Weekly Papers on Quantum Foundations (11)

Authors: K. KowalskiJ. Rembielinski

A detailed study is presented of the relativistic Wigner function for a quantum spinless particle evolving in time according to the Salpeter equation.

Authors: Jeconias Rocha Guimarães

A quantum mechanics representation based on position ($\vec{r}$), linear momentum($\vec{p}$) and energy($E$) eigenvalues is presented here. A set of equations, explicitly independent on wave function, was derived relating these observables. In this view, a particle has a known trajectory and at any point on space there is a linear momentum associated. Trajectory here, can be viewed as if a measurement were taken continuously. This picture does not change current quantum mechanics interpretation, rather it comes as a new route of calculation. Also, wave function can be retrieved performing an integration in all space for linear momentum. Equations derived in this work, present a potential dependent on linear momentum originating what we call quantum force. A particle experiences a total force whose resultant is composed by classic and quantum force, evolving on time according to it. In terms of evaluation, a single particle could be described by a set of auxiliary particles named as wave particles(WP). They will start with a range of initial conditions and will collectively describe probabilistic aspects of quantum mechanics. We expect this route could be applied to many problems, such as multi-body systems.

Authors: Edward J. Gillis

Because quantum measurements have probabilistic outcomes they can seem to violate conservation laws in individual experiments. Despite these appearances, strict conservation of momentum, energy, and angular momentum can be shown to follow from the assumption that the entangling interactions that constitute measurements induce a real collapse of the wave function. The essential idea is that measured systems always have some pre-existing entanglement relations with (usually larger) systems, and that apparent changes in conserved quantities in the measured system are correlated with compensating changes in these larger systems. Since wave function collapse is mediated by entanglement relations a full accounting of the relevant quantities requires a computation over all interacting, entangled systems. The demonstrations by Gemmer and Mahler[1], and by Durt[2,3], that entanglement is a generic result of interaction are central to the argument. After briefly reviewing the status of conservation laws in various interpretations of the quantum measurement process I present a stochastic collapse equation that insures conservation of the relevant quantities in all situations.

Authors: Holger F. Hofmann

In quantum mechanics, joint measurements of non-commuting observables are only possible if a minimal unavoidable measurement uncertainty is accepted. On the other hand, correlations between non-commuting observables can exceed classical limits, as demonstrated by the violation of Bell’s inequalities. Here, the relation between the uncertainty limited statistics of joint measurements and the limits on expectation values of possible input states is analyzed. It is shown that the experimentally observable statistics of joint measurements explain the uncertainty limits of local states, but result in less restrictive bounds when applied to identify the limits of non-local correlations between two separate quantum systems. A tight upper bound is obtained for the four correlations that appear in the violation of Bell’s inequalities and the statistics of pure states saturating the bound is characterized. The results indicate that the limitations of quantum non-locality are a necessary consequence of the local features of joint measurements, suggesting the possibility that quantum non-locality could be explained in terms of the local characteristics of quantum statistics.

Authors: Sibel BaskalYoung S. KimMarilyn E. Noz

It is noted that the single-variable Heisenberg commutation relation contains the symmetry of the $Sp(2)$ group which is isomorphic to the Lorentz group applicable to one time-like dimension and two space-like dimensions, known as the $O(2,1)$ group. According to Paul A. M. Dirac, from the uncertainty commutation relations for two variables, it possible to construct the de Sitter group $O(3,2)$, namely the Lorentz group applicable to three space-like variables and two time-like variables. By contracting one of the time-like variables in $O(3,2)$, it is possible, to construct the inhomogeneous Lorentz group $IO(3,1)$ which serves as the fundamental symmetry group for quantum mechanics and quantum field theory in the Lorentz covariant world. This $IO(3,1)$ group is commonly known as the Poincar\’e group.

Authors: Diederik AertsJonito Aerts ArguëllesLester BeltranSuzette GerienteMassimiliano Sassoli de BianchiSandro SozzoTomas Veloz

We provide a general description of the phenomenon of entanglement in bipartite systems, as it manifests in micro and macro physical systems, as well as in human cognitive processes. We do so by observing that when genuine coincidence measurements are considered, the violation of the ‘marginal laws’, in addition to the Bell-CHSH inequality, is also to be expected. The situation can be described in the quantum formalism by considering the presence of entanglement not only at the level of the states, but also at the level of the measurements. However, at the “local'” level of a specific joint measurement, a description where entanglement is only incorporated in the state remains always possible, by adopting a fine-tuned tensor product representation. But contextual tensor product representations should only be considered when there are good reasons to describe the outcome-states as (non-entangled) product states. This will not in general be true, hence, the entangement resource will have to generally be allocated both in the states and in the measurements. In view of the numerous violations of the marginal laws observed in physics’ laboratories, it remains unclear to date if entanglement in micro-physical systems is to be understood only as an ‘entanglement of the states’, or also as an ‘entanglement of the measurements’. But even if measurements would also be entangled, the corresponding violation of the marginal laws (no-signaling conditions) would not for this imply that a superluminal communication would be possible.

Authors: Stephen Boughn

The concept of “reality” is often raised in the context of philosophical foundations of physics or interpretations of quantum mechanics. When this term is so raised, it is a warning to me that I am about to be led down a rabbit hole. Such diversions usually lead nowhere unless you consider endless discussions of Schrodinger’s cat, wave function collapse, quantum non-locality, and parallel universes to be useful. A prime example is the famous Einstein, Podolsky, and Rosen paper wherein they concluded that the quantum wave function cannot provide a complete description of physical reality. In this essay I suggest that, in physics discourse, the term “reality” should be avoided at all costs.

Authors: Otto C. W. KongWei-Yin Liu (Nat’l Central U., Taiwan)

We discuss the notion about physical quantities as having values represented by real numbers, and its limiting to describe nature to be understood in relation to our appreciation that the quantum theory is a better theory of natural phenomena than its classical analog. Getting from the algebra of physical observables to their values on a fixed state is, at least for classical physics, really a homomorphic map from the algebra into the real number algebra. The limitation of the latter to represent the values of quantum observables with noncommutating algebraic relation is obvious. We introduce and discuss the idea of the noncommutative values of quantum observables and its feasibility, arguing that at least in terms of the representation of such a value as an infinite set of complex number, the idea makes reasonable sense theoretically as well as practically.

Authors: Henry LammScott LawrenceYukari Yamauchi (for the NuQS Collaboration)

A general scheme is presented for simulating gauge theories, with matter fields, on a digital quantum computer. A Trotterized time-evolution operator that respects gauge symmetry is constructed, and a procedure for obtaining time-separated, gauge-invariant operators is detailed. We demonstrate the procedure on small lattices, including the simulation of a 2+1D non-Abelian gauge theory.

Authors: J. MartonA. PichlerA. AmirkhaniS. BartalucciM. BazziS. BertolucciM. BragadireanuM. CargnelliA. ClozzaC. CurceanuR. Del GrandeL. De PaolisJ.-P. EggerC. FioriniC. GuaraldoM. IliescuM. LaubensteinE. MilottiM. MilucciD. PietreanuK. PiscicchiaA. ScordoH. ShiD. SirghiF. SirghiL. SperandioO. Vazquez-DoceJ. Zmeskal

The VIP2 (VIolation of the Pauli Exclusion Principle) experiment at the Gran Sasso underground laboratory (LNGS) is searching for possible violations of standard quantum mechanics predictions in atoms at very high sensitivity. We investigate atomic transitions with precision X-ray spectroscopy in order to test the Pauli Exclusion Principle (PEP) and therefore the related spin-statistics theorem. We will present our experimental method for the search for “anomalous” (i.e. Pauli-forbidden) X-ray transitions in copper atoms, produced by “new” electrons, which could have tiny probability to undergo Pauli-forbidden transition to the ground state already occupied by two electrons. We will describe the VIP2 experimental setup, which is taking data at LNGS presently. The goal of VIP2 is to test the PEP for electrons with unprecedented accuracy, down to a limit in the probability that PEP is violated at the level of 10$^{-31}$. We will present current experimental results and discuss implications of a possible violation.

French, Steven (2019) From a Lost History to a New Future: Is a Phenomenological Approach to Quantum Physics Viable? [Preprint]
Eva, Benjamin and Hartmann, Stephan and Rafiee Rad, Soroush (2019) Learning from Conditionals. [Preprint]

Author(s): James Klatzow, Jonas N. Becker, Patrick M. Ledingham, Christian Weinzetl, Krzysztof T. Kaczmarek, Dylan J. Saunders, Joshua Nunn, Ian A. Walmsley, Raam Uzdin, and Eilon Poem

Experiments demonstrate a quantum-coherence-induced power increase for quantum heat engines over their classical counterparts.


[Phys. Rev. Lett. 122, 110601] Published Wed Mar 20, 2019

North, Jill (2019) Formulations of Classical Mechanics. [Preprint]

Authors: Elias C. VagenasAhmed Farag AliHassan Alshal

Motivated by a recent work by Yongwan Gim, Hwajin Um, and Wontae Kim, we investigate the validity of the no-cloning theorem in the context of generalized uncertainty principle. In particular, in the presence of linear and quadratic terms of momentum in generalized uncertainty principle, we first compute the energy density at a given modified temperature and then using the modified Stefan-Boltzmann law we derive the modified Page time. Finally, we calculate the modified required energy for the information to be encoded into a message and be sent to an observer inside the black hole.

Authors: Ram BrusteinA.J.M. MedvedK. Yagi

Black hole (BH) thermodynamics was established by Bekenstein and Hawking, who made abstract theoretical arguments about the second law of thermodynamics and quantum theory in curved spacetime respectively. Testing these ideas experimentally has, so far, been impractical because the putative flux of Hawking radiation from astrophysical BHs is too small to be distinguished from the rest of the hot environment. Here, it is proposed that the spectrum of emitted gravitational waves (GWs) after the merger of two BHs, in particular the spectrum of GW150914, can be used to infer a lower limit on the magnitude of the entropy of the post-merger BH. This lower bound is potentially significant as it could be of the same order as the Bekenstein-Hawking entropy. To infer this limit, we first assume that the result of the merger is an ultracompact object with an external geometry which is Schwarzschild or Kerr, but with an outer surface which is capable of reflecting in-falling GWs rather than fully absorbing them. If the absence of deviations from the predictions of general relativity in detected GW signals will be verified, we will then obtain a bound on the minimal redshift factor of GWs that emerge from the vicinity of the object’s surface. This lack of deviations would also mean that the remnant of the merger has to have a strongly absorbing surface and must then be a BH for all practical purposes. We conclude that a relationship between the minimal redshift factor and the BH entropy, which was first proposed by ‘t Hooft, could then be used to set a lower bound on the entropy of the post-merger BH.

Authors: Richard J. Szabo

We give a pedagogical introduction to the nonassociative structures arising from recent developments in quantum mechanics with magnetic monopoles, in string theory and M-theory with non-geometric fluxes, and in M-theory with non-geometric Kaluza-Klein monopoles. After a brief overview of the main historical appearences of nonassociativity in quantum mechanics, string theory and M-theory, we provide a detailed account of the classical and quantum dynamics of electric charges in the backgrounds of various distributions of magnetic charge. We apply Born reciprocity to map this system to the phase space of closed strings propagating in R-flux backgrounds of string theory, and then describe the lift to the phase space of M2-branes in R-flux backgrounds of M-theory. Applying Born reciprocity maps this M-theory configuration to the phase space of M-waves probing a non-geometric Kaluza-Klein monopole background. These four perspective systems are unified by a covariant 3-algebra structure on the M-theory phase space.

Authors: Vitaly Vanchurin

We consider the quantum partition function for a system of quantum spinors and then derive an equivalent (or dual) classical partition function for some scalar degrees of freedom. The coupling between scalars is non-trivial (e.g. a model on 2-sphere configuration space), but the locality structure of the dual system is preserved, in contrast to the imaginary time formalism. We also show that the measure of integration in the classical partition function can be formally expressed through relativistic Green’s functions which suggests a possible mechanism for the emergence of a classical space-time from anti-commutativity of quantum operators.

Publication date: Available online 8 March 2019

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

Author(s): Valia Allori

Abstract

Against what is commonly accepted in many contexts, it has been recently suggested that both deterministic and indeterministic quantum theories are not time-reversal invariant, and thus time is handed in a quantum world. In this paper, I analyze these arguments and evaluate possible reactions to them. In the context of deterministic theories, first I show that this conclusion depends on the controversial assumption that the wave-function is a physically real scalar field in configuration space. Then I argue that answers which restore invariance by assuming the wave-function is a ray in Hilbert space fall short. Instead, I propose that one should deny that the wave-function represents physical systems, along the lines proposed by the so-called primitive ontology approach. Moreover, in the context of indeterministic theories, I argue that time-reversal invariance can be restored suitably redefining its meaning.

Publication date: Available online 9 March 2019

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

Author(s): Tom McLeish, Mark Pexton, Tom Lancaster

Abstract

There has been growing interest in systems in condensed matter physics as a potential source of examples of both epistemic and ontological emergence. One of these case studies is the fractional quantum Hall state (FQHS). In the FQHS a system of electrons displays a type of holism due to a pattern of long-range quantum entanglement that some argue is emergent. Indeed, in general, quantum entanglement is sometimes cited as the best candidate for one form of ontological emergence. In this paper we argue that there are significant formal and physical parallels between the quantum FQHS and classical polymer systems. Both types of system cannot be explained simply by considering an aggregation of local microphysical properties alone, since important features of each are globally determined by topological features. As such, we argue that if the FQHS is a case of ontological emergence then it is not due to the quantum nature of the system and classical polymer systems are ontologically emergent as well.

Publication date: Available online 15 March 2019

Source: Physics Letters A

Author(s): Anindita Bera, Debmalya Das, Aditi Sen(De), Ujjwal Sen

Abstract

Based on the statistical concept of the median, we propose a quantum uncertainty relation between semi-interquartile ranges of the position and momentum distributions of arbitrary quantum states. The relation is universal, unlike that based on the mean and standard deviation, as the latter may become non-existent or ineffective in certain cases. We show that the median-based one is not saturated for Gaussian distributions in position. Instead, the Cauchy-Lorentz distributions in position turn out to be the one with the minimal uncertainty, among the states inspected, implying that the minimum-uncertainty state is not unique but depends on the measure of spread used. Even the ordering of the states with respect to the distance from the minimum uncertainty state is altered by a change in the measure. We invoke the completeness of Hermite polynomials in the space of all quantum states to probe the median-based relation. The results have potential applications in a variety of studies including those on the quantum-to-classical boundary and on quantum cryptography.

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