When are events frame independent and why?

Question

Why is it that if an event happens, and a clock at the same location that the event happened at says that its a certain time when the event happens, observers in EVERY reference frame agree on the time on that clock when the event happened?

I understand special relativity as encompassing all the un-intuitive results that arise from the observed fact that the speed of light is constant in all inertial reference frames.

So, seeing as there are so many un-intuitive results that emerge, I'd kind of like an explanation to my question different from "its intuitive that it would be so...". I know it is, since if we were to ask the person that experienced the event at the clock, and we disagreed with them...well, that would be quite strange.

But is there a way to explain this also arising from the constant speed of light...or perhaps from some fact about our universe which I'm missing?

Thanks!

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Example:

Say that Bob is in the back of a train of length $L_P$ riding past Alice, and there's a clock at the front of the train, and at the back of the train.

When the back of the train (Bob) passes Alice, both of their clocks say zero, and Alice sees the clock at the front of the train say $-\frac{vL_P}{c^2}$.

The way I interpret this is that events happening at the front of the train in in Bob's conception of "NOW" still have $\frac{vL_P}{c^2}$ seconds until they happen for Alice...that's also why she sees the front of the train closer to herself than the back of the train sees the front of the train to itself - she is literally seeing a past version of the front of the train, which wouldn't have traveled as far.

However, say that when the front of the train reads $2$ according to Bob, a bird crashes into that clock. Why is it that Bob and Alice would both have to agree that the front of the train read $2$ when the bird crashed into it, even if from the point in time at which Bob passed Alice, Alice had to wait longer for the bird to crash into it than Bob did?

Answer 1

Why is it that if an event happens , and a clock at the same location that the event happened at says that its a certain time when the event happens, observers in EVERY reference frame agree that the clock said that time when the event happened?

That clock records the event by making a record:

• punches a hole in paper with the hands
• takes a photograph of the hands
• makes a digital copy of the reading

Any observer can then read that record and see what it says. It’ll always be the same: everybody will see “21:23:45 Jan 6 2020” on the photograph.

It might take a while to see it if the observer is far away. An observers own clock might have made a different record because it saw a different time. But nobody will disagree what a particular clock said for a particular event.

Answer 2

When the bird hits the clock, the bird and clock will have the same frame of reference. So, sooner or later, everyone everywhere will see the clock reading the same when the bird hits it, regardless of their own clocks.