The last time I heard a lecture on special relativity was more than 30 years ago.
If someone single-handely in one article (1) revises one of the best-tested theories of a century, (2) performs an experiment that defies all standard predictions and (3) derives some new math for ellipses, if this person has no university affiliation, if he is given the last possible time slot in a German physics conference in a subgroup titled 'alternative approaches' (if you have ever organised a conference you know what that means) then the probability is extremely high that he's a crank, a maverick, a quack.
I haven't tried to understand all he writes, but my quack detector has sounded alarm:
(1) Feist's way of citing is quite unconventional (only very old articles and of recent times only more or less popular books).
(2) His way of formulating hypotheses is not that of someone open to refutation but of someone who knows beforehand what he'll find.
(3) He doesn't ask the obvious questions (assuming for the sake of argument he is right) like why the myons arising from cosmic radiation reaching the outer atmosphere can be detected by counters on earth when they on the average only travel for about 600 m without the benefit of relativistic time dilation (I think that is what is alluded to in Susan's post).
There are many lively debates about relativity and some alternative theories (relativity has won all tests yet except for those theories making identical predictions), but this is from a tiny subgroup of relativity revisionists. They are about as right as holocaust revisionists, though I guess much nicer on a personal level.