Download An Axiomatic Basis for Quantum Mechanics: Volume 1 by Günther Ludwig (auth.) PDF

By Günther Ludwig (auth.)

ISBN-10: 3642700314

ISBN-13: 9783642700316

This e-book is the 1st quantity of a two-volume paintings, that's a more robust model of a preprint [47] released in German. We search to infer the funda­ psychological thoughts of quantum mechanics exclusively from an outline of macroscopic units. The microscopic structures resembling electrons, atoms, and so forth. has to be detected at the foundation of the macroscopic habit of the units. This detection resembles the detection of the dinosaurs at the foundation offossils. during this first quantity we improve a common description of macroscopic structures through trajectories in country areas. This normal description is a foundation for the designated de­ scription of units which includes components, the place the 1st half is performing on the second one. The microsystems are found as platforms transmitting the motion. Axioms which describe basic empirical buildings of the interactions among the 2 elements of every machine, provide upward push to a derivation of the Hilbert house constitution of quantum mechanics. probably, those axioms (and for this reason the Hilbert house constitution) may perhaps fail to explain different nation-states than the constitution of atoms and mole­ cules, for example the "elementary particles". This publication vitamins ref. [2]. either jointly not just provide an in depth starting place of quantum mechanics but additionally an answer in precept of the measuring problem.

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Extra info for An Axiomatic Basis for Quantum Mechanics: Volume 1 Derivation of Hilbert Space Structure

Example text

The elements of K (Y) are also called "ensembles of trajectories". 2). Again one starts from the opinion that a preparation procedure a determines the statistical distribution of the trajectories y = g (x) with x E a. To each k E C (Y) this statistical distribution should assign an expectation value, especially to each k E L(Y) a value from [0, 1]. To each a E 9:" thus corresponds a mapping 32 II Pretheories for Quantum Mechanics LCY) ~[O, I]; and vice versa the statistical distribution of the trajectories is described by Ua .

3 Trajectory Preparation and Registration Procedures 35 Therefore, it suffices to consider instead of Y its compact subset 8m , in order to represent the trajectory effects by continuous functions over 8m and the trajectory ensembles by elements of K(8m). e. of ii, equals the whole 8 m, for k E L (8m) and k =1= 0 follows

Therefore, U a can be extended to all of L (Y) as an affine mapping and thus to all of C (Y) as a linear norm continuous mapping. Consequently, one can identify U a with an element of the Banach space C' (Y) dual to C(¥). From L (Y) ~ [0, 1] follows U a E K (Y) with K (Y) the basis of the base normed Banach space C' (Y) - that is, K (Y) = {u I U E C:" (Y) and (u, 1) = l} with C:" (Y) the positive cone of C' (Y). 2) and therefore the elements of 9:" are called "trajectory preparation procedures".

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