Measurement and quantum indeterminateness

Albert and Loewer^[1] have recently clarified their earlier objection to the interactive interpretation presented in Healey^[2]. They now charge that this interpretation fails to solve a problem of which the measurement problem is but a special case. The general problem is to reconcile quantum mechanics with theprima facie determinateness of such dynamical properties as the positions of macroscopic objects. In response I defend both the preeminent significance of determinate measurement outcomes and the claim that the models of Healey^[3] go a long way toward securing their determinateness.1. They note ironically that the proponent of this interpretation must argue that since a natural measure of the set of states whose biorthonormal expansion has equal amplitudes is zero these states should be neglected. In fact these states werenot neglected in Healey^[2] (see pp. 98-100) where I argued that even though the resulting indeterminateness in any such states would be real, it would be rapidly removed by subsequent environmental interactions.     

Formalism and Interpretation in Quantum Theory

Quantum Mechanics can be viewed as a linear dynamical theory having a familiar mathematical framework but a mysterious probabilistic interpretation, or as a probabilistic theory having a familiar interpretation but a mysterious formal framework. These points of view are usually taken to be somewhat in tension with one another. The first has generated a vast literature aiming at a “realistic” and “collapse-free” interpretation of quantum mechanics that will account for its statistical predictions. The second has generated an at least equally large literature aiming to derive, or at any rate motivate, the formal structure of quantum theory in probabilistically intelligible terms. In this paper I explore, in a preliminary way, the possibility that these two programmes have something to offer one another. In particular, I show that a version of the measurement problem occurs in essentially any non-classical probabilistic theory, and ask to what extent various interpretations of quantum mechanics continue to make sense in such a general setting. I make a start on answering this question in the case of a rudimentary version of the Everett interpretation.     

A Testable Theory for the Emergence of the Classical World

The transition from the quantum to the classical world is not yet understood. Here, we take a new approach. Central to this is the understanding that measurement and actualization cannot occur except on some specific basis. However, we have no established theory for the emergence of a specific basis. Our framework entails the following: (i) Sets of N entangled quantum variables can mutually actualize one another. (ii) Such actualization must occur in only one of the 2^N possible bases. (iii) Mutual actualization progressively breaks symmetry among the 2^N bases. (iv) An emerging “amplitude” for any basis can be amplified by further measurements in that basis, and it can decay between measurements. (v) The emergence of any basis is driven by mutual measurements among the N variables and decoherence with the environment. Quantum Zeno interactions among the N variables mediates the mutual measurements. (vi) As the number of variables, N, increases, the number of Quantum Zeno mediated measurements among the N variables increases. We note that decoherence alone does not yield a specific basis. (vii) Quantum ordered, quantum critical, and quantum chaotic peptides that decohere at nanosecond versus femtosecond time scales can be used as test objects. (viii) By varying the number of amino acids, N, and the use of quantum ordered, critical, or chaotic peptides, the ratio of decoherence to Quantum Zeno effects can be tuned. This enables new means to probe the emergence of one among a set of initially entangled bases via weak measurements after preparing the system in a mixed basis condition. (ix) Use of the three stable isotopes of carbon, oxygen, and nitrogen and the five stable isotopes of sulfur allows any ten atoms in the test protein to be discriminably labeled and the basis of emergence for those labeled atoms can be detected by weak measurements. We present an initial mathematical framework for this theory, and we propose experiments.     

QED Derived from the Two-Body Interaction

We have shown in a previous paper that the Dirac bispinor can vary like a four-vector and that Quantum Electrodynamics (QED) can be reproduced with this form of behaviour.⁽¹⁾ In Part I of this paper, we show that QED with the same transformational behaviour also holds in an alternative space we call M-space. We use the four-vector behaviour to model the two-body interaction in M and show that this has similar physical properties to the usual model in L which it predicts. In Part II of this paper we use M-space to show that QED can be reduced to two simple rules for a two-body interaction.     

Can the Statistical Interpretation of Quantum Mechanics be Inferred from the Schrödinger Equation?—Bell and Gottfried

In his paper titled ‘Against “measurement”?’ [Physics World 3(8), 33–40 [1990]], Bell criticised arguments that use the concept of measurement to justify the statistical interpretation of quantum theory. Among these was the text of Gottfried [Quantum Mechanics (Benjamin, New York, [1966])]. Gottfried has replied to this criticism, claiming to show that, for systems with both continuous and discrete degrees of freedom, the statistical interpretation for the discrete variables is implied by requiring that the continuous variables are described classically. In the present paper, Gottfried’s argument is criticised. It is suggested that he takes over aspects of classical physics which are in conflict with the classical limit of the Schrödinger equation. He incorrectly assumes that, in the output from a Stern-Gerlach apparatus, the wave-function of any ion is restricted to one or another of the beams.     

A Transactional Analysis of Interaction-Free Measurements

The transactional interpretation of quantum mechanics is applied to the “interaction-free” measurement scenario of Elitzur and Vaidman and to the Quantum Zeno effect version of the measurement scenario by Kwiat et al. It is shown that the non-classical information provided by the measurement scheme is supplied by the probing of the intervening object by incomplete offer and confirmation waves that do not form complete transactions or lead to real interactions.     

Objectivity in Perspective: Relationism in the Interpretation of Quantum Mechanics

Pekka Lahti is a prominent exponent of the renaissance of foundational studies in quantum mechanics that has taken place during the last few decades. Among other things, he and coworkers have drawn renewed attention to, and have analyzed with fresh mathematical rigor, the threat of inconsistency at the basis of quantum theory: ordinary measurement interactions, described within the mathematical formalism by Schrödinger-type equations of motion, seem to be unable to lead to the occurrence of definite measurement outcomes, whereas the same formalism is interpreted in terms of probabilities of precisely such definite outcomes. Of course, it is essential here to be explicit about how definite measurement results (or definite properties in general) should be represented in the formalism. To this end Lahti et al. have introduced their objectification requirement that says that a system can be taken to possess a definite property if it is certain (in the sense of probability 1) that this property will be found upon measurement. As they have gone on to demonstrate, this requirement entails that in general definite outcomes cannot arise in unitary measuring processes.In this paper we investigate whether it is possible to escape from this deadlock. As we shall argue, there is a way out in which the objectification requirement is fully maintained. The key idea is to adapt the notion of objectivity itself, by introducing relational or perspectival properties. It seems that such a “relational perspective” offers prospects of overcoming some of the long-standing problems in the interpretation of quantum mechanics.     

Low temperature radio-frequency transverse susceptibility measurements using a CMOS oscillator circuit

A transverse susceptibility (TS) measurement system based on a simple inverter CMOS cell oscillator cross-coupled to a LC tank is presented. The system has been implemented to operate at a Quantum Design Physical Properties Measurement System (PPMS). We introduce several improvements with respect to similar currently operating TS measurement equipments. The electronics have been redesigned to use CMOS transistors as active devices, which simplifies the circuit design and enlarge the tuning range, thus making the proposed electronic block more feasible, predictable, and precise. Additionally, we propose a newly designed sample holder, which facilitates the procedure to change a sample and improves reproducibility of the circuit. Our design minimizes the thermal leak of the measuring probe by one order of magnitude, allowing to measure from 1.8 K in standard PPMS systems, thanks to the use of a low temperature beryllium–copper coaxial cable instead of the conventional RG402 Cu coaxial cable employed in the insert for the PPMS in similar systems. The data acquisition method is also simplified, so that the measuring sequences are implemented directly in the PPMS controller computer by programming them in the Quantum Design MultiVu software that controls the PPMS. We present the test measurements performed on the system without sample to study the background signal and stability of the circuit. Measurements on a Gd₂O₃ calibrating sample yield to the estimation of the system sensitivity, which is found to be on the order of 10⁻⁶ emu. Finally, measurements on a TmCo₂ Laves phase sample with a ferrimagnetic transition temperature around 4 K are described, demonstrating that the developed system is well suited to explore interesting magnetic phenomena at this temperature scale.     

Quantum mechanics presented as harmonic analysis

This paper grew out of a desire on the part of its author to be able to explain, for philosophy, the significance of Quantum Mechanics. The traditional formulation, based on Hilbert spaces and operators on them, leaves much to be desired if, for example, one is interested in the theory of physical measurement. (It may fairly be asked what the operation on a state function of partial differentiation really has to do with the actual business of measuring the momentum associated with that state function.) Of great interest here, of course, are the uncertainty relations. They have done much to still the deterministic belief that nature is, at least theoretically, ultimately controllable. They have conjured up again the venerable questions about form versus substance in the theory of matter. They are, then, as fundamental to philosophy today as any other contemporary issue. And yet their explication is deeply problematical because of the relatively complicated form of the usual presentation of these relations. There will be more on this topic in the second section, together with what I believe to be a ‘simplest-possible’ reformulation. The reformulation of Quantum Mechanics which is presented below takes its inspiration from the point of view that measurement (or physical knowledge) requires conservation laws, and that these in turn invariably involve symmetry, and hence groups. Thus, as with the uncertainty relations, a concomitant part of knowledge is an associatedinability to know which arises out of a symmetry group. Less than that is accomplished here. However, Quantum Mechanicsis brought significantly closer to group theory, and ease of interpretation. Further, the techniques are sufficiently simple, mathematically, and in terms of justification of the methods used, that they might well be substituted for the traditional approach for the teaching of this subject to undergraduates.     

Quantum theory as a universal physical theory

The problem of setting up quantum theory as a universal physical theory is investigated. It is shown that the existing formalism, in either the conventional or the Everett interpretation, must be supplemented by an additional structure, the interpretation basis. This is a preferred ordered orthonormal basis in the space of states. Quantum measurement theory is developed as a tool for determining the interpretation basis. The augmented quantum theory is discussed.     

Intrinsic Properties of Quantum Systems

A new realist interpretation of quantum mechanics is introduced. Quantum systems are shown to have two kinds of properties: the usual ones described by values of quantum observables, which are called extrinsic, and those that can be attributed to individual quantum systems without violating standard quantum mechanics, which are called intrinsic. The intrinsic properties are classified into structural and conditional. A systematic and self-consistent account is given. Much more statements become meaningful than any version of Copenhagen interpretation would allow. A new approach to classical properties and measurement problem is suggested. A quantum definition of classical states is proposed.     

超导临界温度级数公式的应用

从超导临界温度级数公式(1)出发,得到了B类超导体同位素效应的表达。在μ^*=0及μ^*≠0时,我们得到了T_c上限的级数表达式,其结果与数值解符合甚好。最后,在μ^*=0时,讨论了T_c与各种谱参数的关系。由级数表达式可以清楚地看出,当固定不同参数时,T_c的行为完全不同,从而统一解释了不同作者关于声子谱对T_c影响的不同结论。我们着重指出,在大多数情况下,级数公式(1)仅取前两项,可作为数值解的很好近似,从而大大简化了级数公式。预计可以由此简化公式出发研究其它问题。 关键词：     

Ultracold Rydberg atoms for efficient storage of terahertz frequency signals using electromagnetically induced transparency

Quantum communication with terahertz (THz) frequency signals has many advantages like reduced attenuation and scintillation effects in certain atmospheric conditions along with very high level of data security. In this work, we propose a scheme to realize Quantum Memory (QM) for efficient storage of terahertz (THz) frequency signals using Electromagnetically Induced Transparency (EIT) in an ultracold atomic medium of ⁸⁷Rb Rydberg atoms prepared in a Two Dimensional Magneto Optical Trap (2D-MOT). The uniqueness of our scheme lies in the choice of the energy levels involved in the EIT process, all three of which have been chosen to be the Rydberg levels (enabling signal beam to be in THz) in a lambda type arrangement. This first of its kind proposal reveals that atomic media are a potential candidate for devising QMs which can store THz frequency signals. We have estimated that the Optical Depth (OD) in our scheme can reach a very high value of 690, very high maximum obtainable storage efficiency (η) of ～99%, the group velocity ($v_g$) can be as low as 5.07 × 10³ m/s, and the Delay Bandwidth Product (DBP) can be as high as 9.5. All of these estimates emphasize the feasibility of our scheme as a QM device for efficient storage of THz pulses.     

The Copenhagen Variant of the Modal Interpretation and Quantum theory of measurement

The implications of the Copenhagen Variant of the Modal Interpretation of Quantum Mechanics are studied in the context of the quantum theory of measurement. Two formulations of this interpretation are discussed. Both of them imply specifications of the notion of measurement which go beyond the minimal calibration condition of a measurement. The weaker one implies some algebraic and topological constrains on the measurement coupling, whereas the stronger formulation of the same interpretation implies that measurements are necessarily of the first kind.     

Solid state and fibre optic laser doppler velocimeters

Laser Doppler velocimetry (LDV) has become established as an important technique for the measurement of velocities of macroscopic objects and fluids: the dynamic range is large (～10^-6-10⁵ ms^-1) and the measurement is absolute and non-invasive. However, the size and cost of LDV has restricted its use in some areas. This paper presents two separate approaches to reduce these problems: we describe a compact LDV system incorporating a solid state laser diode and also an investigation of the feasibility of a fibre optic LDV system in which the conventional optical components are replaced by fibre optics.The experimental arrangement used for the solid state LDV system was of the Doppler difference type; i.e. a system of parallel interference fringes is focused in the measurement volume, so that a particle passing through this volume produces a scattered light signal which is intensity modulated. In its simplest form, the technique cannot determine the direction of motion of the particle, but this difficulty may be overcome by causing the fringes to ‘move’ within the measurement volume with known velocity. In the present experiments, the laser output frequency was modulated by modulating its drive current; since the path lengths of the two beams interfering in the measurement volume were unequal, fringe motion was achieved.The fibre optic LDV experiment was also of the Doppler difference type, and it was demonstrated that the necessary stabilised interference fringe system could be projected using a fibre optic system. An electronic servo was devised to compensate for the random differential thermal drifts in the fibres which would otherwise have produced unacceptable drifts in the fringe pattern.     

Pseudo-Hermitian Approach to Energy-Dependent Klein-Gordon Models

The relativistic Klein-Gordon system is studied as an illustration of Quantum Mechanics using non-Hermitian operators as observables. A version of the model is considered containing a generic coordinate- and energy-dependent phenomenological mass-term m ²(E,x). We show how similar systems may be assigned a pair of the linear, energy-independent left- and right-acting Hamiltonians with quasi-Hermiticity property and, hence, with the standard probabilistic interpretation.     

The Observer Determination

Quantum measurement requires an observer to prepare a specific measuring device among alternatives where the prepared basis of states, representing the device, is the way the observer interprets quantum reality into his macroscopic word. We redefine that observer role through a new concept: The observer determination, that is, a selection between the measurement options facing the observer. Unlike the measurement itself that is rationalized as dictated by nature, the observer determination can neither be measured nor proven to be true or false. In this paper we propose a mathematical formalism demonstrating how to define the observer determination. Moreover, we present a scheme showing how the apparently subjective observer determination transform into a measurable quantity.     

Is the Epistemic View of Quantum Mechanics Incomplete?

One of the most tantalizing questions about the interpretation of Quantum Theory is the objective vs. subjective meaning of quantum states. Here, by focusing on a typical EPR experiment upon which a selection procedure is performed on one side, we will confront the fully epistemic view of quantum states with its results. Our statement is that such a view cannot be considered complete, although the opposite attitude would also pose well-known problems of interpretation.This paper is dedicated to Prof. Franco Selleri on the occasion of his 70th birthday