# Weekly Papers on Quantum Foundations (24)

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.

Positive-operator-valued measures in the Hamiltonian formulation of quantum mechanics

PRA: Fundamental concepts

on 2015-6-12 2:00pm GMT

Author(s): D. Arsenović, N. Burić, D. B. Popović, M. Radonjić, and S. Prvanović

In the Hilbert space formulation of quantum mechanics, ideal measurements of physical variables are discussed using the spectral theory of Hermitian operators and the corresponding projector-valued measures (PVMs). However, more general types of measurements require the treatment in terms of positiv…

[Phys. Rev. A 91, 062114] Published Fri Jun 12, 2015

Problem of Time: Temporal Relationalism Compatibility of Other Local Classical Facets Completed. (arXiv:1506.03517v1 [gr-qc])

on 2015-6-12 9:07am GMT

Authors: Edward Anderson

Temporal Relationalism (TR) is that there is no time for the universe as a whole at the primary level. Time emerges rather at a secondary level; one compelling idea for this is Mach’s time is to be abstracted from change’. TR leads to, and better explains, the well-known Frozen Formalism Problem encountered in GR at the quantum level. Indeed, abstraction from change is a type of emergent time resolution of this.Moreover, the Frozen Formalism Problem is but one of the many Problem of Time facets, which are furthermore notoriously interconnected. The other local and already classically present facets are as follows. 2) The GR Thin Sandwich involves a subcase of Best Matching, which is one particular implementation of Configurational Relationalism. 3) The Constraint Closure Problem, 4) the Problem of Observables or Beables, 5) Spacetime Relationalism, 6) the Spacetime Construction Problem, and 7) the Foliation Dependence Problem as resolved in classical GR by Refoliation Invariance. In this Article, I bring together the individual classical resolutions of these, and how these can be rendered compatible with TR. Having covered that in detail for 2) to 6) elsewhere, the rest of the current Article is dedicated to the detailed form that 7) and its TR compatible modification takes. I.e. I consider TR implementing foliations, the TR versions of Refoliation Invariance and the associated TR version of hypersurface kinematics and hypersurface deformations. These require a TR counterpart of the Arnowitt–Deser–Misner split.

Completing Quantum Mechanics with Quantized Hidden Variables. (arXiv:1506.03485v1 [quant-ph])

on 2015-6-12 9:06am GMT

Authors: S.J. van Enk

I explore the possibility that a quantum system S may be described {\em completely} by the combination of its standard quantum state $|\psi\rangle$ and a (hidden) quantum state $|\phi\rangle$ (that lives in the same Hilbert space), such that the outcome of any standard projective measurement on the system S is determined once the two quantum states are specified. I construct an algorithm that retrieves the standard quantum-mechanical probabilities, which depend only on $|\psi\rangle$, by assuming that the (hidden) quantum state $|\phi\rangle$ is drawn at random from some fixed probability distribution Pr(.) and by averaging over Pr(.). Contextuality and Bell nonlocality turn out to emerge automatically from this algorithm as soon as the dimension of the Hilbert space of S is larger than 2. If $|\phi\rangle$ is not completely random, subtle testable deviations from standard quantum mechanics may arise in sequential measurements on single systems.

Flux formulation of loop quantum gravity: classical framework

Classical and Quantum Gravity – latest papers

on 2015-6-12 12:00am GMT

We recently introduced a new representation for loop quantum gravity (LQG), which is based on the BF vacuum and is in this sense much nearer to the spirit of spin foam dynamics. In the present paper we lay out the classical framework underlying this new formulation. The central objects in our construction are the so-called integrated fluxes, which are defined as the integral of the electric field variable over surfaces of codimension one, and related in turn to Wilson surface operators. These integrated flux observables will play an important role in the coarse graining of states in LQG, and can be used to encode in this context the notion of curvature-induced torsion. We furthermore define a continuum phase space as the modified projective limit of a family of discrete phase spaces based on triangulations. This continuum phase space yields a continuum (holonomy-flux) algebra of observables. We show that the corresponding Poisson algebra is closed by computing the Poisson bracket…

Scalar material reference systems and loop quantum gravity

Classical and Quantum Gravity – latest papers

on 2015-6-12 12:00am GMT

In the past, the possibility to employ (scalar) material reference systems in order to describe classical and quantum gravity directly in terms of gauge invariant (Dirac) observables has been emphasized frequently. This idea has been picked up more recently in loop quantum gravity with the aim to perform a reduced phase space quantization of the theory, thus possibly avoiding problems with the (Dirac) operator constraint quantization method for a constrained system. In this work, we review the models that have been studied on the classical and/or the quantum level and parametrize the space of theories considered so far. We then describe the quantum theory of a model that, to the best of our knowledge, has only been considered classically so far. This model could arguably be called the optimal one in this class of models considered as it displays the simplest possible true Hamiltonian, while at the same time reducing all constraints of general relativity.

“Hot Entanglement”? — A Nonequilibrium Quantum Field Theory Scrutiny. (arXiv:1506.02941v1 [hep-th])

on 2015-6-10 1:31am GMT

Authors: Jen-Tsung HsiangB. L. Hu

The possibility of maintaining entanglement in a quantum system at finite, even high, temperatures — the so-called hot entanglement’ — has obvious practical interest, but also requires closer theoretical scrutiny. Since quantum entanglement in a system evolves in time and is continuously subjected to environmental degradation, a nonequilibrium description by way of open quantum systems is called for. To identify the key issues and the contributing factors that may permit `hot entanglement’ to exist, or the lack thereof, we carry out a model study of two spatially-separated, coupled oscillators in a shared bath depicted by a finite-temperature scalar field. From the Langevin equations we derived for the normal modes and the entanglement measure constructed from the covariance matrix we examine the interplay between direct coupling, field-induced interaction and finite separation on the structure of late-time entanglement. We show that the coupling between oscillators plays a crucial role in sustaining entanglement at intermediate temperatures and over finite separations. In contrast, the field-induced interaction between the oscillators which is a non-Markovian effect, becomes very ineffective at high temperature. We determine the critical temperature above which entanglement disappears to be bounded in the leading order by the inverse frequency of the center-of-mass mode of the reduced oscillator system, a result not unexpected, which rules out hot entanglement in such settings.

A Quantum Focussing Conjecture. (arXiv:1506.02669v1 [hep-th])

on 2015-6-10 1:31am GMT

We propose a universal inequality that unifies the Bousso bound with the classical focussing theorem. Given a surface $\sigma$ that need not lie on a horizon, we define a finite generalized entropy $S_\text{gen}$ as the area of $\sigma$ in Planck units, plus the von Neumann entropy of its exterior. Given a null congruence $N$ orthogonal to $\sigma$, the rate of change of $S_\text{gen}$ per unit area defines a quantum expansion. We conjecture that the quantum expansion cannot increase along $N$. This extends the notion of universal focussing to cases where quantum matter may violate the null energy condition. Integrating the conjecture yields a precise version of the Strominger-Thompson Quantum Bousso Bound. Applied to locally parallel light-rays, the conjecture implies a Quantum Null Energy Condition: a lower bound on the stress tensor in terms of the second derivative of the von Neumann entropy. We sketch a proof of this novel relation in quantum field theory.

Extending quantum mechanics entails extending special relativity. (arXiv:1506.03058v1 [quant-ph])

on 2015-6-10 1:31am GMT

Authors: S. AravindaR. Srikanth

The complementarity of signaling and local randomness in the resources required to simulate singlet statistics is generalized here by relaxing the assumption of free will in the choice of measurement settings. The complementarity implies that under the assumption of full free will, simulation resources with reduced randomness will be signaling. It would appear at first sight that an ontological extension based on such a simulation protocol would contradict no-signaling and free will. We prove that this is not so, by constructing such an extension through the “oblivious embedding” of the protocol in a Newtonian spacetime. Relativistic or other intermediate spacetimes are ruled out as the locus of the embedding because they would permit the violation of no-signaling at the operational level by virtue of hidden influence inequalities. This implies that predictively superior extensions of quantum mechanics (QM) must be Lorentz non-covariant. However, the operational theory reproduced by the extensions will be compatible with no-signaling and Lorentz covariance. This clarifies why in principle there is no obstacle to the compatibility of extensions of QM such as Bohmian mechanics and GRW-type collapse theories with special relativity. Certain arguments against the extendability of QM, due to Conway and Kochen (2009) and Colbeck and Renner (2012), are attributed to their assumption that the spacetime of the extensions has Minkowskian causal structure.

Quantum mechanics and the principle of maximal variety. (arXiv:1506.02938v1 [quant-ph])

on 2015-6-10 1:31am GMT

Authors: Lee Smolin

Quantum mechanics is derived from the principle that the universe contain as much variety as possible, in the sense of maximizing the distinctiveness of each subsystem.

The quantum state of a microscopic system is defined to correspond to an ensemble of subsystems of the universe with identical constituents and similar preparations and environments. A new kind of interaction is posited amongst such similar subsystems which acts to increase their distinctiveness, by extremizing the variety. In the limit of large numbers of similar subsystems this interaction is shown to give rise to Bohm’s quantum potential. As a result the probability distribution for the ensemble is governed by the Schroedinger equation.

The measurement problem is naturally and simply solved. Microscopic systems appear statistical because they are members of large ensembles of similar systems which interact non-locally. Macroscopic systems are unique, and are not members of any ensembles of similar systems. Consequently their collective coordinates may evolve deterministically.

This proposal could be tested by constructing quantum devices from entangled states of a modest number of quits which, by its combinatorial complexity, can be expected to have no natural copies.

Origin of structure: Statistical characterization of the primordial density fluctuations and the collapse of the wave function. (arXiv:1503.01417v2 [gr-qc] UPDATED)

on 2015-6-09 1:45am GMT

Authors: Gabriel LeonDaniel Sudarsky

The statistical properties of the primordial density perturbations has been considered in the past decade as a powerful probe of the physical processes taking place in the early universe. Within the inflationary paradigm, the properties of the bispectrum are one of the keys that serves to discriminate among competing scenarios concerning the details of the origin of cosmological perturbations. However, all of the scenarios, based on the conventional approach to the so-called “quantum-to-classical transition” during inflation, lack the ability to point out the precise physical mechanism responsible for generating the inhomogeneity and anisotropy of our universe starting from and exactly homogeneous and isotropic vacuum state associated with the early inflationary regime. In past works, we have shown that the proposals involving a spontaneous dynamical reduction of the quantum state provide plausible explanations for the birth of said primordial inhomogeneities and anisotropies. In the present manuscript we show that, when considering within the context of such proposals, the characterization of the spectrum and bispectrum turn out to be quite different from those found in the traditional approach, and in particular, some of the statistical features, must be treated in a different way leading to some rather different conclusions.

Two Experimental Tests to Distinguish Decoherence from the Slicing Theory of Measurement. (arXiv:1506.02581v1 [physics.gen-ph])

on 2015-6-09 1:45am GMT

Authors: Clifford Chafin

Here we propose a pair of experiments to distinguish the recently proposed “slicing theory” of quantum measurement, which gives a transient many worlds picture, and decoherence. Since these two theories are essentially “opposites” in their approach and both claim to arise from the many body Schr\”odinger equation itself, there is no chance of them being equivalent representations of the same reality. It will be explicitly shown that each theory gives very different answers to the questions of back reaction and revival of phase effects after measurement. We suggest that the kinds of isolated systems now possible in optical traps is now sufficient to generate a selective distinction between these two theories. In particular we show that the slicing theory gives examples of interference from “revival of histories” in controlled examples but no back reaction on the measurement devices whereas decoherence gives the opposite.

Gauge invariance in simple mechanical systems. (arXiv:1506.02027v1 [quant-ph])

on 2015-6-09 1:45am GMT

This article discusses and explains the Hamiltonian formulation for a class of simple gauge invariant mechanical systems consisting of point masses and idealized rods. The study of these models may be helpful to advanced undergraduate or graduate students in theoretical physics to understand, in a familiar context, some concepts relevant to the study of classical and quantum field theories. We use a geometric approach to derive the Hamiltonian formulation for the model considered in the paper: four equal masses connected by six ideal rods. We obtain and discuss the meaning of several important elements, in particular, the constraints and the Hamiltonian vector fields that define the dynamics of the system, the constraint manifold, gauge symmetries, gauge orbits, gauge fixing, and the reduced phase space.

A quantum kinematics for asymptotically flat gravity

Classical and Quantum Gravity – latest papers

on 2015-6-08 12:00am GMT

We construct a quantum kinematics for asymptotically flat gravity based on the Koslowski–Sahlmann (KS) representation. The KS representation is a generalization of the representation underlying loop quantum gravity (LQG) which supports, in addition to the usual LQG operators, the action of ‘background exponential operators’, which are connection dependent operators labelled by ‘background’ su (2) electric fields. KS states have, in addition to the LQG state label corresponding to one dimensional excitations of the triad, a label corresponding to a ‘background’ electric field that describes three dimensional excitations of the triad. Asymptotic behaviour in quantum theory is controlled through asymptotic conditions on the background electric fields that label the states and the background electric fields that label the operators . Asymptotic conditions on the triad are imposed as conditions on the background electric field state label while confining the LQG spi…

Splitting the Source Term for the Einstein Equation to Classical and Quantum Parts

Latest Results for Foundations of Physics

on 2015-6-07 12:00am GMT

Abstract

We consider the special and general relativistic extensions of the action principle behind the Schrödinger equation distinguishing classical and quantum contributions. Postulating a particular quantum correction to the source term in the classical Einstein equation we identify the conformal content of the above action and obtain classical gravitation for massive particles, but with a cosmological term representing off-mass-shell contribution to the energy–momentum tensor. In this scenario the—on the Planck scale surprisingly small—cosmological constant stems from quantum bound states (gravonium) having a Bohr radius a as being $$\Lambda =3/a^2$$ .