Relational EPR

We study the EPR-type correlations from the perspective of the relational interpretation of quantum mechanics. We argue that these correlations do not entail any form of “non-locality”, when viewed in the context of this interpretation. The abandonment of strict Einstein realism implied by the relational stance permits to reconcile quantum mechanics, completeness, (operationally defined) separability, and locality.     

Against ‘Realism’

We examine the prevalent use of the phrase “local realism” in the context of Bell’s Theorem and associated experiments, with a focus on the question: what exactly is the ‘realism’ in ‘local realism’ supposed to mean? Carefully surveying several possible meanings, we argue that all of them are flawed in one way or another as attempts to point out a second premise (in addition to locality) on which the Bell inequalities rest, and (hence) which might be rejected in the face of empirical data violating the inequalities. We thus suggest that the phrase ‘local realism’ should be banned from future discussions of these issues, and urge physicists to revisit the foundational questions behind Bell’s Theorem.     

Weak measurement and Bohmian conditional wave functions

It was recently pointed out and demonstrated experimentally by Lundeen et al. that the wave function of a particle (more precisely, the wave function possessed by each member of an ensemble of identically-prepared particles) can be “directly measured” using weak measurement. Here it is shown that if this same technique is applied, with appropriate post-selection, to one particle from a perhaps entangled multi-particle system, the result is precisely the so-called “conditional wave function” of Bohmian mechanics. Thus, a plausibly operationalist method for defining the wave function of a quantum mechanical sub-system corresponds to the natural definition of a sub-system wave function which Bohmian mechanics uniquely makes possible. Similarly, a weak-measurement-based procedure for directly measuring a sub-system’s density matrix should yield, under appropriate circumstances, the Bohmian “conditional density matrix” as opposed to the standard reduced density matrix. Experimental arrangements to demonstrate this behavior–and also thereby reveal the non-local dependence of sub-system state functions on distant interventions–are suggested and discussed.     

Entanglement and statistical independence for mixed quantum states

We show that three conditions associated with “entanglement,”viz., non-locality, non-factorisability and statistical dependence, are equivalent for pure states, and that non-factorisability and statistical dependence are equivalent for mixed states. Discussion then reinforces the generally held view that the key condition for mixed states is nonseparability.     

Holography and Non-Locality in a Closed Vacuum-Dominated Universe

A closed vacuum-dominated Friedmann universe is asymptotic to a de Sitter space with a cosmological event horizon for any observer. The holographic principle says the area of the horizon in Planck units determines the maximum number of bits of information about the universe that will ever be available to any observer. The wavefunction describing the probability distribution of mass quanta associated with bits of information on the horizon is the boundary condition for the wavefunction specifying the probability distribution of mass quanta throughout the universe. Local interactions between mass quanta in the universe cause quantum transitions in the wavefunction specifying the distribution of mass throughout the universe, with instantaneous non-local effects throughout the universe.     

Non-Linear Quantum Mechanics and High Energy Cosmic Rays

We point out that the presence of energetic cosmic rays above the GZK cutoff may be explained by fundamental non-linearities in quantum mechanics at the Planck level.     

Einstein-Podolsky-Rosen non-separability and Feynman non-locality

It is argued, using the Feynman transition amplitude for the annihilation of an electron-positron pair into two photons, that the Einstein-Podolsky-Rosen non-separability (especially when discussed in polarization terms) and the Feynman non-locality (as exemplified in the case of the electron-positron system) are indeed the same concept. This gives strong support to the view that the EPR correlation occurs through the pair of timelike vectors joining the measurements to the point of severance of the subsystems.An interesting byproduct of the argument is that, given the four energy-momenta and polarization states which are involved, the overall system is in general neither P- nor C-, but is PC-invariant, so that the generalized Landau symmetry concept could have been suggested by quantum electrodynamics.     

Facts,Values and Quanta

Quantum mechanics is a fundamentally probabilistic theory (at least so far as the empirical predictions are concerned). It follows that, if one wants to properly understand quantum mechanics, it is essential to clearly understand the meaning of probability statements. The interpretation of probability has excited nearly as much philosophical controversy as the interpretation of quantum mechanics. 20th century physicists have mostly adopted a frequentist conception. In this paper it is argued that we ought, instead, to adopt a logical or Bayesian conception. The paper includes a comparison of the orthodox and Bayesian theories of statistical inference. It concludes with a few remarks concerning the implications for the concept of physical reality.     

Bell Diagonal and Werner State Generation: Entanglement,Non-Locality,Steering and Discord on the IBM Quantum Computer

We propose the first correct special-purpose quantum circuits for preparation of Bell diagonal states (BDS), and implement them on the IBM Quantum computer, characterizing and testing complex aspects of their quantum correlations in the full parameter space. Among the circuits proposed, one involves only two quantum bits but requires adapted quantum tomography routines handling classical bits in parallel. The entire class of Bell diagonal states is generated, and several characteristic indicators, namely entanglement of formation and concurrence, CHSH non-locality, steering and discord, are experimentally evaluated over the full parameter space and compared with theory. As a by-product of this work, we also find a remarkable general inequality between “quantum discord” and “asymmetric relative entropy of discord”: the former never exceeds the latter. We also prove that for all BDS the two coincide.     

Are there realistically interpretable local theories?

Although it rests on strongly established proofs, the statement that no realistically interpretable local theory is compatible with some experimentally testable predictions of quantum mechanics seems at first sight to be incompatible with a few general ideas and clear-cut statements occurring in recent theoretical work by Griffiths, Omnès, and Ballentine and Jarrett. It is shown here that in fact none of the developments due to these authors can be considered as a realistically interpretable local theory, so that there is no valid reason for suspecting that the existing proofs of the statement in question are all flawed.     

Classical Mechanics and Quantum Mechanics

The Newton equation of motion is derived from quantum mechanics.     

量子理论的诞生和发展——从量子论到量子力学

简要叙述 ,从普朗克 190 0年首次对电磁波提出量子假设到狄拉克 192 8年对电子提出相对论性方程这段时间内 ,量子理论特别是量子力学诞生和发展的演化过程 .内容分黑体辐射和量子假设 ;老量子论的兴与衰 ;第一条通向量子力学的路———对应原理 ,包括矩阵力学 ,狄拉克的q -数 ;第二条通向量子力学的路———波粒二象性 ,波动力学 ;以及量子力学初步成长 (指 192 7年的表象理论、不确定关系、氦原子及氢分子和 192 8年的狄拉克相对性电子理论 )五个部分 .     

纪念普郎克发现量子论100周年

简要地回顾了普郎克发现量子论和由量子论发展为量子力学的简明历程,以及量子力学对科学和人类社会的贡献,讨论了科学创新的评价标准问题,指出量子力学应得到最高的评价,亦即是美学评价标准、学术评价标准和实践评价标准的统一,还讨论了江泽民主席所提出的“三个代表”的理论,指出这一理论应成为评价一切科学工作的根本标准,也是评价我国各方面工作的根本标准,指出我国科学工作除了要集中力量于解决足以影响国民经济或国防建设的全局的8－10个重大科学技术问题外,还要集中一定的力量于看起来是“无用”的基础研究,当前正在发展中的物理学的第四次大突破,就是值得关注的问题之一。     

A Continuous Transition Between Quantum and Classical Mechanics. I

In spite of its popularity, it has not been possible to vindicate the conventional wisdom that classical mechanics is a limiting case of quantum mechanics. The purpose of the present paper is to offer an alternative formulation of mechanics which provides a continuous transition between quantum and classical mechanics via environment-induced decoherence.     

Maximally causal quantum mechanics

We present a new causal quantum mechanics in one and two dimensions developed recently at TIFR by this author and V Singh. In this theory both position and momentum for a system point have Hamiltonian evolution in such a way that the ensemble of system points leads to position and momentum probability densities agreeing exactly with ordinary quantum mechanics     

q-Deformation of algebraic structures of quantum and classical mechanics

There exists a coassociative and cocommutative coproduct in the linear space spanned by the two algebraic products of a classical Hamilton algebra (the algebraic structure underlying classical mechanics [1]). The transition from classical to quantum Hamilton algebra (the algebraic structure underlying quantum mechanics) is anħ-deformation which preserves not only the Lie property of the classical Hamilton algebra but also the coassociativity and cocommutativity of the above coproduct. By explicit construction we obtain the algebraic structures of theq-deformed Hamilton algebras which preserve the said properties of the coproduct. Some algorithms of these structures are obtained and their implications discussed. The problem of consistency of time evolution with theq-deformed kinematical structure is discussed. A characteristic distinction between the parametersħ andq is brought out to stress the fact thatq cannot be regarded as a fundamental constant.     

Foundations of Quantum Mechanics: The Connection Between QM and the Central Limit Theorem

In this paper we unravel the connection between the quantum mechanical formalism and the Central limit theorem (CLT). We proceed to connect the results coming from this theorem with the derivations of the Schrödinger equation from the Liouville equation, presented by ourselves in other papers. In those papers we had used the concept of an infinitesimal parameter x that raised some controversy. The status of this infinitesimal parameter is then elucidated in the framework of the CLT. Finally, we use the formal apparatus developed in our previous papers and the results of the present one to advance an alternative objective interpretation of quantum mechanics in which its relations with the classical framework are made explicit. The relations between our approach and those using the Wigner–Moyal transformation are also addressed.     

Quantum Machine and Semantic Realism Approach: a Unified Model

The Geneva–Brussels approach to quantum mechanics (QM) and the semantic realism (SR) nonstandard interpretation of QM exhibit some common features and some deep conceptual differences. We discuss in this paper two elementary models provided in the two approaches as intuitive supports to general reasonings and as a proof of consistency of general assumptions, and show that Aerts’ quantum machine can be embodied into a macroscopic version of the microscopic SR model, overcoming the seeming incompatibility between the two models. This result provides some hints for the construction of a unified perspective in which the two approaches can be properly placed.