Is the Hilbert Space Language Too Rich?
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In order to answer this question, we analyse different phenomena occurring in general experimental set-ups arranged to analyse the properties of some unknown beams of particles. We arrive at the conclusion that sometimes the Hilbert space language appears to be too rich and also that there are some phenomena where the notion of transition probability disappears and any attempt to introduce it leads to the possibility of infinitely many inequivalent descriptions. Our analysis encouraged us to ask the question whether the Hilbert space language is not too rich in the more realistic situations, for example to deal with high-energy elementary particle scattering phenomena. A programme of investigations in that direction is formulated.
In the polemic with axiomatic quantum mechanics it is shown that the pure state concept can be formulated independently of the existence of any maximal filter.
KeywordsHilbert Space Transmission Probability Initial Beam Registration Ratio Usual Quantum
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