# Stephan Schlamminger

## The equivalence principle

The equivalence principle (ep) is the principal assumption on which general relativity has been built.

The equivalence principle says that one cannot distinguish between a gravitational field and an accelerated reference frame, as long as the gravitational field is locally uniform. One important consequence of the equivalence principle is that all bodies (independent of mass and composition) have to accelerate with the same rate in an gravitational field. This feature of the equivalence principle is usually called universality of the free fall (uff).

In practice searches for uff violations are reframed as searches for new interactions, that violate the ep. In general, the potential of this putative interaction for two point masses PM1 and PM2 a distance r apart can be written as, where α denotes the strenght relative to gravity, q1/q2 quantify the amount of charge of PM1/PM2, and μ1/μ2 the atomic mass of PM1/PM2, Vn is the Newtonian potential, and λ is the Compton wavelength of the exchange boson, which is a measure of the interaction range.

The two graphs below show the current limit for α as a function of λ. The area above the solid line is excluded with 95% confidence. For the upper graph the baryon (=protons and neutrons) number has been assumed for the charge. For the lower graph the neutron number has been assumed. Note that for infite ranges λ an interactions 10 orders of magnitude weaker than gravity can be excluded.

Key to the lines in the plots:

PU65 | P. G. Roll, R. Krotkov, and R. H. Dicke, Ann. Phys. 26, 442 (1964). |

MSU72 | V. G. Braginsky and V. I. Panov, JETP 34, 463 (1972). |

EW94 | Y. Su et al., Phys. Rev. D 50, 3614 (1994). |

EW99 | G. L. Smith et al., Phys. Rev. D 61, 22001 (2000). |

LLR04 | J. G. Williams, S. G. Turyshev, and D. H. Boggs, Phys. Rev. Lett. 93, 261101 (2004). |

EW08-Ti | S. Schlamminger et al., Phys. Rev. Lett. 100, 041101 (2008). |

EW08 | T. Wagner et al., to be published. |

Presentation given for Phys-294, 4Mar2010 (4.3 MB)

04/30/11