Quantum Mechanics and Computation

In quantum computation non classical features such as superposition states and entanglement are used to solve problems in new ways, impossible on classical digital computers.We illustrate by Deutsch algorithm how a quantum computer can use superposition states to outperform any classical computer. We comment on the view of a quantum computer as a massive parallel computer and recall Amdahls law for a classical parallel computer. We argue that the view on quantum computation as a massive parallel computation disregards the presence of entanglement in a general quantum computation and the non classical way in which parallel results are combined to obtain the final output.     

Quantum Particles as Conceptual Entities: A Possible Explanatory Framework for Quantum Theory

We put forward a possible new interpretation and explanatory framework for quantum theory. The basic hypothesis underlying this new framework is that quantum particles are conceptual entities. More concretely, we propose that quantum particles interact with ordinary matter, nuclei, atoms, molecules, macroscopic material entities, measuring apparatuses,  in a similar way to how human concepts interact with memory structures, human minds or artificial memories. We analyze the most characteristic aspects of quantum theory, i.e. entanglement and non-locality, interference and superposition, identity and individuality in the light of this new interpretation, and we put forward a specific explanation and understanding of these aspects. The basic hypothesis of our framework gives rise in a natural way to a Heisenberg uncertainty principle which introduces an understanding of the general situation of ‘the one and the many’ in quantum physics. A specific view on macro and micro different from the common one follows from the basic hypothesis and leads to an analysis of Schrödinger’s Cat paradox and the measurement problem different from the existing ones. We reflect about the influence of this new quantum interpretation and explanatory framework on the global nature and evolutionary aspects of the world and human worldviews, and point out potential explanations for specific situations, such as the generation problem in particle physics, the confinement of quarks and the existence of dark matter.     

Computer-Supported Resolution of Measurement Conflicts: A Case-Study in Materials Science

Resolving conflicts between different measurements ofa property of a physical system may be a key step in a discoveryprocess. With the emergence of large-scale databases and knowledgebases with property measurements, computer support for the task ofconflict resolution has become highly desirable. We will describe amethod for model-based conflict resolution and the accompanyingcomputer tool KIMA, which have been applied in a case-study inmaterials science. In order to be a useful aid to scientists, the toolneeds to be integrated with other tools in a computer-supporteddiscovery environment. We will give an outline of such acomputer-supported discovery environment and argue that its use mightlead to new ways of doing science, so-called computer regimes.     

Anthropic Fluctuations vs. Weak Anthropic Principle

A modern assessment of the classical Boltzmann-Schuetz argument for large-scale entropy fluctuations as the origin of our observable cosmological domain is given.The emphasis is put on the central implication of this picture which flatly contradicts the weak anthropic principle as an epistemological statement about the universe. Therefore, to associate this picture with the anthropic principle as it is usually done is unwarranted. In particular, Feynman's criticism of theanthropic principle based on the entropy-fluctuation picture is a product of this semantic confusion.     

Applications of quantum statistics in psychological studies of decision processes

We present a new approach to the old problem of how to incorporate the role of the observer in statistics. We show classical probability theory to be inadequate for this task and take refuge in the epsilon-model, which is the only model known to us caapble of handling situations between quantum and classical statistics. An example is worked out and some problems are discussed as to the new viewpoint that emanates from our approach.Supported by the I UAP-III no. 9.     

Data Model and Classification by Trees: The Minimum Variance Reduction (MVR) Method

O (n ⁴), where n is the number of objects. We describe the application of the MVR method to two data models: the weighted least-squares (WLS) model (V is diagonal), where the MVR method can be reduced to an O(n ³) time complexity; a model arising from the study of biological sequences, which involves a complex non-diagonal V matrix that is estimated from the dissimilarity matrix Δ. For both models, we provide simulation results that show a significant error reduction in the reconstruction of T, relative to classical agglomerative algorithms.     

Spin and Wind Directions II: A Bell State Quantum Model

In the first half of this two-part article (Aerts et al. in Found Sci. doi: 10.1007/s10699-017-9528-9, 2017b), we analyzed a cognitive psychology experiment where participants were asked to select pairs of directions that they considered to be the best example of Two Different Wind Directions, and showed that the data violate the CHSH version of Bell’s inequality, with same magnitude as in typical Bell-test experiments in physics. In this second part, we complete our analysis by presenting a symmetrized version of the experiment, still violating the CHSH inequality but now also obeying the marginal law, for which we provide a full quantum modeling in Hilbert space, using a singlet state and suitably chosen product measurements. We also address some of the criticisms that have been recently directed at experiments of this kind, according to which they would not highlight the presence of genuine forms of entanglement. We explain that these criticisms are based on a view of entanglement that is too restrictive, thus unable to capture all possible ways physical and conceptual entities can connect and form systems behaving as a whole. We also provide an example of a mechanical model showing that the violations of the marginal law and Bell inequalities are generally to be associated with different mechanisms.     

Ephemeral Properties and the Illusion of Microscopic Particles

Founding our analysis on the Geneva-Brussels approach to quantum mechanics, we use conventional macroscopic objects as guiding examples to clarify the content of two important results of the beginning of twentieth century: Einstein?CPodolsky?CRosen??s reality criterion and Heisenberg??s uncertainty principle. We then use them in combination to show that our widespread belief in the existence of microscopic particles is only the result of a cognitive illusion, as microscopic particles are not particles, but are instead the ephemeral spatial and local manifestations of non-spatial and non-local entities.     

The Observer Effect

Founding our analysis on the Geneva-Brussels approach to the foundations of physics, we provide a clarification and classification of the key concept of observation. An entity can be observed with or without a scope. In the second case, the observation is a purely non-invasive discovery process; in the first case, it is a purely invasive process, which can involve either creation or destruction aspects. An entity can also be observed with or without a full control over the observational process. In the latter case, the observation can be described by a symmetry breaking mechanism, through which a specific deterministic observational process is selected among a number of potential ones, as explained in Aerts’ hidden measurement approach. This is what is called a product test, or product observation, whose consequences are that outcomes can only be predicted in probabilistic terms, as it is the case in typical quantum measurements. We also show that observations can be about intrinsic (stable) properties of the observed entity, or about relational (ephemeral) properties between the observer and observed entities; also, they can be about intermediate properties, neither purely classical, nor purely quantum. Our analysis allows us to propose a general conceptual characterization of quantum measurements, as observational processes involving three aspects: (1) product observations, (2) pure creation aspects and (3) ephemeral relational properties. We also discuss the important concept of non-spatiality and emphasize some of the differences and similarities between quantum and classical/relativistic observations.     

On the Foundations of Constructive Mathematics – Especially in Relation to the Theory of Continuous Functions

We discuss the foundations of constructive mathematics, including recursive mathematics and intuitionism, in relation to classical mathematics. There are connections with the foundations of physics, due to the way in which the different branches of mathematics reflect reality. Many different axioms and their interrelationship are discussed. We show that there is a fundamental problem in BISH (Bishop’s school of constructive mathematics) with regard to its current definition of ‘continuous function’. This problem is closely related to the definition in BISH of ‘locally compact’. Possible approaches to this problem are discussed. Topology seems to be a key to understanding many issues. We offer several new simplifying axioms, which can form bridges between the various branches of constructive mathematics and classical mathematics (‘reuniting the antipodes’). We give a simplification of basic intuitionistic theory, especially with regard to so-called ‘bar induction’. We then plead for a limited number of axiomatic systems, which differentiate between the various branches of mathematics. Finally, in the appendix we offer BISH an elegant topological definition of ‘locally compact’, which unlike the current definition is equivalent to the usual classical and/or intuitionistic definition in classical and intuitionistic mathematics, respectively.     

量子纠缠及其哲学意义

20世纪90年代以来,兴起了量子信息论,量子纠缠从理论走向实践.量子纠缠是量子信息与量子隐形传态的关键.量子纠缠是一个特殊的超空间、非定域的量子关联.它涉及非定域性、内部时空、个体性、纠缠资源、相互作用、对称性、同一性等一系列重大的哲学问题,拓展出新的哲学意义.     

“南极”术语翻译引发的思考:语言经济原则与非同质术语翻译

在当代的语言环境下,非同质术语做同质化翻译的现象并不鲜见。作者以地理术语南极一词的翻译为例展开讨论,阐明具有不同内涵概念的术语在翻译过程中会被简化为同形异义词,从而违反了术语学一词一义的原则。作者主张,对于非同质术语应力避同质化翻译;概念相近、内涵不同的同类词应有明显区别,专词专译,使它们的中文译名的区别如同英文原名那样鲜明。同时指出,社会文化导向对于非同质术语的正确翻译也是具有一定影响力的,在这一方面应予以重视。     

The ‘Galilean Style in Science’ and the Inconsistency of Linguistic Theorising

Chomsky’s principle of epistemological tolerance says that in theoretical linguistics contradictions between the data and the hypotheses may be temporarily tolerated in order to protect the explanatory power of the theory. The paper raises the following problem: What kinds of contradictions may be tolerated between the data and the hypotheses in theoretical linguistics? First a model of paraconsistent logic is introduced which differentiates between week and strong contradiction. As a second step, a case study is carried out which exemplifies that the principle of epistemological tolerance may be interpreted as the tolerance of week contradiction. The third step of the argumentation focuses on another case study which exemplifies that the principle of epistemological tolerance must not be interpreted as the tolerance of strong contradiction. The reason for the latter insight is the unreliability and the uncertainty of introspective data. From this finding the author draws the conclusion that it is the integration of different data types that may lead to the improvement of current theoretical linguistics and that the integration of different data types requires a novel methodology which, for the time being, is not available.     

Discovering the Principle of Finality in Computational Machines

In this essay we argue that the notion of machine necessarily includes its being designed for a purpose. Therefore, being a mechanical system is not enough for being a machine. Since the experimental scientific method excludes any consideration of finality on methodological grounds, it is then also insufficient to fully understand what machines are. Instead in order to understand a machine it is first required to understand its purpose, along with its structure, in clear parallel with Aristotle’s final and formal causes. Obviously, purpose and structure are not machine components that can physically interact with other components; nonetheless they are essential to understanding their operation. This casts an interesting light on the relationship between mind and body: for just as an artifact’s finality and structure explain its operation, so also consciousness is the explanation—not the efficient cause—of specifically human behavior. What machines and human beings have in common is that, in order to understand them, it is necessary to appeal to the principle of finality. Yet while finality is given and extrinsic in the case of machines, we human beings are characterized by the ability to self-propose our own ends. Since the principle of finality is essential to understanding the production of machines, the traditional view in modern Western philosophy that finality lies beyond the scope of objective/scientific knowledge should be rectified to allow for a genuine science of the artificial. We think a correct understanding of final causality will overcome current resistance to this principle.     

华蘅芳《积较术》数学方法分析

在《积较术》中,基于独特的差分定义,华蘅芳构造了一个与Ｎｅｗｔｏｎ有限差分公式完全不同的差分体系,针对各种数表的使用,华蘅芳设计了一种”乘表相加“的计算方法。算理分析表明,这一算法与近代矩阵乘法一致。对《积较术》 中的数学思想与数学方法的分析,揭示了清末传统数学研究所的生长点及其在向近代数学转变过程的积极意义。     

“南极”术语翻译引发的思考:语言经济原则与非同质术语翻译

在当代的语言环境下,非同质术语做同质化翻译的现象并不鲜见。作者以地理术语“南极”一词的翻译为例展开讨论,阐明具有不同内涵概念的术语在翻译过程中会被简化为同形异义词,从而违反了术语学“一词一义”的原则。作者主张,对于非同质术语应力避同质化翻译;概念相近、内涵不同的同类词应有明显区别,专词专译,使它们的中文译名的区别如同英文原名那样鲜明。同时指出,社会文化导向对于非同质术语的正确翻译也是具有一定影响力的,在这一方面应予以重视。     

Quantum Superpositions and the Representation of Physical Reality Beyond Measurement Outcomes and Mathematical Structures

In this paper we intend to discuss the importance of providing a physical representation of quantum superpositions which goes beyond the mere reference to mathematical structures and measurement outcomes. This proposal goes in the opposite direction to the project present in orthodox contemporary philosophy of physics which attempts to “bridge the gap” between the quantum formalism and common sense “classical reality”—precluding, right from the start, the possibility of interpreting quantum superpositions through non-classical notions. We will argue that in order to restate the problem of interpretation of quantum mechanics in truly ontological terms we require a radical revision of the problems and definitions addressed within the orthodox literature. On the one hand, we will discuss the need of providing a formal redefinition of superpositions which captures explicitly their contextual character. On the other hand, we will attempt to replace the focus on the measurement problem, which concentrates on the justification of measurement outcomes from “weird” superposed states, and introduce the superposition problem which focuses instead on the conceptual representation of superpositions themselves. In this respect, after presenting three necessary conditions for objective physical representation, we will provide arguments which show why the classical (actualist) representation of physics faces severe difficulties to solve the superposition problem. Finally, we will also argue that, if we are willing to abandon the (metaphysical) presupposition according to which ‘Actuality = Reality’, then there is plenty of room to construct a conceptual representation for quantum superpositions.