The continuum problem and reality

Details The continuum problem and reality The continuum problem and reality

2002-04-16

arxiv.org/abs/quant-ph/0204090v6

Physics

Quantum Physics

16 pages, no figures

Scientific paper

Set-theoretical, physical, and intuitive notions of continuum are compared. It is shown that the independence of the continuum hypothesis determines status and properties of the set of intermediate cardinality. The intermediate set is a hierarchy of non-equivalent infinite sets. Its description consist of autonomous theories. In particular, quantum mechanics, classical mechanics, and geometrical optics should be regarded as components of the complete description of the intermediate set. The intermediate sets may be produced as a result of a fission of a continuous interval. The simplest schemes of the fission are considered. Some analogy with the Standard Model is pointed out.

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