The Stern-Gerlach Experiment Revisited

The Stern-Gerlach-Experiment (SGE) of 1922 is a seminal benchmark experiment of quantum physics providing evidence for several fundamental properties of quantum systems. Based on today's knowledge we illustrate the different benchmark results of the SGE for the development of modern quantum physics and chemistry. The SGE provided the first direct experimental evidence for angular momentum quantization in the quantum world and thus also for the existence of directional quantization of all angular momenta in the process of measurement. It measured for the first time a ground state property of an atom, it produced for the first time a `spin-polarized' atomic beam, it almost revealed the electron spin. The SGE was the first fully successful molecular beam experiment with high momentum-resolution by beam measurements in vacuum. This technique provided a new kinematic microscope with which inner atomic or nuclear properties could be investigated. The original SGE is described together with early attempts by Einstein, Ehrenfest, Heisenberg, and others to understand directional quantization in the SGE. Heisenberg's and Einstein's proposals of an improved multi-stage SGE are presented. The first realization of these proposals by Stern, Phipps, Frisch and Segr\`e is described. The set-up suggested by Einstein can be considered an anticipation of a Rabi-apparatus. Recent theoretical work is mentioned in which the directional quantization process and possible interference effects of the two different spin states are investigated. In full agreement with the results of the new quantum theory directional quantization appears as a general and universal feature of quantum measurements. One experimental example for such directional quantization in scattering processes is shown. Last not least, the early history of the `almost' discovery of the electron spin in the SGE is revisited.Comment: 50pp, 17 fig

Contribution to understanding the mathematical structure of quantum mechanics

Probabilistic description of results of measurements and its consequences for understanding quantum mechanics are discussed. It is shown that the basic mathematical structure of quantum mechanics like the probability amplitudes, Born rule, commutation and uncertainty relations, probability density current, momentum operator, rules for including the scalar and vector potentials and antiparticles can be obtained from the probabilistic description of results of measurement of the space coordinates and time. Equations of motion of quantum mechanics, the Klein-Gordon equation, Schrodinger equation and Dirac equation are obtained from the requirement of the relativistic invariance of the space-time Fisher information. The limit case of the delta-like probability densities leads to the Hamilton-Jacobi equation of classical mechanics. Many particle systems and the postulates of quantum mechanics are also discussed.Comment: 21 page

Locality for quantum systems on graphs depends on the number field

Adapting a definition of Aaronson and Ambainis [Theory Comput. 1 (2005), 47--79], we call a quantum dynamics on a digraph "saturated Z-local" if the nonzero transition amplitudes specifying the unitary evolution are in exact correspondence with the directed edges (including loops) of the digraph. This idea appears recurrently in a variety of contexts including angular momentum, quantum chaos, and combinatorial matrix theory. Complete characterization of the digraph properties that allow such a process to exist is a long-standing open question that can also be formulated in terms of minimum rank problems. We prove that saturated Z-local dynamics involving complex amplitudes occur on a proper superset of the digraphs that allow restriction to the real numbers or, even further, the rationals. Consequently, among these fields, complex numbers guarantee the largest possible choice of topologies supporting a discrete quantum evolution. A similar construction separates complex numbers from the skew field of quaternions. The result proposes a concrete ground for distinguishing between complex and quaternionic quantum mechanics.Comment: 9 page

The historical origins of corruption in the developing world: a comparative analysis of East Asia

A new approach has emerged in the literature on corruption in the developing world that breaks with the assumption that corruption is driven by individualistic self-interest and, instead, conceptualizes corruption as an informal system of norms and practices. While this emerging neo-institutionalist approach has done much to further our understanding of corruption in the developing world, one key question has received relatively little attention: how do we explain differences in the institutionalization of corruption between developing countries? The paper here addresses this question through a systematic comparison of seven developing and newly industrialized countries in East Asia. The argument that emerges through this analysis is that historical sequencing mattered: countries in which the "political marketplace" had gone through a process of concentration before universal suffrage was introduced are now marked by less harmful types of corruption than countries where mass voting rights where rolled out in a context of fragmented political marketplaces. The paper concludes by demonstrating that this argument can be generalized to the developing world as a whole

Clientelism and corruption: Institutional adaptation of state capture strategies in view of resource scarcity in Greece

How do strategies of state capture adapt to tight fiscal conditions? The article uses a historical institutionalist approach and content analysis to study the case of Greece. Three theoretically relevant patterns of institutional adaptation are unearthed: first, limited resources for state capture do indeed trigger self-limitation initiatives as expected, but these initiatives replace costly benefits with less costly ones. Second, different forms of capture have different implications for the terms of political competition. Third, there is a mutually reinforcing relationship between clientelism and corruption, which becomes pronounced in the creative ways by which strategies of capture adjust to shifting opportunities and constraints. Clients are appointed in state offices and extract bribes directly from citizens. ‘Client corruption’ replaces extraction from the state with extraction through the state, which is less costly for the public finances: the benefit the governing party gives to its clients is the ‘right’ to extract rents for themselves