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# Quantum Mechanics from Focusing and Symmetry

Foundations of Physics (Impact Factor: 1.14). 02/2008; DOI: 10.1007/s10701-008-9239-8

Source: arXiv

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Inge Helland, Apr 05, 2013 Available from: Data provided are for informational purposes only. Although carefully collected, accuracy cannot be guaranteed. The impact factor represents a rough estimation of the journal's impact factor and does not reflect the actual current impact factor. Publisher conditions are provided by RoMEO. Differing provisions from the publisher's actual policy or licence agreement may be applicable.

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**ABSTRACT:**The author starts with the implicit statement that there are as many cultural differences in the world as there are different cultures. These cultural differences may lead (from time to time) to cultural clashes and lack of understanding. Furthermore, these differences even exist in science, although science is considered by many as extremely objective. But Helland claims that large parts of science are far from absolute and culturally independent on the one hand, but on the other hand, science comes as close to the objective ideal as possible by any human endeavor. So what seems worthwhile in her view is a systematic study of the remaining cultural elements in science, and this is the topic of the book. The book is written under the hypothesis that there exists a common mathematical scientific language which can be used in making inference on empirical data and in making predictions. Included in this hypothesis is the quantum theory or at least parts of it. The reason for the inclusion is the so-called epistemological interpretation of quantum mechanics, which is popular among some groups of physicists. The book contains nine chapters and starts with a discussion of the concept of complementarity in qualitative terms, leading to the concept of state space. The following chapter gives a brief introduction into statistical theory for mathematicians as well as for physicists. In chapter three, Helland presents in a rigorous mathematical way concepts from group theory in order to extend standard statistical theory. Chapter four discusses a logical connection between an extended statistical theory and basic quantum theory. A proof of this connection is presented in the fifth chapter. In chapter six, Helland discusses various topics and problems in quantum theory, including entanglement, Bell’s inequality, Planck’s constant, the Schrödinger equation, and various paradoxes among others. The consequences for statistics resulting from the theory developed thus far are explored in chapter seven, and a link to linear models is drawn. In chapter eight the author illustrates that the extensions proposed for statistical theory can be useful in understanding methods developed by other scientific cultures. And in the final chapter nine Helland tries to apply the main way of thinking on the process of learning from data to various everyday learning processes. - [Show abstract] [Hide abstract]

**ABSTRACT:**A new foundation of quantum mechanics for systems symmetric under a compact symmetry group is proposed. The foundation is given by a link to classical statistics and coupled to the concept of parameter. A vector of parameters is called an inaccessible c-variable if experiments can be provided for the single parameter, but no experiment can be provided for . This is related to the concept of complementarity in quantum mechanics, but more generally to contrafactual parameters. Using these concepts and some weak assumption, the Hilbert space of quantum mechanics is constructed. The complete set of axioms of quantum mechanics is provided by proving Born's formula under weak assumptions.Journal of Physics Conference Series 06/2009; 174(1):012031. DOI:10.1088/1742-6596/174/1/012031 - [Show abstract] [Hide abstract]

**ABSTRACT:**Every experiment or observational study is made in a context. This context is being explicitly considered in this book. To do so, a conceptual variable is defined as any variable which can be defined by (a group of) researchers in a given setting. Such variables are classified. Sufficiency and ancillarity are defined conditionally on the context. The conditionality principle, the sufficiency principle and the likelihood principle are generalized, and a tentative rule for when one should not condition on an ancillary is motivated by examples. The theory is illustrated by the case where a nuisance parameter is a part of the context, and for this case, model reduction is motivated. Model reduction is discussed in general from the point of view that there exists a mathematical group acting upon the parameter space. It is shown that a natural extension of this discussion also gives a conceptual basis from which essential parts of the formalism of quantum mechanics can be derived. This implies an epistemological basis for quantum theory, a kind of basis that has also been advocated by part of the quantum foundation community in recent years. Born's celebrated formula is shown to follow from a focused version of the likelihood principle together with some reasonable assumptions on rationality connected to experimental evidence. Some statistical consequences of Born's formula are sketched. The questions around Bell's inequality are approached by using the conditionality principle for each observer. The objective aspects of the world are identified with the ideal inference results upon which all observers agree (epistemological objectivity).