Let us take an observatory with a certain clock and space axes. We may have many still objects in our space with known positions (distances, angles). All of them belong to and constitute our observatory. We observe a moving body by recording time and observed positions, thus we obtain r(t), v(t), where r and v are 3D vectors. Now we may have two situations: non-relativistic and relativistic. In the non-relativistic situation the observed r(t) and v(t) are the instant, actual body data. In the relativistic one r(t) and v(t) are the retarded data. Knowing the light velocity we can always recalculate the “instant” data from retarded r(t), v(t).

 

For directly observed data we must use the Lorentz transformations if we want to recalculate our observed (retarded) data from one observatory to another (where the other data are also retarded or "directly observable" ones). But transforming the “instant” or “actual” data from one RF to another is different: it is just the Galilean transformations. There is no c in the “instant” data by definition.

 

So which data are more fundamental, real or reliable – instant or retarded?

Edited February 17, 201015 yr by Bob_for_short

the instant data can be taken from both reference frames. there is no c in any of them hence both are equally real. just depends on the observers' choice of rf.

When we write the field E(r,t) at a given t, is it an ensemble of instant or differently retarded values?

The perceived events are real for the observer, who is coincident (in space and time) with the photon detection (or emission). His data is already historical, as is all his data. He can only know where the objects were. His calculations for distant objects by tracing light paths only provides apparent positions, i.e. where he thinks they are. Time dilation due to his motion has altered his perception.