In some threads here and on other forums it was mentioned that a universe could have no upper speed limit only if it had a preferred frame of reference as opposed to "our" relativity. I'm wondering to what degree could such a universe be designed to "mimic" our own? Could there be a phenomena similar to the Lorentz factor and its consequences (magnetism, blueshift et cetera) but without actual relativity? I want a universe where different frames of reference doesn't lead to time-travel. I have this idea that physics, chemistry etc looks "normal" (but of course isn't) until someone tries to simulate FTL by actually performing the tachyonic antitelephone experiment, but could this be done with "faked" FTL instead of an actual FTL signal, say two devices distanced "n" from each other switching on within less than n/c time interacting with a beam of "relativistic" particles or something?