A Brief Note on Discrete Space Effects
نویسنده
چکیده
We discuss briefly discrete space effects and show that this leads to space reflection asymmetry and also a minor modification of Einstein’s energy-mass formula. Snyder[1] had shown how it is possible to consider discrete space time consistently with the Lorentz transformation. Discrete space time continues to receive attention over the years from several scholars (Cf. for example [2, 3, 4, 5, 6, 7] for details). Indeed in the Dirac’s relativistic theory of the electron, this discretization is evident averages over the Compton scale are required to eliminate Zitterbewegung effects and non Hermitian position operators and to recover meaningful physics[8, 9] and that includes special relativity. It is in this light that a recent formulation of an electron in terms of a Kerr-Newman metric becomes meaningful[9, 10, 11] and further this leads to a meaningful, if phenomenological mass spectrum [12, 13, 14]. All this pleasingly dovetails with the fact that if the minimum space time cut offs are taken at the Compton scale, then we have a non commutative geometry viz., [x, y] = 0(l) (1) and similar equations, and which further, leads directly to the Dirac equation (Cf.[15] for details). This can be easily seen from the fact that, given (1), the usual infinitessimal coordinate shift in Minkowski space, is, ψ′(xj) = [1 + ıǫ(ıǫljkxk ∂ ∂xj ) + 0(ǫ2)]ψ(xj) (2)
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