Home

Introduction

Experiments

Equivalence Principle

What is the EP?

What have we done?

What could we see?

Where are we going?

Inverse Square Law

Spin-Coupled Forces

LISA

Axion Search

Lunar Ranging

Big G

Results

People

Publications

Links

Internal

The Eöt-Wash Group:
Laboratory Tests of Gravitational and sub-Gravitational Physics

Equivalence Principle Violations

The equivalence principle (EP) states that all laws of special relativity hold locally, regardless of the kind of matter involved, and for a long time there was no reason to doubt this. Modern quantum theories, however, often require that at some scale the EP must be violated. Usually, the scale is small, no more than a few centimeters.

What sorts of forces violate the equivalence principle? In a way, one type of EP violation is familiar: any vector field which couples to a mass must violate the equivalence principle. To see this, consider electromagnetism, which is a vector field. There are two electrical charges; a positive charge behaves quite differently from a negative charge in an electric field. The existance of a charge and an anticharge is a general feature of vector fields. Then, if a vector field coupled to mass, there would have to be a mass and an antimass which would behave oppositely in the same gravitational field and therefore violate the EP.

Scalar fields also produce EP violations. Scalar charges, unlike vector charges, are not conserved. The statement of charge conservation for a vector charge is Lorentz invariant. The charge of an object is the integral of the time component of its vector current density, which picks up a factor under Lorentz transformation, over a volume element, which picks up a factor 1/. Therefore, the integral as a whole is Lorentz invariant. For a scalar charge, the relevant integral is a charge density (a Lorentz scalar) integrated over a volume; only the volume picks up a factor under a Lorentz transformation, so scalar charges are not conserved and depend on .

Now, strange things can happen because of that factor. Quarks inside the protons and neutrons are highly relativistic; electrons surrounding the nucleus move more slowly (v/c ~ Z). We therefore expect scalar interactions to be composition dependent, since larger atoms' electrons are much farther away from the nucleus and move much more slowly.

---

© 1987-2008 Eöt-Wash Group. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation, DOE or NASA. Trouble? Comments? Contact cah49#at#u.washington.edu