Ya. B. Zeldovich All-Moscow Seminar of Astrophysicists

Hypothesis of violation of the Newtonian Invers Square Law (ISL) for the gravitational attraction of test masses is discussed. It is considered from the point of view experimental constrains which can be derived from astrophysical and laboratory measurements. A special attention is given to recent laboratoty tests of ISL for small distances (less 0.1 mm), so as it provides an experimental limits for a size of conceivable compact extra dimentions introduced in fundamental theory for explanation so called "hierarchial problems" in the partical physics and cosmology. At the confidetial limit 95% cavendish type experiments confirm the gravitational ISL up to the distances on the order of 10 mkm; Below at the level of 1 mkm measurements of Casimir quantum electrodynamic force also reject an existance of such scale extra dimentions or hypothetical new forces (unknown interactions). For the more small scale the gravitational attraction becames unmesurable and possible limits for extra dimentions might be obtained only from quantum electrodynamic and nuclear experiments.