By Günther Ludwig (auth.)

This ebook is the 1st quantity of a two-volume paintings, that's a better 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 platforms similar to electrons, atoms, and so forth. needs 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 strengthen a common description of macroscopic platforms via trajectories in kingdom areas. This normal description is a foundation for the unique de­ scription of units which include elements, the place the 1st half is performing on the second one. The microsystems are found as structures transmitting the motion. Axioms which describe common empirical constructions of the interactions among the 2 elements of every equipment, supply upward push to a derivation of the Hilbert area constitution of quantum mechanics. potentially, those axioms (and for this reason the Hilbert area constitution) could fail to explain different geographical regions than the constitution of atoms and mole­ cules, for example the "elementary particles". This publication supplementations ref. [2]. either jointly not just provide an intensive starting place of quantum mechanics but additionally an answer in precept of the measuring problem.

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

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If one proceeds from a theory as sketched in § I, then Mrn and Y will in any case be viewed as sets of "real facts" ascertained by the pretheories (in the sense of [3] § 10). 4 Y represents a relation between an x E Mrn and some y E Y. e. e.

3 resp. ) that was and and We first introduce the set em={cic=anb, where aEqm,bE~m}' The set a n b precisely pictures "all systems prepared under a for which the digital indication b has occurred". The frequencies with which the different b occur are of physical interest. As a portrait for this we introduce the structure /", of species selection procedure (SP) generated by em (see § I) and assume: APS 6 /m is a structure of species statistical selection procedures (SSP). I"m (al n b lO , a2 n b lO ) = Agm (at.

On Km (Y) = Km (8 m)! One uses to call Em the set of objective properties of the systems from Mm. We shall see in § 5 how this is meant. 4 Y holds, the a E g:r, were just to produce systems x with trajectories g (x) from Y and hence with g (x) from II Pretheories for Quantum Mechanics 36 Sm = Sm n Y. Then, for all u E rp (g~), the u-measure of Sm \Sm should vanish. 3). (J U E U E That (J is of ii-measure zero is equivalent to (J being of u-measure zero for all rpm (g~). Thus (J is also of u-measure zero for all u E Km (Y) = Km (Sm)' and all Km(S",).

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