Toward a microrealistic version of quantum mechanics. Part II

In this paper, possible objections to the propensity microrealistic version of quantum mechanics proposed in Part I are answered. This version of quantum mechanics is compared with the statistical, particle, microrealistic viewpoint, and a crucial experiment is proposed designed to distinguish between these two microrealistic versions of quantum mechanics.Part I of this paper appeared inFound. Phys. 6, 275 (1976).     

Proposal for a quantum delayed-choice experiment

Gedanken experiments help to reconcile our classical intuition with quantum mechanics and nowadays are routinely performed in the laboratory. An important open question is the quantum behavior of the controlling devices in such experiments. We propose a framework to analyze quantum-controlled experiments and illustrate it by discussing a quantum version of Wheeler's delayed-choice experiment. Using a quantum control has several consequences. First, it enables us to measure complementary phenomena with a single experimental setup, pointing to a redefinition of complementarity principle. Second, it allows us to prove there are no consistent hidden-variable theories having "particle" and "wave" as realistic properties. Finally, it shows that a photon can have a morphing behavior between particle and wave. The framework can be extended to other experiments (e.g., Bell inequality).     

Principles of maximally classical and maximally realistic quantum mechanics

Recently Auberson, Mahoux, Roy and Singh have proved a long standing conjecture of Roy and Singh: In 2N-dimensional phase space, a maximally realistic quantum mechanics can have quantum probabilities of no more than N+1 complete commuting cets (CCS) of observables coexisting as marginals of one positive phase space density. Here I formulate a stationary principle which gives a nonperturbative definition of a maximally classical as well as maximally realistic phase space density. I show that the maximally classical trajectories are in fact exactly classical in the simple examples of coherent states and bound states of an oscillator and Gaussian free particle states. In contrast, it is known that the de Broglie-Bohm realistic theory gives highly nonclassical trajectories.     

The Einstein Podolsky Rosen Paradox and Local Hidden—Variables Theories

Einstein's severe critique of quantum mechanics took its ultimate form in the so-called Einstein Podolsky Rosen (EPR) paradox. The latter remained a subject of mere dispute, until a remarkable progress was initiated in 1964 by Bell who showed that quantum mechanical correlations specific for an EPR type experiment cannot be reproduced in any local hidden—variables theory. Afterwards, realistic versions of EPR experiments have been conceived and, in fact, carried out. The objective of the present paper is to give a review of this recent exciting development, both theoretical and experimental, which reveals one of the most striking features of quantum theory, the “quantum interconnectedness of distant systems”.     

Simple Version of the Greenberger-Horne-Zeilinger (GHZ) Argument Against Local Realism

Here is a simple, clear, useful proof that quantum mechanics contradicts Einstein, Podolsky, and Rosen's local realistic assumptions. It is a variant of the powerful argument first worked out by Daniel Mordechai Greenberger, Michael A. Horne, and Anton Zeilinger. This version uses the eigenstates of two orthogonal spin components for three spin-1/2 particles. No operator or matrix algebra is necessary. A novel discussion of the background and history serves to introduce this proof and to place it in the context of Danny's work.     

Bohmian Mechanics and Quantum Information

Many recent results suggest that quantum theory is about information, and that quantum theory is best understood as arising from principles concerning information and information processing. At the same time, by far the simplest version of quantum mechanics, Bohmian mechanics, is concerned, not with information but with the behavior of an objective microscopic reality given by particles and their positions. What I would like to do here is to examine whether, and to what extent, the importance of information, observation, and the like in quantum theory can be understood from a Bohmian perspective. I would like to explore the hypothesis that the idea that information plays a special role in physics naturally emerges in a Bohmian universe.     

Quantum mechanics without the projection postulate and its realistic interpretation

It is widely held that quantum mechanics is the first scientific theory to present scientifically internal, fundamental difficulties for a realistic interpretation (in the philosophical sense). The standard (Copenhagen) interpretation of the quantum theory is often described as the inevitable instrumentalistic response. It is the purpose of the present article to argue that quantum theory doesnot present fundamental new problems to a realistic interpretation. The formalism of quantum theory has the same states—it will be argued—as the formalisms of older physical theories and is capable of the same kinds of philosophical interpretation. This result is reached via an analysis of what it means to give a realistic interpretation to a theory. The main point of difference between quantum mechanics and other theories—as far as the possibilities of interpretation are concerned—is the special treatment given tomeasurement by the projection postulate. But it is possible to do without this postulate. Moreover, rejection of the projection postulate does not, in spite of what is often maintained in the literature, automatically lead to the many-worlds interpretation of quantum mechanics. A realistic interpretation is possible in which only the reality ofone (our) world is recognized. It is argued that the Copenhagen interpretation as expounded by Bohr is not in conflict with the here proposed realistic interpretation of quantum theory.     

New formulation of quantum mechanics

A reformulation of the mathematical foundations of quantum mechanics is presented. This new framework is based on the concepts of measurement, generalized action, and a unique universal influence function. The main axiom is that the probability of a measurement outcome is the sum (or integral) of the influences between pairs of alternatives that result in the outcome when the measurement is executed. The framework provides answers to various puzzling questions of traditional quantum mechanics. Moreover, it gives a realistic model that extends the usual quantum mechanical formalism.     

The variable detection approach: a wave particle Model

The conceptual problems that quantum mechanics poses has been noticed by numerous authors [1]. From the early beginnings it has been questioned even by some of its creators: Planck, Eherenfest, Einstein, Schrödinger and de Broglie [2-9]. The problem of the collapse of the wave function, its compatibility with special relativity, the question of its completeness, the meaning of the uncertainty relations, etc., are some of the points that have still not received a satisfactory answer. Certainly a large part of these problems would not exist if the theory could get a realistic and local formulation.On the other hand, quantum mechanics has proven to be extremely good from a pragmatic point of view. It seems to make sense to create a theory that at the same time is realistic and local and close to quantum mechanics, without coinciding exactly with it, because Bell's theorem [10] forbids explicitly this possibility.The hope of a realistic and local explanation of the world has not been excluded experimentally. However, since the most extended opinion in the scientific community is just the opposite, we shall explain once more where lies the error of their arguments. Section 1 deals with the weak and strong Bell's inequalities, quoting the different approaches to solve the EPR paradox. In Sec. 2 one of these approaches is developed, the one usually called Enhancement or Variable-Detection-Probability Model. In Sec. 3, and with the same approach, we display one of these models that is basically an enrichment of the Einstein-de Broglie's version of quantum mechanics.     

Quantum tunneling times: A crucial test for the causal program?

It is generally believed that Bohm's version of quantum mechanics is observationally equivalent to standard quantum mechanics. A more careful statement is that the two theories will always make the same predictions for any question or problem that is well posed in both interpretations. The transit time of a particle between two points in space is not necessarily well defined in standard quantum mechanics, whereas it is in Bohm's theory since there is always a particle following a definite trajectory. For this reason tunneling times (in a scattering configuration through a potential barrier may be a situation in which Bohm's theory can make a definite prediction when standard quantum mechanics can make none at all. I summarize some of the theoretical and experimental prospects for an unambiguous comparison in the hope that this question will engage the attention of more physicists, especially those experimentalists who now routinely actually do gedanken experiments.     

Violation of Locality Beyond Bell's Theorem for Multiparticle Perfect Correlations

We present the analogous inequalities of Bell's inequality for N-qubit system predicted respectively by realistic theory, quantum mechanics, local theory, local realistic theory, and local quantum theory on the same Bell-type joint experiment. It is shown that quantum mechanics can be interpreted by hidden-variable theories while being incompatible to any local theory. A necessary condition for the separability of N-qubit system is derived.     

Lineshapes in collision-induced absorption

We present the classical and quantum versions of collision induced absorption spectra for three exactly solvable 1-D models, and obtain the asymptotic behaviour at high frequency. It is found that the quantum spectra fall off more slowly than the classical, and for realistic systems, they both fall off more slowly than exponential. An improved version of the Landau-Lifshitz WKB method is suggested as a numerically viable method for calculating the high frequency wing in quantum spectra and is tested on the exactly solvable models. The error is found to be negligible in two models and tolerable in the third model, even for the least classical system. Our discussion of an extension of the method using exact wavefunctions increases its scope beyond the collision induced absorption problem.     

Ground state structure in supersymmetric quantum mechanics

We present a rigorous analysis of the vacuum structure of two models of supersymmetric quantum mechanics. They are the quantum mechanics versions of the two-dimensional N = 1 and N = 2 Wess-Zumino quantum field models. We find that the N = 2 quantum mechanics has degenerate vacua. The space of vacuum states is bosonic, and its dimension is determined by the topological properties of the superpotential.     

The chaotic ball: An intuitive analogy for EPR experiments

Actual realisations of EPR experiments donot demonstrate non-locality. A model is presented that should enable non-specialists as well as specialists to understand how easy it is to find realistic explanations for the observations. The model also suggests new areas where realistic (hidden-variable) models can give valid predictions whilst quantum mechanics fails. It offers straightforward explanations for some anomalies that Aspect was unable to account for, providing perhaps the first experimental evidence that a hidden-variable theory can besuperior to quantum mechanics. The apparent success of quantum mechanics in predicting results is shown to be largely due to the use of unjustifiable and biased analysis of the data. Data that has been discarded because it did not lead to a valid Bell's test may give further evidence that hidden variables exist.     

A POSSIBLE UNIFICATION OF THE COPENHAGEN AND THE BOHM INTERPRETATIONS USING LOCAL REALISM

It is well-known in the physics community that the Copenhagen interpretation of quantum mechanics is very different from the Bohm interpretation. Usually, a local realistic model is thought to be even further from these two, as in its purest form it cannot even yield the probabilities from quantum mechanics by the Bell theorem. Nevertheless, by utilizing the efficiency loophole such a model can mimic the quantum probabilities, and more importantly, in this paper it is shown that it is possible to interpret this latter kind of local realistic model such that it contains elements of reality as found in the Bohm interpretation, while retaining the complementarity present in the Copenhagen interpretation.     

关于本科生量子力学教学的一些体会

简要介绍几年来我给北京大学物理学院三年级本科生讲授"量子力学A"课程的一些经验和体会.为了使学生们能够较为容易地理解量子力学的基本概念和原则,我尝试着从科学史的角度进行讲述,取得了较好的效果.同时,恰当地打一些比喻,对于学生们深刻领会某些相对来说抽象的概念也有很大帮助.     

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 quantum version of the classical Szilard engine

A reinvention of the classical Maxwel demon was proposed by Szilard around the time quantum mechanics was developed. His model continues to attract great interest, especially quantum versions of it. A quantum formulation of the Szilard engine is introduced and investigated here. It is made to operate through specified cycles in such a way that all thermodynamic quantities which pertain to the system can be evaluated exactly in closed form along each sequence of steps through a cycle. It is shown that as a result of the structure of the model, it is possible to calculate and compare various thermodynamic quantities as the engine proceeds around a well defined specific cycle.     

Foundations of quantum probability

This paper presents an overview of the foundations of quantum probability. The main concepts in this theory are measurements and generalized actions. These concepts correspond to the usual quantum observables and states. Probabilities are computed by means of a universal influence function. We first derive the form of the universal influence function and then construct the amplitude and probability of a measurement with respect to a given generalized action. It is shown that traditional quantum mechanics can be derived as a special case of this theory and moreover the theory gives a complete realistic interpretation of quantum mechanics. It is demonstrated that spins of any order can be described within this framework and a realistic solution to the EPR problem can be achieved.