Simultaneity doesn't refer to
seeing events at the same time, it is already based on "compensating for info travel distance" (with each observer assuming that info travels at c in their own rest frame). For example, if in the year 2010 as measured by my clocks I see the light from an event which is 10 light-years away as measured by my rulers, and then in the year 2020 I see the light from an event which is 20 light years away, I will label these two events as "simultaneous" in my frame. But if each observer follows a similar procedure for "compensating for info travel distance", they will
disagree about whether events are simultaneously. Take a look at the thought-experiment Einstein uses to illustrate this
here and
here, which is also illustrated in a little animation
http://www.cord.edu/dept/physics/credo/etrain_credo.html , and discussed on pp. 62-63 of Taylor and Wheeler's book
spacetime physics as follows:
I agree, but
if there was a preferred definition of simultaneity, that would require a preferred frame. If we assume there are no preferred frames, there can be no preferred definition of simultaneity.
What do you mean by "shared by all frames" and "not bound by the same apparent time"? Can you give an example?