Quantum Mechanics

The Critique of the Quantum Power of Judgement analyzes the a priori principles which underlie the empirical knowledge provided by quantum theory. In contrast to other transcendental approaches to quantum physics, none of the transcendental principles established by Kant is modified in order to cope with the new epistemological situation that arises with the asumption of the quantum postulate. Rather, by considering Bohr's views, it is argued that classical concepts provide the mathematical formalism of quantum theory with physical reference through (...) symbolic analogies in the strict Kantian sense. The main result of the investigation is the determination of the highest principle under which quantum objects are subsumed. This principle states that the conditions of the possibility of the systematic unity of contextual experience are at the same time the conditions of the possibility of quantum objects. Upon this principle rests the possibility of any a priori synthetic knowledge of quantum objects. Therefore, the Critique of the Quantum Power of Judgement yields the prolegomena to any future quantum metaphysics. (shrink)

Since Rescher's earliest publication of the middle 1950's in this field, the philosophy of science has constituted one focus of his interest and preoccupation. Some dozen of Rescher's contributions to the field are published in the present volume, and they combine to convey his favored way of blending empirical data with philosophical theorizing.

"Die vorliegende Fassung des Textes wurde anhand des englischen Originalmanuskriptes von Franco Selleri unter Mitarbeit von Roman U. Sexl erstellt."--T.p. verso.

The author solves open problems in ontology , set theory , mathematics , modal logic . The author details the ontological commitments and implications of said found solutions . The author currently presents the work as art object . The author proves the need for and gives the solution to a new fundamental theory of algebra . The author also provides the correct pronunciation of "prima facie" , a means for remembering the correct pronunciation of "prima facie" , and suggests (...) others adopt the correct pronunciation of -- it's fun to say the word -- "PRiiiiima FA - 'c''a' " . (shrink)

A recent letter1 by van Kampen stimulated an interesting debate2–4 on the interpretation of quantum mechanics. The central theme of the debate was a criticism to the (also recent) presence in the literature of “voluminous discussions” about the interpretation of quantum mechanics. That there still exists such discussion is what van Kampen calls the “scandal of quantum mechanics.” -/- We claim that a weak point in the debate was a lack of a definition of the term interpretation. In the present (...) note, we would like to make this meaning precise and to show how such a clarification is necessary in order to avoid misunderstandings. The concept of interpretation plays a key role in the history of physics, so we hope the present analysis might be helpful to students. -/- Max Jammer,5 in his famous book, The philosophy of quantum mechanics, distinguishes four different meanings of the word interpretation. In what follows, we restrict our attention to only three different meanings, which we now try to clarify. (shrink)

Explores the confusion among physicists at the beginning of the 20th century when experimental findings kept not fitting into their mechanical view of the universe, the theoretical speculations and experimental innovations they responded with, and the new science that emerged. The mathematical details are set apart in boxes to allow nontechnical readers to engage the flow of the narrative uninterrupted. Paper edition (unseen), $29.95. Annotation copyright by Book News, Inc., Portland, OR.

Authoritative appraisals have qualified this book as an “axiomatic” theory. However, given that its essential content is no more than an analogy, its theoretical organization cannot be axiomatic. Indeed, in the first edition Dirac declares that he had avoided an axiomatic presentation. Moreover, I show that the text aims to solve a basic problem (How quantum mechanics is similar to classical mechanics?). A previous paper analyzed all past theories of physics, chemistry and mathematics, presented by the respective authors non-axiomatically. Four (...) characteristic features of a new model of organizing a theory were recognized. A careful examination of Dirac’s text shows that it actually applied this kind of organization of a theory, confirming formally what Kronz and Lupher suggested through intuitive categories (pragmatism and rigour), i.e. Dirac’s formulation of Quantum mechanics represents a distinct theoretical approach from von Neumann’s axiomatic approach. However, since the second edition Dirac has changed his approach: although relying again on analogy, his theory refers to the axiomatic method. Some considerations on the odd paths which led to the present formulation of QM are added. They suggest that a new foundation of this theory needs to be found. (shrink)

Quantum mechanics (QM) predicts probabilities on the fundamental level which are, via Born probability law, connected to the formal randomness of infinite sequences of QM outcomes. Recently it has been shown that QM is algorithmic 1-random in the sense of Martin–Löf. We extend this result and demonstrate that QM is algorithmic $$\omega$$ -random and generic, precisely as described by the ’miniaturisation’ of the Solovay forcing to arithmetic. This is extended further to the result that QM becomes Zermelo–Fraenkel Solovay random on (...) infinite-dimensional Hilbert spaces. Moreover, it is more likely that there exists a standard transitive ZFC model M, where QM is expressed in reality, than in the universe V of sets. Then every generic quantum measurement adds to M the infinite sequence, i.e. random real $$r\in 2^{\omega }$$, and the model undergoes random forcing extensions M[r]. The entire process of forcing becomes the structural ingredient of QM and parallels similar constructions applied to spacetime in the quantum limit, therefore showing the structural resemblance of both in this limit. We discuss several questions regarding measurability and possible practical applications of the extended Solovay randomness of QM. The method applied is the formalization based on models of ZFC; however, this is particularly well-suited technique to recognising randomness questions of QM. When one works in a constant model of ZFC or in axiomatic ZFC itself, the issues considered here remain hidden to a great extent. (shrink)

An Aristotelian philosophy of nature offers an alternative to reduction for the conception of the inter-theoretical relationships between molecular chemistry and quantum mechanics. A basic ingredient for such an approach is an ontology of fundamental causal powers, and this work aims to develop such an ontology by drawing on quantum-chemical entities, particularly, the electron density. This notion is central to the Quantum Theory of Atoms in Molecules, a theory of molecular structure developed by Richard F. W. Bader, which describes molecules (...) and atoms in terms precisely of the electron density. Then, by identifying a philosophical tension in Bader’s discourse about the nature of electron density, the work will analyze this central notion in terms of the categorical/dispositional distinction regarding properties. The central idea is that electron density can be conceived as categorical and dispositional at once, and this very characterization can avoid Bader’s philosophical tension. (shrink)

The main ideas of the EDWs perspective are in Gabriel Vacariu’s PhD thesis posted online by UNSW (Australia) in 2007!!! I have realized the GREATEST discovery in the history of human knowledge: the EDWs! With discovering the EDWs, I have changed everything in Philosophy, Physics and Cognitive Neuroscience! This has been the main reason, so many people have published UNBELIEVABLE similar ideas to my ideas, many years I published my first works! -/- UNBELIEVABLE, many (hundreds) “great” or small thinkers did (...) the same thing in 2006-2007 and later: they published the same ideas, UNBELIEVABLE similar to my ideas from 2002-2005! They believe they would be considered co-authors of the same new framework of thinking. They did not know that many “professors” would do the same thing: they plagiarized my ideas and they hurry up to published their work as soon as possible (in 2006-2007, depending when they discovered my article 2005). So, in the same 2 years, many people “discovered” the same new framework of thinking, the EDWs perspective, each of them did not think that there would be so many other people doing the same thing, that is, many people “discovered” the same new framework (the greatest challenge in the history of human thinking!) in the same period! Such coincidences (the discovery of the EDWs in the same two years!!!) are quite IMPOSSIBLE!! This is the reason nobody quoted my name, but nobody quoted any name who PLAGIARIZED my ideas… In 2006-2007, I was wondering why nobody quote my name, but in fact, they plagiarized my ideas. Nobody discovered this framework of thinking 2500 years, and in 2-3 years, many people discovered it!!!! IMPOSSIBLE!!!! There were some "professors" who published articles/chapters very close to Bohr's complementarity, Dirac, de Broglie's dualism before 2005 (for instance Carlo Rovelli 1996 or Ladyman), but their works were constructed within the "unicorn world" (Universe/world), therefore, these works had nothing in common with the EDWs perspective!!!! In reality, all of them plagiarized my ideas! It was like many people composed Beethoven Fifth’s Symphony, claiming that they never listen Beethoven! Who would be so stupid to believe them? (shrink)

One of the key episodes of history of modern physics – Paul Dirac’s startling contrivance of the relativistic theory of the electron – is elicited in the context of lucid epistemological model of mature theory change. The peculiar character of Dirac’s synthesis of special relativity and quantum mechanics is revealed by comparison with Einstein’s sophisticated methodology of the General Relativity contrivance. The subtle structure of Dirac’s scientific research program and first and foremost the odd principles that put up its powerful (...) heuristics is scrutinized with special emphasis on the highly controversial tenet of “mathematical beauty.” It is contended that despite the relentless Dirac’s remarks denigrating the controversial role of philosophy one can trace its indirect influence through Arthur Eddington’s and Hermann Weyl’s whimsical mathematical models. Accordingly, the milestones of Dirac’s research programme realization in the distinctive context of the applied epistemological doctrine are indicated. (shrink)

The main ideas of the EDWs perspective are in Gabriel Vacariu’s PhD thesis posted online by UNSW (Australia) in 2007!!! I have realized the GREATEST discovery in the history of human knowledge: the EDWs! With discovering the EDWs, I have changed everything in Philosophy, Physics and Cognitive Neuroscience! This has been the main reason, so many people have published UNBELIEVABLE similar ideas to my ideas, many years I published my first works! -/- UNBELIEVABLE, many (hundreds) “great” or small thinkers did (...) the same thing in 2006-2007 and later: they published the same ideas, UNBELIEVABLE similar to my ideas from 2002-2005! They believe they would be considered co-authors of the same new framework of thinking. They did not know that many “professors” would do the same thing: they plagiarized my ideas and they hurry up to published their work as soon as possible (in 2006-2007, depending when they discovered my article 2005). So, in the same 2 years, many people “discovered” the same new framework of thinking, the EDWs perspective, each of them did not think that there would be so many other people doing the same thing, that is, many people “discovered” the same new framework (the greatest challenge in the history of human thinking!) in the same period! Such coincidences (the discovery of the EDWs in the same two years!!!) are quite IMPOSSIBLE!! This is the reason nobody quoted my name, but nobody quoted any name who PLAGIARIZED my ideas… In 2006-2007, I was wondering why nobody quote my name, but in fact, they plagiarized my ideas. Nobody discovered this framework of thinking 2500 years, and in 2-3 years, many people discovered it!!!! IMPOSSIBLE!!!! There were some "professors" who published articles/chapters very close to Bohr's complementarity, Dirac, de Broglie's dualism before 2005 (for instance Carlo Rovelli 1996 or Ladyman), but their works were constructed within the "unicorn world" (Universe/world), therefore, these works had nothing in common with the EDWs perspective!!!! In reality, all of them plagiarized my ideas! It was like many people composed Beethoven Fifth’s Symphony, claiming that they never listen Beethoven! Who would be so stupid to believe them? (shrink)

In a recent paper (Berry in Eur J Phys 42: 015401, 2020), the boundaries of superoscillatory regions (the regions where a function oscillates faster than its fastest Fourier component) of waves described by the Helmholtz equation in a uniform medium were related to zeros of the quantum potential, arising in the Madelung formulation of quantum mechanics. We generalize this result, showing that the relativistic counterpart, which is, essentially, a Klein-Gordon equation, exhibits the same behaviour, but in spacetime, giving rise to (...) anomalous values for the local mass (instead of local momenta, in the classical case). This amounts to the generalization of the condition for superoscillations from the magnitude of a vector, to the norm of a four-vector. For a photon, boundaries of superoscillatory regions are surfaces on which the photon’s trajectory is locally light-like, separating time-like and space-like regions, which correspond to real and imaginary local mass, respectively. (shrink)

Dynamic quantum logic (DQL) is studied to represent the proposition of dynamism in quantum information theory as traditional quantum logic cannot deal with it. Although DQL includes many important notions for quantum physics and quantum information theory, there are still missing elements. Some concepts of measuring a specific physical quantity cannot be represented in the exiting DQL. In this study, we add a new concept of measurement to DQL, and discuss the property of this new logic.

In 1966, Paul Feyerabend published a short essay on the relation between dialectical materialist philosophy and Niels Bohr’s quantum theory, in which he develops several provocative ideas about the relations between science, ideology and society. I use Feyerabend’s essay to construct an account of his ‘Dadaist’ philosophical methodology. I argue that Dadaism is an ironic form of intellectual seriousness, such that the Dadaist is prepared to take any idea or practice seriously as a potentially valuable contribution to collective human thought (...) and action (despite any diverging personal convictions), especially if they find such engagement to be lacking in their local culture. I identify a weakness in Feyerabend’s formulation of Dadaism, so far as it is conceived as a matter of individual epistemic character and thus fails to account for the role of the social structure of intellectual activity. This weakness can be remedied by supplementing philosophical Dadaism with descriptions of the kinds of institutions and incentive structures that might cultivate its constitutive epistemic dispositions. (shrink)

Karl Popper and Paul Feyerabend were among the most influential philosophers of science of the twentieth century. Extensive studies have been dedicated to the development of their controversial relationship, which saw Feyerabend turning from a student and supporter of Popper to one of his harshest critics. Yet, it is not as well known that the rift between Popper and Feyerabend arose mainly in the context of their studies on the foundations of quantum mechanics, which has been the main subject of (...) their discussions for about two decades. This paper reconstructs in detail their diatribe over the foundations of quantum mechanics, emphasising also the major role that their personal relationship played in their distancing. (shrink)

The paper explains why the de Broglie-Bohm theory reduces to Newtonian mechanics in the macroscopic classical limit. The quantum-to-classical transition is based on three steps: (i) interaction with the environment produces effectively factorized states, leading to the formation of effective wave functions and hence decoherence; (ii) the effective wave functions selected by the environment–the pointer states of decoherence theory–will be well-localized wave packets, typically Gaussian states; (iii) the quantum potential of a Gaussian state becomes negligible under standard classicality conditions; therefore, (...) the effective wave function will move according to Newtonian mechanics in the correct classical limit. As a result, a Bohmian system in interaction with the environment will be described by an effective Gaussian state and–when the system is macroscopic–it will move according to Newtonian mechanics. (shrink)

At the heart of chemistry lies the periodic system of chemical elements. Despite being the cornerstone of modern chemistry, the overall structure of the periodic system has never been fully understood from an atomic physics point of view. Group-theoretical models have been proposed instead, but they suffer from several limitations. Among others, the identification of the correct symmetry group and its decomposition into subgroups has remained a problem to this day. In an effort to deepen our limited understanding of the (...) periodic law, we have extended the traditional Lie algebraic framework to account for the peculiar degeneracy structure of the periodic system. Starting from the four-dimensional hidden symmetry and accidental degeneracy of the hydrogen atom, as first revealed by Fock in 1935, our research has mainly focussed on the way this SO(4) symmetry of the Coulomb potential gets broken in the periodic system as a consequence of the transformation of the hydrogenic (n, l) filling order to the Madelung (n+l, n) order due to electronic repulsions, relativistic effects and spin-orbit couplings. In this PhD dissertation, a new left-step format of the periodic table is first proposed on the basis of the Madelung rule. Following the particle physics tradition, the chemical elements are then considered as various states of some 'atomic matter', which is described by a non-compact spectrum-generating dynamical Lie group. The chemical elements are shown to form a basis for a single infinite-dimensional degeneracy space of the SO(4,2) ⊗ SU(2) group. An explanation for the period doubling is then proposed in terms of a particular symmetry breaking of the SO(4,2) group to the anti de Sitter SO(3,2) group. The Madelung rule is rationalised on the basis of nonlinear Lie algebras which reflect the screening of the Coulomb hole. This opens new perspectives for a symmetry-based understanding of how the periodic law emerges from its quantum mechanical foundations, and holds the future promise of complementing our current phenomenological approach by a direct atomic physics approach. (shrink)

Research and engineering in the quantum domain involve long chains of activity involving theory development, hypothesis formation, experimentation, device prototyping, device testing, and many more. At each stage multiple paths become possible, and of the paths pursued, the majority will lead nowhere. Our quantum metascience approach provides a strategy which enables all stakeholders to gain an overview of those developments along these tracks, that are relevant to their specific concerns. It provides a controlled vocabulary, built out of terms that are (...) designed to be maximally comprehensible to all groups of stakeholders and across all the sub-fields of the quantum domain. (shrink)

本书受教育部2004年哲学社会科学研究重大课题攻关项目“当代科学哲学的发展趋势研究”(04JZD0004)、国家社会科学基金项目“测量难题的模态解释——量子力学前沿中的哲学问题”(05CZX008)和 教育部人文社会科学重点研究基地——山西大学科学技术哲学研究中心基金资助.

Following an article by John von Neumann on infinite tensor products, we develop the idea that the usual formalism of quantum mechanics, associated with unitary equivalence of representations, stops working when countable infinities of particles (or degrees of freedom) are encountered. This is because the dimension of the corresponding Hilbert space becomes uncountably infinite, leading to the loss of unitary equivalence, and to sectorisation. By interpreting physically this mathematical fact, we show that it provides a natural way to describe the (...) “Heisenberg cut”, as well as a unified mathematical model including both quantum and classical physics, appearing as required incommensurable facets in the description of nature. (shrink)

This book develops new forms of logic: Operator Logic, Probabilistic Operator Logic and Quantum Operator Logic. It then proceeds to create a new view of metaphysics, Relativistic Quantum Metaphysics, for physical Reality. It then derives the form of The Standard Model of Elementary Particles. In particular it derives the origin of parity violation, the origin of the Strong interactions, and the origin of its peculiar symmetry. Also developed are new formalisms for Logic that are of interest in themselves. While mathematics (...) is essential in the latter stages of the book it is presented with sufficient text discussion to make what it is doing understandable to the non-mathematical reader. Generally the jargon of Philosophy, Logic and Physics is avoided as much as possible. But the second part of this book is very mathematical of necessity. In it the form of The Standard Model is derived in detail from a fundamental set of principles. (shrink)

科学の最先端として「物理学の世紀」を演出し、医療やIT、情報工学などさまざまな分野を革新し続けている量子力学。しかしその理論は直観的にはまったく「理解できない」ものだった。量子力学の登場で、世界は、そ して科学の意味はいかに変わったのか...。いままで誰も語れなかった「本当の」量子物理学の世界。.

Se concentrant sur les differences entre la constitution de l'objectivite dans la mecanique classique et dans la mecanique quantique, cet ouvrage explore les interpretations transcendantales de la theorie quantique standard. Patricia Kauark-Leite y examine les changements epistemologiques apportes par la physique quantique pour verifier si la philosophie transcendantale est toujours valide. Elle dresse un bilan des differentes approches transcendantales, montrant les modulations des principes a priori pour expliquer le probleme de l'objectivation en mecanique quantique. En conclusion, l'auteur defend et adopte (...) une interpretation pragmatique transcendantale, dont la tache principale est de donner une justification philosophique a la dimension necessairement intersubjective de l'objectivite quantique. (shrink)

Quantum Systems in Chemistry and Physics: Progress in Methods and Applications is a collection of 33 selected papers from the scientific contributions presented at the 16th International Workshop on Quantum Systems in Chemistry and Physics (QSCP-XVI), held at Ishikawa Prefecture Museum of Art in Kanazawa, Japan, from September 11th to 17th, 2011. The volume discusses the state of the art, new trends, and the future of methods in molecular quantum mechanics and their applications to a wide range of problems in (...) physics, chemistry, and biology. The breadth and depth of the scientific topics discussed during QSCP-XVI appears in the classification of the contributions in six parts: I. Fundamental Theory II. Molecular Processes III. Molecular Structure IV. Molecular Properties V. Condensed Matter VI. Biosystems. Quantum Systems in Chemistry and Physics: Progress in Methods and Applications is written for advanced graduate students as well as for professionals in theoretical chemical physics and physical chemistry. The book covers current scientific topics in molecular, nano, material, and bio sciences and provides insights into methodological developments and applications of quantum theory in physics, chemistry, and biology that have become feasible at end of 2011. (shrink)

Introduction -- Quantum information: basic relevant concepts and applications -- Theory -- Part I. Atomic processes -- Coulombic entanglement: one-step single photoionization of atoms -- Coulombic entanglement: one-step double photoinonization of atoms -- Coulombic entanglement: two-step double photoinonization of atoms -- Fine-structure entanglement: bipartite states of flying particlees with rest mass different from zero -- Bipartite states and flying electronic qubits -- Part II. Molecular processes -- One-step double photoionization of molecules -- Two-step double photoionization of molecules -- Part III. (...) Miscellaneous -- Conclusions and prospectives. (shrink)

Written for advanced undergraduates, physicists, and historians and philosophers of physics, this book tells the story of the development of our understanding of quantum phenomena through the extraordinary years of the first three decades of the twentieth century. Rather than following the standard axiomatic approach, this book adopts a historical perspective, explaining clearly and authoritatively how pioneers such as Heisenberg, Schrodinger, Pauli and Dirac developed the fundamentals of quantum mechanics and merged them into a coherent theory, and why the mathematical (...) infrastructure of quantum mechanics has to be as complex as it is. The author creates a compelling narrative, providing a remarkable example of how physics and mathematics work in practice. The book encourages an enhanced appreciation of the interaction between mathematics, theory and experiment, helping the reader gain a deeper understanding of the development and content of quantum mechanics than any other text at this level. (shrink)

Introduction: The law of causality and its methodology -- Recent causal realism in quantum physics -- The law of causality : Hume, Quine and quantum physics -- Ontological and probabilistic causalisms -- Laplacean causalism in quantum physics -- Ontological commitment in quantum physics -- Causality in some quantum experiments -- Interpretations of important results in quantum physics -- Causality in the EPR paradox: Part 1. The physics -- Causality in the EPR paradox: Part 2. The physical ontology -- Causality in (...) a new double slit experiment and in EPR -- Causality in the special theory of relativity -- Micro-physical and cosmic causal continuity -- Conclusion: Causal ubiquity in the micro-world. (shrink)

Recently the interest in Bohm realist interpretation of quantum mechanics has grown. The important advantage of this approach lies in the possibility to introduce non-locality ab initio, and not as an "unexpected host". In this book the authors give a detailed analysis of quantum potential, the non-locality term and its role in quantum cosmology and information. The different approaches to the quantum potential are analysed, starting from the original attempt to introduce a realism of particles trajectories (influenced by de Broglie's (...) pilot wave) to the recent dynamic interpretation provided by Goldstein, Durr, Tumulka and Zanghì, and the geometrodynamic picture, with suggestion about quantum gravity. Finally we focus on the algebraic reading of Hiley and Birkbeck school, that analyse the meaning of the non-local structure of the world, bringing important consequences for the space, time and information concepts. (shrink)

The theory of Lebesgue and Sobolev spaces with variable integrability is experiencing a steady expansion, and is the subject of much vigorous research by functional analysts, function-space analysts and specialists in nonlinear analysis. These spaces have attracted attention not only because of their intrinsic mathematical importance as natural, interesting examples of non-rearrangement invariant function spaces but also in view of their applications, which include the mathematical modeling of electrorheological fluids and image restoration.The main focus of this book is to provide (...) a solid functional analytic background for the study of differential operators on spaces with variable integrability. It includes some novel stability phenomena which the authors have recently discovered.At the present time, this is the only book which focuses systematically on differential operators on spaces with variable integrability. The authors present a concise, natural introduction to the basic material and steadily move toward differential operators on these spaces, leading the reader quickly to current research topics. (shrink)

Die Quantentheorie stellt eines der anspruchsvollsten und erfolgreichsten Theorieprojekte der Menschheitsgeschichte dar. Sie ist eine, wenn nicht die Universaltheorie der Physik. Die Geschichte ihrer Deutung und die Auseinandersetzung um ihre Interpretation berührt jedoch weitaus mehr als nur das Feld der theoretischen Physik. Eine solche Theorieanlage zerstört ontologische Gewissheiten. Sie stellt den Beobachter in Frage und sie lässt uns ahnen, was zu erwarten ist, wenn wir uns in anderen Feldern mit komplexen Phänomenen beschäftigen, die mit der Beobachterproblematik infiziert sind. Als transklassische (...) Physik ist die Quantentheorie gleichsam auf "Welten ohne Grund" gebaut und enttäuscht damit die Hoffnung, sich Sinnfragen durch die Physik oder Mathematik entledigen zu können. Homolog zu den Hochformen mystischer Reflexion kann uns die Auseinandersetzung um die Deutung der Quantenphysik allerdings eine Ahnung vermitteln, was das Geheimnis der konditionierten Koproduktion von System und Umwelt - Reflexion und Welt - für uns bedeuten kann, und uns möglicherweise dabei helfen, in Welten ohne Grund heimisch zu werden. Hierbei wird deutlich, dass hochgetriebene Theorie, die sich in ihren Abstraktionen in hohem Maße von der lebensweltlichen Wirklichkeit löst, nicht im Widerspruch zur Möglichkeit von Welterkenntnis steht. Im Gegenteil, erst ein hinreichend elaboriertes und mit eigenen, intern konditionierten Konsistenzzwängen ausgestattetes Theoriegebilde stellt die Bedingung zur Möglichkeit von Reflexion und Erkenntnisgewinnung dar. (shrink)