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

By Günther Ludwig (auth.)

ISBN-10: 3642700292

ISBN-13: 9783642700293

ISBN-10: 3642700314

ISBN-13: 9783642700316

This booklet is the 1st quantity of a two-volume paintings, that's a far better model of a preprint [47] released in German. We search to infer the funda­ psychological options of quantum mechanics exclusively from an outline of macroscopic units. The microscopic structures resembling 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 enhance a basic description of macroscopic platforms by way of trajectories in nation areas. This common description is a foundation for the precise de­ scription of units such as elements, the place the 1st half is performing on the second one. The microsystems are found as platforms transmitting the motion. Axioms which describe normal empirical constructions of the interactions among the 2 elements of every gadget, supply upward push to a derivation of the Hilbert area constitution of quantum mechanics. very likely, those axioms (and accordingly the Hilbert area constitution) may well 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 supply an in depth origin of quantum mechanics but in addition an answer in precept of the measuring problem.

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

Example text

7",. 3) Ym is called the set of "effect processes" or "questions". 1 The following assertions hold for the function Pm: . (i) 0 ~ Pm (a,f) ~ 1. 7", with Pm (a,/o) (iii) For each a E P/", there is an II E Y m with Pm (a, fi) Pm (0 ai'/) = 1=1 = 1. e. ai * 0 and ai n n (iv) For a decomposition a = = o. aj = 0 for i * j) one gets ~ AiPm (:i:~) for all IEYm, where 0 < Ai= Ag.. (a, ai) ~ 1 1 n i=1 (v) For boI. ". (boI. b02) Pm (a,12) for all a E g~. n (vi) For ji = (bo, bi) with bo = n L. U bi (b i n i=1 Pm (a,ji) = 1.

As has already been stated, the order interval [0, Qo] is the set of digital indications on the measuring device Qo. As a subset of &m, this interval [0, Qo] is a Boolean ring well known to computer technologists as the logical switch ring. e. the order interval [0, bo] in ~m which we shall write ~m (b o) and which is a Boolean set ring. Often one denotes (somewhat leger) the b E '~m (b o) as the digital responses of the registration method bo although the mapping &m ~ ~m need not be injective.

E. Qfiner than Qo) means that Q is finer than the "trivial" indication QQ. Hence, the order interval [0, Qo] in ;jm is just the set of all digital indications on the device QQ. 2) are imposed. 110m , We must yet describe the physical fact that the norms of the measuring devices fluctuate statistically. All experimental physicists know this. They take pains to keep these fluctuations as small as possible, but take them into consideration in the "error estimates" of their measurements. 1, then by the additional requirement of a statistics which is involved in the relation denoted below by APS 3.

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An Axiomatic Basis for Quantum Mechanics: Volume 1 Derivation of Hilbert Space Structure by Günther Ludwig (auth.)

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