Different reference frames give same results (also in Bell's spaceship thought experiment)

The right question to ask is how do different reference frames give the same results. 'Result' here means that something very concrete happens, a thread breaks, for example.

Knowing what happens is quite trivial: For example in your case 1, if anything happened it would happen without any good reason in one frame. So in all frames nothing happens inside that box where the two charges and the thread are.

There is a frame where a magnetic field appears. The field appears when the charges start moving, that is the reason for the appearance of the field. This is appearance of a field is not a very concrete thing, it is a frame dependent thing, or a relative thing.

So the problem we should be thinking about is: In the frame where the electro-magnetic force between the balls changes, why does the thread not break, or not even stretch just a little bit more?

Different reference frames give same results (also in Bell's spaceship thought experiment)

The right question to ask is how do different reference frames give the same results. 'Result' here means that something very concrete happens, a thread breaks, for example.

Knowing what happens is quite trivial: For example in your case 1, if anything happened it would happen without any good reason in one frame. So in all frames nothing happens inside that box where the two charges and the thread are.

There is a frame where a magnetic field appears. The field appears when the charges start moving, that is the reason for the appearance of the field. This is appearance of a field is not a very concrete thing, it is a frame dependent thing, or a relative thing.

So the problem we should be thinking about is: In the frame where the electro-magnetic force between the balls changes, why does the thread not break, or not even stretch just a little bit more?

If the spring force in the spring is a Coulomb force, then the spring is same kind of thing as the two charges balls. Problem is solved now, for one type of spring.

Different reference frames give same results (also in Bell's spaceship thought experiment)

The right question to ask is how do different reference frames give the same results. 'Result' here means that something happens, a thread breaks, for example.

Knowing what happens is quite trivial: For example in your case 1, if anything happened it would happen without any good reason in one frame. So in all frames nothing happens inside that box where the two charges and the thread are.

There is a frame where a magnetic field appears. The field appears when the charges start moving, that is the reason for the appearance of the field.

So the problem we should be thinking about is: In the frame where the electro-magnetic force between the balls changes, why does the thread not break, or not even stretch just a little bit more?

Different reference frames give same results (also in Bell's spaceship thought experiment)

The right question to ask is how do different reference frames give the same results. 'Result' here means that something very concrete happens, a thread breaks, for example.

Knowing what happens is quite trivial: For example in your case 1, if anything happened it would happen without any good reason in one frame. So in all frames nothing happens inside that box where the two charges and the thread are.

There is a frame where a magnetic field appears. The field appears when the charges start moving, that is the reason for the appearance of the field. This is appearance of a field is not a very concrete thing, it is a frame dependent thing, or a relative thing.

So the problem we should be thinking about is: In the frame where the electro-magnetic force between the balls changes, why does the thread not break, or not even stretch just a little bit more?