Abstract |
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Instead of assuming a priori that one should be able to measure space and time intervals of arbitrarily small size, it seems more reasonable to introduce the concept of an ultimate limit for the smallest measurable distance, whose value (a) is left unspecified. this leads, however, to a generalization of relativistic quantum mechanics, since one has to consider three universal constants: /b c/, /b h/ and /b a/. The author has considered a lattice for the possible eigenvalues of the space-time coordinates (/b x/, /b y/, /b z/, /b ct/) and replaced the usual differential field equations by finite difference equations. Such a generalization of the Gordon-Klein equation leads to new aspects when the particle energy tends towards /b hc///b a/, as he has shown previously. But this second order finite difference equation is also equivalent to a set of first order finite difference equations, which correspond to a generalization of the usual Dirac equations. It appears, however, that one has to introduce spinors of rank eight, at least, and that this is an expression of the internal degrees of freedom which are associated with spin, charge and a distinction between left and right. |