I'd like to test for understanding.neufer wrote:
It's not that we don't care...
it's simply that we don't know precisely when the explosion "actually" happened.
Hence, we'll just call the accurately known spacetime interval Δs "the time":https://en.wikipedia.org/wiki/Spacetime wrote:
In four-dimensional spacetime, the analog to distance is the spacetime interval Δs:
of the inertial frame of reference in which they are recorded.
I get the space-time interval (from past physics coursework), and understand where you are coming from. However, we now know that the distance between galaxy clusters and galaxies is expanding at an accelerated rate.
So even though Hubble's constant is about 67.8 km/s per mega parsec (i.e. only discernible at mega-parsec distances and it is a constant), that rate of expansion was only valid for a certain moment in time. 7000 light years is too small a distance for it to be relevant for us observing the evolution of the Veil Nebula, but shouldn't the accelerated expansion of space matter when think about the distance in the past that we are observing?
For example, NGC 1300 is measured as being 70 x 10^6 ly (or about 21.5 mega-parsecs) away. We picture some time To in the past when Earth and NGC 1300 were a given distance Do away from each other, then space expanded between both objects. The expansion moves Earth a distance Dist(t) from the location at To AND it moves NGC 1300 the same amount from the location it had at To. So the current distance between Earth and NGC 1300 is Do + 2 Dist(t). [using spherical coordinates, the motion involves one radial direction] "Dist(t)" means distance as a function of time, and we know this function includes an acceleration term.
Let's say that Do was 10 x 10^6 ly. Then by current time tc, Earth and NGC 1300 have moved apart by 60 x 10^6 ly. Thus: Do + 2 Dist(tc) = 70 x 10^6 ly = 10 + (2x30) mega light years. In this case, the light from NGC 1300 seen on earth at tc did not start its journey 70 x 10^6 ly in the past, rather (10 + 30) = 40 x 10^6 ly.
Do you see a problem with this reasoning?