Weekly Papers on Quantum Foundations (19)

Authors: John Realpe-Gómez

Here we derive the formalism of quantum theory from two intuitive principles: (i) inference is a physical process performed by physical systems, observers, which are part of the experimental setup— this implies non-commutativity; (ii) experiments must be described from a first-person perspective— this leads to self-reference, complementarity, and a picture of reality similar to that of some millenarian spiritual traditions. Quantum dynamics is the iterative construction of the observer’s subjective state. Using available experimental data, we show the quantum of action is the result of the additional energy required to transition from unconscious to conscious perception.

Authors: Aleksandrina NikolovaGavin BrennenTobias J. OsborneGerard MilburnThomas M. Stace

In a seminal paper (Page and Wootters 1983) Page and Wootters suggest time evolution could be described solely in terms of correlations between systems and clocks, as a means of dealing with the “problem of time” stemming from vanishing Hamiltonian dynamics in many theories of quantum gravity. Their approach to relational time centres around the existence of a Hamiltonian and the subsequent constraint on physical states. In this paper we present a “state-centric” reformulation of the Page and Wootters model better suited to theories which intrinsically lack Hamiltonian dynamics, such as Chern–Simons theories. We describe relational time by encoding logical “clock” qubits into anyons—the topologically protected degrees of freedom in Chern–Simons theories. The timing resolution of such anyonic clocks is determined by the universality of the anyonic braid group, with non-universal models naturally exhibiting discrete time. We exemplify this approach using SU(2)$_2$ anyons and discuss generalizations to other states and models.

Authors: Kensuke Kobayashi

Mesoscopic systems — small electric circuits working in quantum regime — offer us a unique experimental stage to explorer quantum transport in a tunable and precise way. The purpose of this Review is to show how they can contribute to statistical physics. We introduce the significance of fluctuation, or equivalently noise, as noise measurement enables us to address the fundamental aspects of a physical system. The significance of the fluctuation theorem (FT) in statistical physics is noted. We explain what information can be deduced from the current noise measurement in mesoscopic systems. As an important application of the noise measurement to statistical physics, we describe our experimental work on the current and current noise in an electron interferometer, which is the first experimental test of FT in quantum regime. Our attempt will shed new light in the research field of mesoscopic quantum statistical physics.

Authors: Nathan Argaman

This Comment argues that two assumptions, which are presented as basic assumptions of Bell’s theorem in [J. Handsteiner et al., Phys. Rev. Lett. 118, 060401 (2017)] and elsewhere, in fact follow from more basic premises. Measurement independence follows from (i) the use of free variables and (ii) the causal arrow of time. Determinism follows from (i) local causality and (ii) perfect correlations (predicted by quantum mechanics). In particular, it is pointed out that the measurement-independence violating toy model of [M.J.W. Hall, Phys. Rev. Lett. 105, 250404 (2010)], is based on a retro-causal model. While this may be controversial, it should be possible to achieve concensus on the much simpler matter of what the basic assumptions of Bell’s theorem are.

Authors: Anha BhatSanjib DeyMir FaizalChenguang HouQin Zhao

We study the correction of the energy spectrum of a gravitational quantum well due to the combined effect of the braneworld model with infinite extra dimensions and generalized uncertainty principle. The correction terms arise from a natural deformation of a semiclassical theory of quantum gravity governed by the Schr\”odinger-Newton equation based on a minimal length framework. The two fold correction in the energy yields new values of the spectrum, which are closer to the values obtained in the GRANIT experiment. This raises the possibility that the combined theory of the semiclassical quantum gravity and the generalized uncertainty principle may provide an intermediate theory between the semiclassical and the full theory of quantum gravity. We also prepare a schematic experimental set-up which may guide to the understanding of the phenomena in the laboratory.

Publication date: Available online 9 May 2017
Source:Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics
Author(s): Silvia De Bianchi
This paper focuses on Hermann Weyl’s two-component theory and frames it within the early development of different theories of spinors and the history of the discovery of parity violation in weak interactions. In order to show the implications of Weyl’s theory, the paper discusses the case study of Ettore Majorana’s symmetric theory of electron and positron (1937), as well as its role in inspiring Case’s formulation of parity violation for massive neutrinos in 1957. In doing so, this paper clarifies the relevance of Weyl’s and Majorana’s theories for the foundations of neutrino physics and emphasizes which conceptual aspects of Weyl’s approach led to Lee’s and Yang’s works on neutrino physics and to the solution of the theta-tau puzzle in 1957. This contribution thus sheds a light on the alleged “re-discovery” of Weyl’s and Majorana’s theories in 1957, by showing that this did not happen all of a sudden. On the contrary, the scientific community was well versed in applying these theories in the 1950s on the ground of previous studies that involved important actors in both Europe and United States.

Authors: Philip PearleAnthony Rizzi

We give a complete quantum analysis of the Aharonov-Bohm (AB) magnetic phase shift involving three entities, the electron, the charges constituting the solenoid current, and the vector potential. The usual calculation supposes that the solenoid’s vector potential may be well-approximated as classical. The AB shift is then acquired by the quantized electron moving in this vector potential. Recently, Vaidman presented a semi-classical calculation, later confirmed by a fully quantum calculation of Pearle and Rizzi, where it is supposed that the electron’s vector potential may be well-approximated as classical. The AB shift is then acquired by the quantized solenoid charges moving in this vector potential. Here we present a third calculation, which supposes that the electron and solenoid currents may be well-approximated as classical sources. The AB phase shift is then shown to be acquired by the quantized vector potential. We next show these are three equivalent alternative ways of calculating the AB shift. We consider the exact problem where all three entities are quantized. We approximate the wave function as the product of three wave functions, a vector potential wave function, an electron wave function and a solenoid wave function. We apply the variational principle for the exact Schrodinger equation to this approximate form of solution. This leads to three Schrodinger equations, one each for vector potential, electron and solenoid, each with classical sources for the other two entities. However, each Schrodinger equation contains an additional real c-number term, the time derivative of an extra phase. We show that these extra phases are such that the net phase of the total wave function produces the AB shift. Since none of the three entities requires different treatment from any of the others, this leads to three alternative views of the physical cause of the AB magnetic effect.

Authors: Philip PearleAnthony Rizzi

Following semiclassical arguments by Vaidman we show, for the first time in a fully quantum mechanical way, that the phase shifts arising in the Aharonov Bohm (A-B) magnetic or electric effects can be treated as due to the electric force of a classical electron, respectively acting on quantized solenoid particles or quantized capacitor plates. This is in contrast to the usual approach which treats both effects as arising from non-field producing potentials acting on the quantized electron. Moreover, we consider the problems of interacting quantized electron and quantized solenoid or quantized capacitor to see what phase shift their joint wave function acquires. We show, in both cases, that the net phase shift is indeed the A-B shift (for, one might have expected twice the A-B shift, given the above two mechanisms for each effect.) The solution to the exact Schrodinger equation may be treated (approximately for the magnetic A-B effect, which we show using a variational approach, exactly for the electric A-B effect) as the product of two solutions of separate Schrodinger equations for each of the two quantized entities, but with an extra phase. The extra phase provides the negative of the A-B shift, while the two separate Schrodinger equations without the extra phase each provide the A-B phase shift, so that the product wave function produces the net A-B phase shift.

Quantum physics: Atomic envoy enables molecular control

Nature 545, 7653 (2017). doi:10.1038/545164a

Authors: Wes Campbell

A technique for manipulating molecules uses an intermediary atom to query a nearby molecule’s energy state and produces ‘quantum superpositions’ of these states, a prerequisite for extremely high-precision spectroscopy. See Letter p.203

Authors: Indrajit Sen

Measurement Independence is an assumption used in foundational arguments since the EPR thought experiment in 1935, and assumed in a majority of hidden variable models of QM. In this thesis we review the crucial role of this assumption in several ontological theorems, develop new measurement dependent models having interesting properties, and a protocol for classical simulation of quantum channels using such a model. In particular, a maximally psi-epistemic model is given which is valid for any dimension of Hilbert space(by violating preparation independence assumption).

Authors: Johannes Mesa Pascasio

With purely classical tools a model for a bouncer-walker system of an elementary particle will be derived in this work which reflects the old idea of de Broglie’s particle-wave duality. This model contains, on the one hand, a possible explanation of the work-energy exchange between the two separated motions, thereby providing an energy quantisation as originally postulated by Max Planck. On the other hand, the system perfectly obeys the Bohmian-type law of motion in full accordance with quantum mechanics.

For the calculation of elementary particles’ trajectories a ballistic diffusion equation will be derived which is a special case of a diffusion equation with a time-dependent diffusivity. Therewith the simulation of spreading of an elementary Gaussian is made easy as will be shown herein.

With these tools one also accounts for Born’s rule for multi-slit systems and develops a set of current rules that directly leads to a new formulation of the guiding equation equivalent to the original one of the de Broglie-Bohm theory. As will be shown in this thesis, this tool reproduces Talbot patterns and Talbot distance for an arbitrary multi-slit system.

Moreover, the sweeper effect is shown to arise when the intensity relation of two beams of a double-slit experiment exhibit a big difference. Then, the low-intensity beam is pushed aside in a sense that its initial propagation straight out of the slit is bent towards the side. A sideways screen as an alternative measurement method is proposed.

Landry, Elaine (2017) Plato Was NOT A Mathematical Platonist. [Preprint]
Weinert, Friedel (2013) EPR and the ‘Passage’ of Time. Philosophia Naturalis, 50 (2). pp. 173-199. ISSN ISSN 0031-8027

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