Hi. This question most probably shows my lack of understanding on the topic: why are scalar fields Lorentz invariant? Imagine a field T(x) [x is a vector; I just don't know how to write it, sorry] that tells us the temperature in each point of a room. We make a rotation in the room and now the field is written as T'(x'), where T'(x')=T(x) keeps telling us the temperature at each tile in the room. So, the field is invariant. Now a different example: picture the same room filled with current densities. We have an scalar field J(x) that gives the modulus of the current density at each point. We make an active Lorentz transformation of the room, so our field now becomes J'(x'). By definition, J'(x')=J(x), but the current densities also change at each tile with a Lorentz transformation, so the field should be giving us different numbers. In other words seems to me that this scalar field is not Lorentz invariant.