Is time continuous?

Details Is time continuous? Is time continuous?

2006-05-18

arxiv.org/abs/cond-mat/0605456v1

Physics

Condensed Matter

Other Condensed Matter

5-pages 1-figure To be submitted to Physical Review Letters

Scientific paper

Conventional time is modelled as the one dimensional continuum R^1 of real numbers. This continuity, however, does {\em not} stem from {\em any} fundamental principle. On the other hand, natural time is {\em not} continuous and its values as well as those of the energy, form {\em countable} sets, i.e., with cardinalities either finite or equal to \aleph_0, where this symbol stands for the {\em transfinite} number of natural numbers. For infinitely large number of events, the values of natural time form a {\em denumerable} set, i.e., its cardinality is exactly \aleph_0, while those of conventional time an {\em uncountable} set. This has a drastically larger cardinality, which in the light of the continuum hypothesis becomes equal to 2^{\aleph_0}.

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