Charge conservation and Equivalence principle

The THǫμ formalism was developed to study nonmetric theories of gravitation. In this letter we show that theories that violate Local Lorentz Invariance (LLI) or Local Position Invariance (LPI) also violate charge conservation. Using upper bounds on this violation we can put very stringent limits to violations of Einstein Equivalence Principle (EEP). These limits, in turn, severely restrict string-based models of low energy physics. PACS: 4.80Cc, 11.30-J, 4.50+h There are two theoretical frameworks which stand as the milestones of modern physics: the standard model of special relativistic particle physics, and general relativity as the gravitational theory. The former rests on gauge invariance symmetry, while the latter is built geometrically from EEP. Two observational testable laws follow from them: charge conservation (global gauge symmetry) and the weak equivalence principle (invariance of non gravitational laws in locally inertial frames). The local aspects of both schemes can change dramatically if there are long range interactions whose dynamics cannot be influenced in local experiments. One can even expect that local-frame global gauge invariance (not the same as local gauge invariance) as well as EEP may be violated, even if the complete (global) theory satisfy the invariances mentioned above. Regarding possible violations of EEP, a scheme was developed at the beginning of the seventies ([1]) in order to analyze non metric gravitational theories in spherically symmetric static situations. This theoretical scheme, called the THǫμ formalism, has also been used to “prove” Schiffs conjecture [2]. By non metric we mean theories that present long range fields (gravitation like fields) that couple with matter directly, besides the metric (which may still account for part of the gravitational sector of the theory). For instance, if there is a scalar field with long range interactions that couple directly with matter, then in a local falling frame, where the metric reduces to its Minkowskian form, we may still have timeor space-dependent factors in the local dynamics, which could render a non relativistic invariant local lagrangian. Any “external structure” (e.g. Minkowski-metric external structure replaced by the [dynamical] metric in general relativity [3]) such as the fundamental constants can be suspected of hiding long range fields that have frozen at some value, making the fundamental parameters effectively constant. Unification schemes such as superstring theories [4] and Kaluza-Klein theories [5] have cosmological solutions in which the low energy fundamental constants are functions of time (including possibly the speed of light [6, 7]), thus violating LLI and Local Position Invariance (LPI). Fellow of CONICET Member of CONICET