1. J. P. Hsu:Nuovo Cimento B,80, 183 (1984);,Lett. Nuovo Cimento,41, 305 (1984).
2. J. P. Hsu:Nuovo Cimento B,78, 85 (1983).
3. J. P. Hsu:Nuovo Cimento B,74, 67 (1983). In the frameF 0, in, whichC=c=3·1010 cm/s, we havep=(mv/c)(1-v 2/c2)−1/2. Note that, numerically,J=h/c.
4. J. A. Wheeler:Einsteins Vision (Berlin, 1968).
5. According to fuzzy quantum mechanics only wave packets whose widths †q satisfyS≳†q≳R can be physically realized in Nature. The postulate †q≳R is related to the physical property that it is hard for a particle to have a momentum much larger thanJ/R. Thus the underlying «fuzzy Hilbert space» does not include all square-integrable functionals, in sharp contrast with the usual Hilbert space. The observablesp andq can be considered as «fuzzy matrices» in the fuzzy Hilbert space. These fuzzy matrices cannot be diagonalized and satisfy a new rule of multiplication which can be seen by the following example (see eq. (7)): $$(\psi |\alpha |\varphi ) = \smallint (\psi |q')D^{ - 2} (\bar p_1 ,m)(q'|\alpha |q'')D^{ - 2} (\bar p_2 ,m)(q''|\varphi )dq'dq'',$$ where $$\bar p_1 = - iJ \partial /\partial q', \bar p_2 = - iJ \partial /\partial q'; (\psi |q'), (q'|\alpha |q'')$$ and (q 2|ϕ) are a row, a square and a column «fuzzy matrix» respectively. This illustrates how physical ideas can be brought to bear on mathematical problems related to the fuzzy set theory and the new fuzzy matrix.