"Now" in galaxies billions of light years away Lets say we see a red giant that has 10 million years left before going supernova, and it is 100 million light years away from Earth. Would it be incorrect to say that now, that star has long since gone supernova? My understanding is that we have a plane of simultaneity, and the perceived timing of events can be affected by relative motion between objects. Is this effect large enough to make the idea of "now" meaningless at large distances?
 A: The idea of "now" is dependent on relative velocity (this is the "relativity of simultaneity") and so it's entirely coordinate dependent, and thus not physically meaningful -- we have no way of knowing what's happening "now" at a distant point.
In relativity there is an absolute notion of "past" and "future" for any event A, namely the past and future light cones of A, which consist of all events which could influence A / be influenced by A respectively. But there isn't any absolute "present". Everything outside the light cones, including the "present" of all possible coordinate systems at A, is usually just lumped together as "other".
A: In special relativity (ie ignoring any curvature of spacetime), we each have a plane of simultaneity, which is a 3d 'slice' through spacetime corresponding to 'now' where we are. If you and I are moving relative to each other, our respective planes of simultaneity will be tilted relative to each other. Even for very small degrees of tilt, the planes diverge more and more with distance, so that very far away, what you consider to be simultaneous with 'now' can be much later or much earlier that what I consider to be 'now' at that same distance.
Given that, if we are moving relative to each other, we may disagree about whether a distant event has happened- in your frame, the time of the event might be later than 'now', while in my frame it might be earlier.
That means the concept of 'now' is pretty meaningless at great distances. For example, if you bear in mind that the rotation of the Earth causes your velocity relative to the Earth's axis to reverse every 12 hours, your plane of simultaneity tilts back and forth every day. The effect is small, but increases with distance, so the time in a very distant galaxy that corresponds to 'now' for you here on Earth will swing back and forth every day. If you search on the internet for the relativity of simultaneity you will easily find the relevant formula that will allow you to calculate the associated effects.
The key thing is that the effects of tilted planes of simultaneity depend upon distance, and vanish at relatively small distances, so if you and I pass on the street we will each agree that it is 'now' when we meet no matter how quickly we are moving relative to each other.
