Why the Length of a Quantum String Cannot Be Lorentz Contracted

• Main Authors: Antonio Aurilia, Euro Spallucci
• Format: Article
• Language: English
• Published: Hindawi Limited 2013-01-01
• Series: Advances in High Energy Physics
• Online Access: http://dx.doi.org/10.1155/2013/531696

We propose a quantum gravity-extended form of the classical length contraction law obtained in special relativity. More specifically, the framework of our discussion is the UV self-complete theory of quantum gravity. We show how our results are consistent with (i) the generalized form of the uncertainty principle (GUP), (ii) the so-called hoop-conjecture, and (iii) the intriguing notion of “classicalization” of trans-Planckian physics. We argue that there is a physical limit to the Lorentz contraction rule in the form of some minimal universal length determined by quantum gravity, say the Planck Length, or any of its current embodiments such as the string length, or the TeV quantum gravity length scale. In the latter case, we determine the critical boost that separates the ordinary “particle phase,” characterized by the Compton wavelength, from the “black hole phase,” characterized by the effective Schwarzschild radius of the colliding system.