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We present here a completely operatorial approach, using Hilbert-Schmidtoperators, to compute spectral distances between time-like separated "events ",associated with the pure states of the algebra describing the Lorentzian Moyalplane, using the axiomatic framework given by [13, 14]. The result shows nodeformations of non-commutative origin, as in the Euclidean case.

Spectral Distance on Lorentzian Moyal Plane