Abstract: We will cons
ider the question on whether we can determine the structure of space time b
y making measurements near the worldline of an observer. We will consider b
oth active and passive measurements. For the case of passive measurements&n
bsp; one measures the fronts of light sources near the observer. For the ca
se of active measurements we couple Einstein equations with matter or elect
romagnetic fields and formulate the question of determining the structure o
f space time as the problem of recovering the metric from observations of w
aves near the observer. The method applies to several other inverse problem
s for nonlinear equations, for example the equations of nonlinear acoustics
. No previous knowledge of Lorentzian geometry will be assumed.