interpretation, at least as developed so far, is best seen as a form of the Everett interpretation: namely with an effective or approximate branching, that is induced by environmental decoherence of the familiar kind, and by the Montevideans’ ‘temporal decoherence’.

Reply to Fleming: Symmetries, observables, and the occurrence of events

ScienceDirect Publication: Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics

on 2015-12-12 7:48am GMT

Publication date: November 2015
Source:Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics, Volume 52, Part A
Author(s): Thomas Pashby
In this article I reply to Fleming׳s response to my ‘Time and quantum theory: a history and a prospectus.’ I take issue with two of his claims: (i) that quantum theory concerns the (potential) properties of eternally persisting objects; (ii) that there is an underdetermination problem for Positive Operator Valued Measures (POVMs). I advocate an event-first view which regards the probabilities supplied by quantum theory as probabilities for the occurrence of physical events rather than the possession of properties by persisting objects.

Time in fundamental physics

ScienceDirect Publication: Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics

on 2015-12-12 7:48am GMT

Publication date: November 2015
Source:Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics, Volume 52, Part A
Author(s): Abhay Ashtekar
The first three sections of this paper contain a broad brush summary of the profound changes in the notion of time in fundamental physics that were brought about by three revolutions: the foundations of mechanics distilled by Newton in his Principia, the discovery of special relativity by Einstein and its reformulation by Minkowski, and, finally, the fusion of geometry and gravity in Einstein׳s general relativity. The fourth section discusses two aspects of yet another deep revision that waits in the wings as we attempt to unify general relativity with quantum physics.

Response to Bryan Roberts: A new perspective on T violation

ScienceDirect Publication: Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics

on 2015-12-12 7:48am GMT

Publication date: November 2015
Source:Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics, Volume 52, Part A
Author(s): Abhay Ashtekar
It is surprising that the fundamental, microscopic laws of Nature are not invariant under time reversal. In his article, Three Merry Roads to T-Violation, Dr. Bryan Roberts provided a succinct summary of the theoretical frameworks normally used to interpret the results of the experiments that established this fact. They all rely on the detailed structure of quantum mechanics. In this ‘response’ to Dr. Robert׳s talk, I will show that these experiments can be interpreted using a much more general framework. Consequently, should quantum mechanics be eventually replaced by a new paradigm, e.g., because of quantum gravity, these experiments could still be used to argue that the microscopic laws violate T invariance.

Comment on Ashtekar: Generalization of Wigner׳s principle

ScienceDirect Publication: Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics

on 2015-12-12 7:48am GMT

Publication date: November 2015
Source:Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics, Volume 52, Part A
Author(s): Bryan W. Roberts
Ashtekar׳s generalization of Curie׳s principle and Kabir׳s principle in this volume shows that these principles are robust, obtaining in a variety of modifications of quantum theory. In this note, I illustrate how Wigner׳s principle can be similarly generalized.

[In Depth] Controversial test finds no sign of a holographic universe

Science: Current Issue

on 2015-12-11 12:00am GMT

Working with a few lasers and mirrors, physicists at Fermi National Accelerator Laboratory (Fermilab) in Batavia, Illinois, have been trying to test a wild idea from string theory: that our universe may be like an enormous hologram. Last week, experimenters with the \$2.5 million Fermilab Holometer reported that they had found no evidence to support the “holographic principle.” But critics say the test, which uses laser interferometers to look for telltale jitters in spacetime, was on the wrong track to begin with. The holographic principle springs from the theory of black holes, spherical regions where gravity is so intense that not even light can escape. In theory, a black hole has an amount of disorder, or entropy, that is proportional to its surface area. As entropy is related to information content, some theorists conjectured that the maximum amount of information in any volume of space and time, or spacetime, may be proportional to its surface area. The universe would then work like a like a hologram, in which a 2D pattern captures a 3D image. The idea could guide string theorists in their quest to meld the theories of gravity and quantum mechanics. In 2009 the Fermilab researchers dreamed up a way to test the idea by looking for an effect called “holographic noise.” The experiment hasn’t found it yet, but the researchers say they’ll reconfigure the instruments and try again. Author: Adrian Cho

Pilot-Wave Quantum Theory with a Single Bohm’s Trajectory

Latest Results for Foundations of Physics

on 2015-12-10 12:00am GMT

Abstract

The representation of a quantum system as the spatial configuration of its constituents evolving in time as a trajectory under the action of the wave-function, is the main objective of the de Broglie–Bohm theory (or pilot wave theory). However, its standard formulation is referred to the statistical ensemble of its possible trajectories. The statistical ensemble is introduced in order to establish the exact correspondence (the Born’s rule) between the probability density on the spatial configurations and the quantum distribution, that is the squared modulus of the wave-function. In this work we explore the possibility of using the pilot wave theory at the level of a single Bohm’s trajectory, that is a single realization of the time dependent configuration which should be representative of a single realization of the quantum system. The pilot wave theory allows a formally self-consistent representation of quantum systems as a single Bohm’s trajectory, but in this case there is no room for the Born’s rule at least in its standard form. We will show that a correspondence exists between the statistical distribution of configurations along the single Bohm’s trajectory and the quantum distribution for a subsystem interacting with the environment in a multicomponent system. To this aim, we present the numerical results of the single Bohm’s trajectory description of the model system of six confined planar rotors with random interactions. We find a rather close correspondence between the coordinate distribution of one rotor, the others representing the environment, along its trajectory and the time averaged marginal quantum distribution for the same rotor. This might be considered as the counterpart of the standard Born’s rule when the pilot wave theory is applied at the level of single Bohm’s trajectory. Furthermore a strongly fluctuating behavior with a fast loss of correlation is found for the evolution of each rotor coordinate. This suggests that a Markov process might well approximate the evolution of the Bohm’s coordinate of a single rotor (the subsystem) and, under this condition, it is shown that the correspondence between coordinate distribution and quantum distribution of the rotor is exactly verified.

A Local Interpretation of Quantum Mechanics

Latest Results for Foundations of Physics

on 2015-12-10 12:00am GMT

Abstract

A local interpretation of quantum mechanics is presented. Its main ingredients are: first, a label attached to one of the “virtual” paths in the path integral formalism, determining the output for measurement of position or momentum; second, a mathematical model for spin states, equivalent to the path integral formalism for point particles in space time, with the corresponding label. The mathematical machinery of orthodox quantum mechanics is maintained, in particular amplitudes of probability and Born’s rule; therefore, Bell’s type inequalities theorems do not apply. It is shown that statistical correlations for pairs of particles with entangled spins have a description completely equivalent to the two slit experiment, that is, interference (wave like behaviour) instead of non locality gives account of the process. The interpretation is grounded in the experimental evidence of a point like character of electrons, and in the hypothetical existence of a wave like, the de Broglie, companion system. A correspondence between the extended Hilbert spaces of hidden physical states and the orthodox quantum mechanical Hilbert space shows the mathematical equivalence of both theories. Paradoxical behaviour with respect to the action reaction principle is analysed, and an experimental set up, modified two slit experiment, proposed to look for the companion system.

Paradox at the heart of mathematics makes physics problem unanswerable

Nature News & Comment

on 2015-12-09 12:00am GMT

Gödel’s incompleteness theorems are connected to unsolvable calculations in quantum physics.

Nature News doi: 10.1038/nature.2015.18983

Undecidability of the spectral gap

Nature Latest Research

on 2015-12-09 12:00am GMT

The spectral gap—the energy difference between the ground state and first excited state of a system—is central to quantum many-body physics. Many challenging open problems, such as the Haldane conjecture, the question of the existence of gapped topological spin liquid phases, and the Yang–Mills gap conjecture, concern spectral gaps. These and other problems are particular cases of the general spectral gap problem: given the Hamiltonian of a quantum many-body system, is it gapped or gapless? Here we prove that this is an undecidable problem. Specifically, we construct families of quantum spin systems on a two-dimensional lattice with translationally invariant, nearest-neighbour interactions, for which the spectral gap problem is undecidable. This result extends to undecidability of other low-energy properties, such as the existence of algebraically decaying ground-state correlations. The proof combines Hamiltonian complexity techniques with aperiodic tilings, to construct a Hamiltonian whose ground state encodes the evolution of a quantum phase-estimation algorithm followed by a universal Turing machine. The spectral gap depends on the outcome of the corresponding ‘halting problem’. Our result implies that there exists no algorithm to determine whether an arbitrary model is gapped or gapless, and that there exist models for which the presence or absence of a spectral gap is independent of the axioms of mathematics.

Nature 528 207 doi: 10.1038/nature16059

Tests of Quantum Gravity induced non-locality via opto-mechanical quantum oscillators. (arXiv:1512.02083v1 [gr-qc])

gr-qc updates on arXiv.org

on 2015-12-08 2:33am GMT

Several quantum gravity scenarios lead to physics below the Planck scale characterised by nonlocal, Lorentz invariant equations of motion. We show that such non-local effective field theories lead to a modified Schr\”odinger evolution in the nonrelativistic limit. In particular, the nonlocal evolution of opto-mechanical quantum oscillators is characterised by a spontaneous periodic squeezing that cannot be generated by environmental effects. We discuss constraints on the nonlocality obtained by past experiments, and show how future experiments (already under construction) will either see such effects or otherwise cast severe bounds on the non-locality scale (well beyond the current limits set by the Large Hadron Collider). This paves the way for table top, high precision experiments on massive quantum objects as a promising new avenue for testing some quantum gravity phenomenology.

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Regarding the Hole Argument’ and the Problem of Time’. (arXiv:1512.01798v1 [gr-qc])

gr-qc updates on arXiv.org

on 2015-12-08 2:33am GMT

Authors: Sean GrybKarim P. Y. Thebault

The canonical formalism of general relativity affords a particularly interesting characterisation of the infamous hole argument. It also provides a natural formalism in which to relate the hole argument to the problem of time in classical and quantum gravity. In this paper, we examine the connection between these two much discussed problems in the foundations of spacetime theory along two interrelated lines. First, from a formal perspective, we consider the extent to which the two problems can and cannot be precisely and distinctly characterised. Second, from a philosophical perspective, we consider the implications of various responses to the problems, with a particular focus upon the viability of a `deflationary’ attitude to the relationalist/substantivalist debate regarding the ontology of spacetime. Conceptual and formal inadequacies within the representative language of canonical gravity will be shown to be at the heart of both the canonical hole argument and the problem of time. Interesting and fruitful work at the interface of physics and philosophy relates to the challenge of resolving such inadequacies.

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Centennial of General Relativity (1915-2015); The Schwarzschild Solution and Black Holes. (arXiv:1512.02061v1 [physics.pop-ph])

gr-qc updates on arXiv.org

on 2015-12-08 2:33am GMT

Authors: S. M. Blinder

This year marks the 100th anniversary of Einstein’s General Theory of Relativity (1915-2015). The first nontrivial solution of the Einstein field equations was derived by Karl Schwarzschild in 1916. This Note will focus mainly on the Schwarzschild solution and the remarkable developments which it inspired, the most dramatic being the prediction of black holes. Later extensions of Schwarzschild’s spacetime structure has led to even wilder conjectures, such as white holes and passages to other universes. Penrose diagrams are introduced as compact representations of extended spacetime structures. Stephen Hawking’s derivations of quantum effects in black holes might provide clues to an eventual “Theory of Everything” encompassing both general relativity and quantum mechanics.

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The Geometry of Qubit Weak Values. (arXiv:1512.02113v1 [quant-ph])

quant-ph updates on arXiv.org

on 2015-12-08 2:33am GMT

Authors: J. M. FarinholtA. GhazariansJ. E. Troupe

The concept of a \emph{weak value} of a quantum observable was developed in the late 1980s by Aharonov and colleagues to characterize the value of an observable for a quantum system in the time interval between two projective measurements. Curiously, these values often lie outside the eigenspectrum of the observable, and can even be complex-valued. Nevertheless, the weak value of a quantum observable has been shown to be a valuable resource in quantum metrology, and has received recent attention in foundational aspects of quantum mechanics. This paper is driven by a desire to more fully understand the underlying mathematical structure of weak values. In order to do this, we allow an observable to be \emph{any} Hermitian operator, and use the pre- and post-selected states to develop well-defined linear maps between the Hermitian operators and their corresponding weak values. We may then use the inherent Euclidean structure on Hermitian space to geometrically decompose a weak value of an observable. In the case in which the quantum systems are qubits, we provide a full geometric characterization of weak values.

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Quantum Nondemolition Measurement of a Nonclassical State of a Massive Object

Recent Articles in Phys. Rev. X

on 2015-12-07 3:00pm GMT

Author(s): F. Lecocq, J. B. Clark, R. W. Simmonds, J. Aumentado, and J. D. Teufel

The act of a quantum measurement reduces the uncertainty in the motion of a vibrating membrane below the fundamental quantum limit.

[Phys. Rev. X 5, 041037] Published Mon Dec 07, 2015

From dressed electrons to quasiparticles: The emergence of emergent entities in quantum field theory

ScienceDirect Publication: Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics

on 2015-12-07 11:54am GMT

Publication date: February 2016
Source:Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics, Volume 53
Author(s): Alexander S. Blum, Christian Joas
In the 1970s, the reinterpretation of renormalization group techniques in terms of effective field theories and their subsequent rapid development led to a major reinterpretation of the entire renormalization program, originally formulated in the late 1940s within quantum electrodynamics (QED). A more gradual shift in its interpretation, however, occurred already in the early-to-mid-1950s when renormalization techniques were transferred to solid-state and nuclear physics and helped establish the notion of effective or quasi-particles, emergent entities that are not to be found in the original, microscopic description of the theory. We study how the methods of QED, when applied in different contexts, gave rise to this ontological reinterpretation.