Departamento de Fisica, Universidade Federal
C.P.5008, CEP 58059-970, Joao Pessoa, Pb-Brazil
(on leave from A. Friedmann Laboratory for Theoretical Physics, St.Petersburg, Russia)
We consider Yukawa- and power-type interactions inspired by extra dimensional physics with low-energy compactification scale and by the exchange of light and massless elementary particles, such as dilaton, axion, arion, graviphoton, moduli etc, between the atoms of two closely spaced macrobodies. It is argued that within the submillimeter interaction range, where the Casimir force is the dominant background force, the gravitational experiments of the Eotvos- and Cavendish-type do not lead to strong constraints on the parameters of hypothetical interactions predicted by fundamental elementary particle physics. The constraints obtained from the recent Casimir force measurements by means of a torsion pendulum and an atomic force microscope are collected and compared. New constraints are obtained from the first observation of the lateral Casimir force. We show that the experiments with the Casimir force have already given the possibility to strengthen the previously known constraints up to several thousand times within a wide interaction range. Further strengthening is expected in near future. The conclusion is made that the Casimir force measurements have an advantage over the conventional accelerator and gravitational experiments as a search for hypothetical interactions within the submillimeter interaction range.