Some consequences of spacetime fuzziness

Markus P. Müller

Krzysztof Ruebenbauer

Kourosh Nozari, Behnaz Fazlpour

Finite resolution of spacetime at Planck scale gives it a fuzzy structure (the so-called foamy or fractal spacetime). This fuzzy structure of spacetime is a consequence of quantum fluctuation of geometry itself and can be described within non-commutative geometry and some alternative approaches to quantum gravity. In this paper, some consequences of spacetime fuzziness are studied. Due to this fuzzy structure, some basic notions of ordinary quantum mechanics such as position space representation, wave packet broadening during its propagation and coherent states of quantum mechanical systems should be re-examined.

Jan Hilgevoord, Jos Uffink

Sergey Nikolaevich Mayburov

The quantum spacetime and the phase space with fuzzy structure are investigated as the possible quantization formalism. In this theory, the state of the nonrelativistic particle m corresponds to the element of fuzzy ordered set (Foset), i.e. the fuzzy point. Due to Foset partial (weak) ordering, the m space coordinate x acquires principal uncertainty σ x . It is shown that Schrödinger formalism of quantum mechanics can be completely derived from consideration of m evolution in fuzzy phase space with minimal number of axioms.

F. Selleri