If one admit that the particle has the "real objective(observer independent ?)" trajectory x(t), then if it is "observed" from point O, then, the observed trajectory is x'(t')...One could simplify by taking t'=t, because it is not here an observer transformation. Then, there should exist a relationship of the form x'(t)=x(t-x1(t1)/c)....The problem is that I don't understand anymore the physical intuition that able to say if x1=x or x1=x' and which value t1(=t(?)) should have. Thanks for any simple explanation.