International Journal of Theoretical Physics, Vol. 45, No. 1, January 2006 ( C  2006) DOI: 10.1007/s10773-005-9018-7 Simple Derivation of Minimum Length, Minimum Dipole Moment and Lack of Space–Time Continuity Christoph Schiller 1 Received April 29, 2005; accepted November 19, 2005 Published Online: May 5, 2006 The principle of maximum power makes it possible to summarize special relativity, quantum theory and general relativity in one fundamental limit principle each. Special relativity contains an upper limit to speed; following Bohr, quantum theory is based on a lower limit to action; recently, a maximum power given by c 5 /4G was shown to be equivalent to the full field equations of general relativity. Taken together, these three fundamental principles imply a limit value for every physical observable, from acceleration to size. The new, precise limit values differ from the usual Planck values by numerical prefactors of order unity. Among others, minimum length and time intervals appear. The limits imply that elementary particles are not point-like and suggest a lower limit on electric dipole values. The minimum intervals also imply that the non-continuity of space–time is an inevitable result of the unification of quantum theory and relativity, independently of the approach used. KEY WORDS: minimum length; minimum electric dipole moment; maximum accel- eration; maximum power; maximum force. PACS numbers: 04.20.Cv; 13.40.Em; 04.60.-m. 1. INTRODUCTION Limit values for physical observables are regularly discussed in the literature. There have been studies of smallest distance and smallest time intervals, as well as largest particle energy and momentum values, largest acceleration values and largest space–time curvature values, among others (Ahluwalia, 1994; Amati et al., 1987; Amelino-Camelia, 1994; Aspinwall, 1994; Doplicher et al., 1994; Garay, 1995; Gross and Mende, 1987; Jaekel and Renaud, 1994; Kempf, 1994a,b; Konishi et al., 1990; Loll, 1995; Maggiore, 1993; Mead, 1964; Ng and Van Dam, 1994; Padmanabhan, 1987; Rovelli and Smolin, 1995; Sch¨ on, 1993; Townsend, 1977). Usually, these arguments are based on limitations of measurement apparatuses tailored to measure the specific observable under study. In the following we argue that all these limit statements can be deduced in a simpler 1 Innere Wiener Strasse 52, 81667 M¨ unchen, Germany; e-mail: cs@motionmountain.net. 221 0020-7748/06/0100-0221/0 C  2006 Springer Science+Business Media, Inc.