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Quantum-mechanical implications of thorough probability concept: Fuzzy point particle, finite universe and fuzzy-uncertainty principle

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Lettere al Nuovo Cimento (1971-1985)

Summary

The usual eigenfunctions of co-ordinate and momentum in quantum mechanics are modified so that all wave functions are normalizable and have probability meaning. The co-ordinate q and the momentum p still satisfy qp — pq = iJ and yet they become fuzzy dynamical variables because they no longer have eigenvalues. There emerges a new world picture of fuzzy point particle and finite universe. We obtain a new fuzzy-uncertainty principle: R≲Δq≲S, J/S ≲Δp ≲J/R and ΔqΔp>J, which indicate that the accuracies of co-ordinate and momentum measurements are restricted by a very small radical length R∼10-19cm and a very large cosmic scale S—1010 light-years.

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References

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Authors and Affiliations

  1. Physics Department, Southeastern Massachusetts University, 02747, North Dartmouth, MA

    J. P. Hsu

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  1. J. P. Hsu
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Supported in part by the SMU Research Committee.

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Hsu, J.P. Quantum-mechanical implications of thorough probability concept: Fuzzy point particle, finite universe and fuzzy-uncertainty principle. Lett. Nuovo Cimento 41, 305–310 (1984). https://doi.org/10.1007/BF02739584

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  • DOI: https://doi.org/10.1007/BF02739584

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