Spacetime non-commutativity, generalized uncertainty principle and the ﬁne structure constant Kourosh Nozari * , Behnaz Fazlpour Department of Physics, Faculty of Basic Science, University of Mazandaran, P.O. Box 47416-1467, Babolsar, Iran Accepted 21 April 2006 Communicated by Prof. L. Mavek-Cvnjac Abstract Quantum gravitational eﬀects and spacetime non-commutativity should aﬀect the value of the ﬁne structure con- stant. In this paper, using generalized uncertainty principle, we calculate the modiﬁed ﬁne structure constant in non- commutative spacetime. Ó 2006 Elsevier Ltd. All rights reserved. 1. Introduction Spacetime has a non-commutative structure [1–4]. This non-commutativity has novel implications for the rest of the physics. One of these implications is the possible modiﬁcation of the ﬁne structure constant. Since ﬁne structure constant contains important information regarding the relative strength of fundamental interactions, its numerical value and rel- ative modiﬁcations have their own importance. Recently, from a string theoretical point of view, it has been revealed that in extreme quantum gravity regime, standard uncertainty relation of Heisenberg should be modiﬁed to incorporate quan- tum gravitational eﬀects [5–8]. These extra terms in uncertainty principle are referred as gravitational uncertainties. Here we are going to consider the eﬀects of spacetime non-commutativity on the value of ﬁne structure constant. We use generalized uncertainty principle as our primary input and calculate modiﬁed numerical value of ﬁne structure con- stant. We will show that the value of this modiﬁcation is quantum gravity model dependent and tends to zero when non-commutative and quantum gravity parameters tend to zero. Finally, we discuss the relation between our approach and the other existing approaches to the issue. 2. Fine structure constant in non-commutative space A non-commutative space can be realized by the coordinate operators satisfying ½^ x i ; ^ x j ¼ ih ij ; i; j ¼ 1; 2; 3; ð1Þ 0960-0779/$ - see front matter Ó 2006 Elsevier Ltd. All rights reserved. doi:10.1016/j.chaos.2006.04.050 * Corresponding author. E-mail address: knozari@umz.ac.ir (K. Nozari). Chaos, Solitons and Fractals 31 (2007) 777–781 www.elsevier.com/locate/chaos