Perception and calculating when events happened

[pervect]

I know long distances are difficult to determine, that was my point in my first post. But if we determine that an event that we see was a billion light years away "according to our frame", do we then determine that it happened something other than a billion years ago?

Probably not. See for instance "If the Universe is only 14 billion years old, how can we see objects that are now 47 billion light years away?" in Ned Wright's cosmology FAQ at http://www.astro.ucla.edu/~wright/cosmology_faq.html#ct2 for a counterexample. There are events further away than the age of the universe, so this prescription obviously can't work, and the FAQ provides one way of explaining this.

While it's not mentioned in the above FAQ, I think It's also worth noting that the distances cosmologists report are "cosmological distances" computed in cosmological coordinates, rather than Fermi-Normal distances computed in Fermi-Normal coordinates.

Both distances can be thought of as the distance measured by a "chain of observers" each measuring the distance to the next observer via radar "at the same time". What differs is the notion of simultaneity used to create the chain. For cosmological distances all observers are at rest with respect to the Hubble flow - but are thus all moving away from one another, the notion of distance is not equivalent to that of a ruler where all parts are bound together and not moving with respect to each other.