Abstract:
The basic idea in bi-metric models is that different fields experience different effective metrics. In the context of effective field theories describing fermions 
in a non-trivial vacuum, we find that that the concept of two metrics is difficult to maintain in a quantum theory. As an example of non-trivial vacuum we study 
the case of fermions coupled to fixed external backgrounds that could be remnants from quantum gravity models. Specifically we can show that beyond tree level, 
radiative corrections to particle propagation typically induce higher-order terms that are incompatible with an effective-metric interpretation. This would imply, 
for example, that the trajectory of the particle is not a geodesic with respect to some metric.