[Bored chemist]

I look forward to a viable definition of uniquity.

[Halc]

So in this case my frame has nothing to do with it. The speed of light has everything to do with it. You could argue this about any frame. The distance is the crucial factor. If we take L as a light second, then for every multiple of L, which we label n, then in an ideal vacuum it will take light n seconds to reach us.

Except the spatial distance between events is frame dependent, so the amount of time it takes light to go that distance is also frame dependent.

In a frame where the ball event occurs first, the supernova event S needs to be close enough to be oberved within a minute (your time) of when B occurs.  In the (arbitrary) frame of Earth, sure, the supernova event occurs first, despite your post assuming otherwise.

My contention what that it was quite possible for either to occur before the other, but not definite, and thus any assertion one way or another is an abstract one.

Presumably, there could be RFs, somewhere, in which either event could be seen as preceding the other

There is a RF somewhere where either event actually does precede the other.  It isn't about seeing/observing.  Select an orientation of the 4 axes for your coordinate system so the coordinates of event S has a lower value for the t coordinate than does the B event.

because there is no causative relationship between either

The causal relationship is impossible because the two events are not in each other's light cones. If they are in each other's light cones, they may or may not have a meaningful causal relationship, but the ordering is nevertheless one, then the other: objective, not abstract.

Jeffrey gave an example of a pair of events that are not in each other's light cones, which means the determination of the ordering of those events is frame dependent.

[jeffreyH]

Show me where I said the supernova explosion happened before the ball hit the ground. The information ABOUT the supernova was detected first. Please do not attribute ideas to me that I did not express. That is downright dishonest.

[jeffreyH]

@Halc  you said "Except the spatial distance between events is frame dependent, so the amount of time it takes light to go that distance is also frame dependent."

So what you are saying is the speed of light differs in different frames of reference. What?

[alancalverd]

I look forward to a viable definition of uniquity.

Since anything that might be labelled as an event necessarily involves an increase in entropy, "unique" and "event" may be considered sort of tautologous, like "orange" (adjective) and "orange" (noun).

[Halc]

Show me where I said the supernova explosion happened before the ball hit the ground.

You never said that, and I didn't say you did.

The information ABOUT the supernova was detected first.

You 'expressed' otherwise, my bold:

A ball is dropped and hits the ground just before a super nova appears in the sky.

Trying to get the topic back on track.

This may be rubbish, but consider that X is something, the characteristics of which make it unique, when viewed by an observer in the same RF.

I would say an event X is unique because it is identical to itself and is not a different event.  Any different event Y is going to have some kind of separation with X, but X is always X.  All this is true in any frame, so the RF really doesn't matter in any of this.

So for instance, if event X is where the Titanic first touches the iceberg, that event is that event in any reference frame.  It doesn't mean that the event has the same coordinates x,y,z,t since no coordinate system has been assigned, and if it is, any value for x,y,z,t might specify X.  It has nothing to do with an observer since one observer might be able to see the event and another (in the same frame even) cannot see it, or see it from a different angle.
That event is <1000 km east, -108 years> relative to my event today, but <3000 km west, +5 days> to somebody just getting on the ship.  That's pretty different coordinates from two observers using the same (rotating, not inertial) reference frame.

If, when viewed by on observer in another RF, the perceived characteristics change, such that it appears identical to some other entity; its original “uniqueness” has not been conserved. Alternatively, if its perceived characteristics, in the second RF, are still different from everything else, then “uniqueness” has been conserved

The uniqueness of my Titanic example event does not change for some other entity.  It still has the one characteristic of the Titanic making contact with that ice.

[jeffreyH]

Show me where I said the supernova explosion happened before the ball hit the ground.

You never said that, and I didn't say you did.

The information ABOUT the supernova was detected first.

You 'expressed' otherwise, my bold:

A ball is dropped and hits the ground just before a super nova appears in the sky.

And what alerts us to the supernova appearing in the sky? ESP? Or maybe photons? Do you always feel the need to be vindicated?

[alancalverd]

Since anything that might be labelled as an event necessarily involves an increase in entropy,

How can an event involve an increase of entropy?  Entropy increases over a duration of time, and and event has not duration.

An event is what occurs between "before" and "after". Entropy after is always greater than entropy before. Therefore no entropy increase <=> no event.

[jeffreyH]

An event is what occurs between "before" and "after".

OK, you're working with a completely different definition than the physics one. I'll interpret your answers in light of this private definition.

And there you go again. I know what Alan means.

[alancalverd]

I'd be interested to know what the physics definition of an event might be. I've only been studying physics for the last 65 years, and clearing up after events for the last 60. Seems that I have been wasting my time!

[Bill S (OP)]

Seems that I have been wasting my time!

That depends a lot on how thorough your clearing up has been.  How far our would a guess at, "bordering on obsessive" be? 

[Bill S (OP)]

Except the spatial distance between events is frame dependent, so the amount of time it takes light to go that distance is also frame dependent.

I interpreted this as saying, not that the speed of light was frame dependent, but that if distances varied from RF to RF, the time taken by light to travel these different distances would have to vary, as light would travel at c in each/every case.  Is that right?

[Halc]

I'd be interested to know what the physics definition of an event might be.

https://en.wikipedia.org/wiki/Event_(relativity):

In physics, and in particular relativity, an event is the instantaneous physical situation or occurrence associated with a point in spacetime (that is, a specific place and time).

On the particle physics end of things, (also wiki): "In particle physics, an event refers to the results just after a fundamental interaction took place between subatomic particles", but the OP is talking about the relativistic spacetime definition (the upper one), not the particle physics one.

I've never seen the wording you gave, and am not sure what it means, so clearly I'm not as clever as jeffrey.  Your definition seems to completely discard a localized region of space, so an event could involve 20 galaxies or more.

[alancalverd]

so an event could involve 20 galaxies or more.

We physicists are used to thinking big as well as small. What both of your quoted definitions have in common is the different states of the universe before and after the event. An event involving 20 galaxies would be small beer (almost a local brew) compared with the Big Bang, and whilst we don't have much idea of before, everything we now observe is pretty obviously after something like an event.

Since the universe is by definition never the same after any event, the occurrence of other events guarantees the uniqueness of each. 

[alancalverd]

Seems that I have been wasting my time!

That depends a lot on how thorough your clearing up has been.  How far our would a guess at, "bordering on obsessive" be? 

Way out! I live by "good enough", "engineering tolerance", "acceptable defects",  "anywhere on the runway" and "life is too short...."  I don't remember ever sailing a boat with a fully working toilet, but we never missed a tide.

[jeffreyH]

Just for the record and in support of Alan's point here is part of a reply to a question on another forum. Enjoy!

https://physics.stackexchange.com/questions/389488/what-is-an-event-in-special-relativity

In the original usage, as Einstein used it, an "event" is just something that happens, like a detector clicking. It's just the same as the colloquial meaning.

In the early 20th century, various thought experiments involving hypothetical events, and actual experiments involving physical events, were used to show that general relativity is an excellent model for our universe. In the context of general relativity, spacetime is modeled as a Lorentzian manifold, and physical events are modeled as points in this manifold.

Now, some mathematically minded people choose to forget all this history. They instead say the word "event" is defined as a point in a Lorentzian manifold. This is a clean and consistent definition, but as usual in mathematical physics, it misses the point. The only reason we care about these mathematical "events" is because they form part of a theory that does an excellent job of describing real events. By conflating the two, one glosses over the mountains of experimental work needed to link the two together."