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According to relativity, there is no simultaneous "now" throughout the universe. I assume a question about whether an event has happened in a sense might be invalid as the block universe is a static object. Imagine the question "what happens in Andromeda now?", is that an invalid question? What about "what happens in New York now?"? Or, what about "what happened at the big bang?"?

I am trying to wrap my head around which statements can be made regarding an arbitrary event happening or having happened.

Is it invalid to say that some event might have "happened" for some observers in the universe, but not for others?

ijaubgiaugf
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None of your questions are invalid. While it's true that there is no absolute definition for the concept of "now", that does not make it an invalid concept.

When you ask "What happens in Andromeda now?", most people would assume you are asking what events are occurring in Andromeda at a time that would be described within your own reference frame as simultaneous to the current moment. The obvious answer to the question is "I don't know because the information of those events hasn't had time to reach me yet", but the question still has some validity and can eventually be answered retroactively.

That said, since Andromeda "now" is space-like separated from here and "now", there are observers in other frames of reference that would (eventually) disagree with us about what is happening now in Andromeda. For some observers, it's entirely possible that the events we would recognize as having happened "now" they would say were yet to have occurred. So, in a way, you could say that some events haven't yet happened for some observers in the universe. Or rather, you could say that there are some events that we would say happened before now and some observers would say happened after now.

It should be noted that if two events are time-like separated, then that means there exists an absolute chronological ordering between them. Essentially, what that last statement boils down to is that if we are currently aware of an event that happened before "now", then there does not exist any observer anywhere that would claim it happened after what we call "now". The only events for which there could be a disagreement about whether or not they happened by the time we reached this exact moment of "now" are those that we are too far away from to know about yet.

Of course, just because there is a disagreement sometimes about chronological ordering, it doesn't mean the notion of asking what is happening "now" is invalid. It's just a bit ambiguous and partially unhelpful.

As for asking about what happened at the big bang: The big bang is a moment of time, which means if you point to a position in space that we'd recognize as being at a later point in time, everyone else would agree that it's a later point in time. Additionally, since the big bang represents a moment of time defined as the time when the universe held a certain property, all observers would say that what happened at the big bang was that the universe held that certain property. It's really kinda trivial.

Jim
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In Special Relativity, every event “happens” for every observer. But different observers will assign different coordinates to them and they might disagree on whether one event is before, after, or simultaneous with another event.

In General Relativity, “horizons” can prevent events from being seen by all observers.

G. Smith
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Your question talks about what seem to me to be two different notions: "happened" and "happened now."

What relativists usually talk about is whether event A is in the past light cone of event B. If event B is on the world-line of an observer, and A is inside B's past light cone, then A is an event that, at least in principle, could have been known to the observer at B.

Relativists don't normally talk about "now." It's not a meaningful concept in general relativity.

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The question “what was the weather like in London at the time the Elizabeth Tower clock struck 12:00 on 22.12.2019” is well-posed. Some observers will be unable to answer it due to spacelike separation from the event, but all observers that will know the answer will agree on the same answer.

The question of whether the aforementioned event preceded or succeeded a certain event in Andromeda can have one of three answers: either the spacetime interval between the two was spacelike, meaning observers can disagree which one came first, and neither of two events could have influenced the other; or one of two was first and all observers agree which.

So a certain event will have happened for some observers (who will agree on its outcome) and it won’t have happened for others. As for “now”, in SR you can only talk about “here and now”. To establish some semblance of simultaneity in distant locations, you have to start from a common point in spacetime (e. g. construct two clocks in the same location and then move them to different galaxies), then you can define meaningful calendars. You’ll be able to ask questions like “if our clock, instead of going to our galaxy, went to their galaxy, what would happen in its immediate surroundings at the time it would display such and such time?”, but the answer to that would depend on the exact path through spacetime that it would take to that galaxy. If you fix a certain spacetime path for both clocks, you can say that “now” is when their clock has the same reading as ours, but other pairs of clocks delivered by other means will have differing concepts of “now”.

The best you can do is to say “this event could have causally influenced that event”, i. e. the spacetime interval is timelike. Whenever that is the case, all observers agree on that.

Roman Odaisky
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Is it invalid to say that some event might have "happened" for some observers in the universe, but not for others?

According to both classical mechanics and relativity, if a physical event happens for one observer, it will certainly happen for other observers too. However, in classical mechanics, the occurrence of the event is simultaneous from the standpoint of all observers because of the absoluteness of time (simultaneity ), whereas in relativity, the event may occur in different space-time coordinates from the viewpoint of different observers because simultaneity is not absolute.

It is also emphasized by R.A. Martins [1] that, in any theory which includes a one-to-one space-time coordinate transformation, if an event such as collision, explosion, etc., happens in one coordinate system, it will necessarily happen in another one too.

[1] R. A. Martins, “Length paradox in relativity,” American Journal of Physics 46 (6) 677 (1978).

Mohammad Javanshiry
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    Some people intentionally downvote my answer over and over. It is really an injustice. What's wrong with my answer? – Mohammad Javanshiry Dec 21 '19 at 12:28
  • This answer has only one downvote. What do you mean by "over and over"? Besides, why do you think it was intentional? One can easily click the downvote button by missing something other, e.g. the score :) Jokes aside, I think this answer doesn't touch the main point of the question: the relation of "now" with the "nows" of other observers. – Ruslan Dec 21 '19 at 18:20
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    @Ruslan This is not my first time. For example, please tell me what is wrong with this downvoted answer? https://physics.stackexchange.com/questions/453170/what-is-the-reasoning-behind-1-step-in-einsteins-derivation-of-the-lorentz-tran/519554#519554 – Mohammad Javanshiry Dec 21 '19 at 18:46
  • Well, that answer just does some (physically) meaningless manipulation to prove the obvious. It's technically right, so why meaningless? Because the question itself lacks context, and your answer doesn't make it any clearer, instead looking trivial. I actually wonder why the question is upvoted despite being so unclear. And your going on to ask for upvoting "to uphold the justice" doesn't really make sense: upvotes show appreciation, not a counteraction to someone's disappreciation. – Ruslan Dec 21 '19 at 19:00
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    Anyway, don't think it's someone aiming at you personally. It's most likely that the answers being downvoted are indeed lacking. Another situation I've come across here is something looking like a reader in a bad mood downvoting my highly-upvoted answer (without a comment, of course). Nothing to do about this. Just re-read your answer, look at the question, and if you still don't find anything wrong, forget this downvote. – Ruslan Dec 21 '19 at 19:01
  • "According to both classical mechanics and relativity, if a physical event happens for one observer, it will certainly happen for other observers too." What about the frequently-discussed example of whether anything can ever fall into a black hole? Fixed outside observers and those who are falling into the hole do not agree. – D. Halsey Dec 22 '19 at 22:50
  • @D.Halsey It is possible providing the outside observers can have any correct imagination about the physics of the things falling within the Schwarzschild radius! – Mohammad Javanshiry Dec 22 '19 at 23:06
  • Nothing ever reaches the event horizon, according to outside observers. – D. Halsey Dec 22 '19 at 23:11
  • @D.Halsey Then I do not think that there can be any event that occurs for one observer, whereas it does not for the other. – Mohammad Javanshiry Dec 23 '19 at 07:04
  • I'm sure you know that observers in different frames will disagree about the time when an event happens. When one of the observers is watching the other falling into a black hole, they will disagree by an infinite amount. Would you characterize that as happening in an infinite time, or as never happening? – D. Halsey Dec 23 '19 at 13:53
  • @D.Halsey They may disagree about the time but the occurrence of the events are certain from both viewpoints. Happening at an infinite time does not necessarily equal to not happening. Remember that even in SR an observer, who moves very close to light speed also claims that physical events WRT which he is in motion occur with infinitely large delays. – Mohammad Javanshiry Dec 24 '19 at 07:40