SDSTAFF David:
regarding whether some stars may be burnt out and all we see is the light they emitted long ago, I am not an expert on this but I think the answer is so oversimplified that it comes very close to being erroneous. I do not say it is wrong as I know what you mean and it is the correct oversimplified answer to a very simple question, but…
in the theory of relativity there is no such thing as an absolute concept of now or simultaneously. There is only “absolute before”, “absolute after” and “depends how you look at it”
To say that we do not know how the star looks like “now” maybe a way to express it that we can all understand but strictly speaking it is not true. What you see now is what the star looks like now in space-time. Time is a very elastic concept and there is no such thing as a universal now. Time depends on the conditions of the observer.
An example: suppose I am here on Earth and my cousin is in a spaceship where my light or radio signals take 1 hour to arrive. Further assume he can answer my message instantly. I send him my message and he receives it instantly and sends his reply which I receive instantly and yet from my viewpoint his reply has taken two hours since i sent my message (one hour for my mesage to go there and one more for his reply to get back here). Everything that happened here before I sent my message happened absolutely before. Everything that happened after i received the reply happened absolutely after but, everything that happened between those two events is relative. if my cousin flipped a switch when he received my message, and I flipped a switch after i sent mine but before i received his, there is no absolute answer as to who flipped it first as this depends on the observer.
The concept of simultaneity in relativity is that things that happen along the same ray of light are simultaneous so, from that point of view, you are seeing the star as it is now even if the light took a billion years to get here.
Well, I am not able to express this better. Can someone knowledgeable please do a better job of explaining what I am trying to say?