We study the limits to the localizability of events and reference frames in the κ-Minkowski quantum spacetime. Our main tool will be a representation of the κ-Minkowski commutation relations between coordinates, and the operator and measurement theory borrowed from ordinary quantum mechanics. Spacetime coordinates are described by operators on a Hilbert space, and a complete set of commuting observables cannot contain the radial coordinate and time at the same time. The transformation between the complete sets turns out to be the Mellin transform, which allows us to discuss the localizability properties of states both in space and time. We then discuss the transformation rules between inertial observers, which are described by the quantum κ-Poincaré group. These too are subject to limitations in the localizability of states, which impose further restrictions on the ability of an observer to localize events defined in a different observer's reference

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The static spherically symmetric traversable wormholes are analysed in the Einstein-Cartan theory of gravitation. In particular, we computed the torsion tensor for matter fields with different spin S = 0, 1/2, 1, 3/2. Interestingly, only for certain values of the spin the torsion contribution to Einstein-Cartan field equation allows one to satisfy both flaring-out condition and Null Energy Condition. In this scenario traversable wormholes can be produced by using usual (non-exotic) spinning matter.