Observable Events Curve - World Line

In the preceding posts, Taking Another Look at the Universe, Mathematics for Taking Another Look at the Universe and Concepts in Taking Another Look at the Universe, I raise the notion of maximally distant observed events (MDOEs).  This is in fact how I initially thought of them, and it’s not entirely wrong to do so, so I haven’t gone back to edit out all references to them.  However, when I say “maximally distant”, I mean of all events that we have ever observed out in the universe (noting that, even under the very best of circumstances, we live very slightly in the past due to the time it takes for photons to reach us, be processed and then interpreted to extract useful information), those that we are observing now (same caveat), are the most distant events that happened at the time that they happened (relative to an observational frame of reference) from which photons could have travelled.

It's not as if we can currently observe events that were nearer to us at that time, because the photons have already passed by our location.  Photons from events that were further away have not yet reached us.

Therefore MDOEs are in fact simply “observable events”, which I will refer to in future as OE(s).  The curve given by x'=(ct₀-x).x/ct₀ (for any value of t₀ on the assumption that this is the time between the first event and the time of the observation, in the observational frame of reference) is, similarly, the observable event (OE) curve.

So, to make it perfectly clear, the blue curve below, is the OE curve:

Events below the curve could be thought of as “previously observable events” while those above (but below the grey line) are “future observable events”.  In that sense, the OE curve (and more so the far end of it) could be thought of as a sort of event horizon.

Note that an event should not necessarily be thought of as something happening.  In the sense being used here, an event is a time and location.  There is an implication of something happening because, for an observer to “observe” an event, a photon has to travel to us from that time and location.  However, it is not necessary that the photon be emitted at that event (or “by” that event).

What is entirely possible is that an observed photon was emitted by some sort of phenomenon very close to 13,800 million light years ago.  To reach us, that photon will have travelled through every event that is currently observable to us and would be indistinguishable from a different photon emitted anywhere along that path (so long as it had the appropriate energy/wavelength/frequency at time of emission).

In other words, the OE curve represents a photon’s world line.