Dear Basudeba,
I highly appreciate your justified criticism of my essay. When I pointed to the relationship between analycity and causality, I referred to what is well known to electrical engineers like me: "... causality implies the analyticity condition is satisfied, and conversely, analyticity implies causality of the corresponding stable physical system", cf. http://en.wikipedia.org/wiki/Kramers%E2%80%93Kronig_relation. When demanding "Analytic in the upper half of the complex plane", mathematics and signal processing usually consider the frequency domain the complex plane.
I did not anticipate possible mistakes by readers like you who are not very familiar with the notion http://en.wikipedia.org/wiki/Analytic_function . Admittedly, we engineers are using the expression analytic signal (http://en.wikipedia.org/wiki/Analytic_signal ) almost synonymous to the representation of an originally one-sided and real-valued signal in complex domain.
Incidentally, http://en.wikipedia.org/wiki/Analytic_continuation is Heaviside's trick.
Thank you for criticizing my use of "analycity" in a too parsimonious and therefore mistakable manner.
While I tend to agree with many of your opinions, I do not consider it helpful to discuss some differences most of which would in the end perhaps boil down to problems I have with your as I guess uncommon terminology. At least I do not see how you are answering questions that arose from my essay. For instance, I would be interested in a further elaboration of the alternative to length contraction that I am suggesting.
Regards,
Eckard