> On which basis was this pairing between position and time "decided"?
Three partially correct answers of the same question:
1) Nobody decided it. It is just how the universe is.
2) You have the formulas where the space-something appear, and you randomly try propose to replace something with things you know, like mass, time, color, ... It is actually more easy, because using the units you know that something must be measured in seconds, so it discards a lot of possibilities.
3) You have the "classic" formulas where space appears https://en.wikipedia.org/wiki/Lorentz_transformation that were actually discovered almost 20 years before the work of Einstein. And you rewrite them in the equivalent of the "vectorial" notation. In the usual space it is like replacing (x,y,z) with a big X and never looking inside X. If you try it, the only way you can success is if you group (ct,x,y,z).
The trick is to look carefully at the calculation and try to think what you can arrange it to be able to rewrite the calculation in the correct form.
For example with momentum, you look carefully and realize you must add energy as the fourth component.
If you choose to group space and time, and you choose to group momentum and energy, then you must use the same choose in all the formulas. You can not choose a different grouping for each formula.
But sometimes it is not so easy. With speed you realize that it is too bad to be fixed, and you must define another speed-like-thing and then give another formula that transform the "real speed that you measure in a lab" and the "abstract speed-like-thing that you use in the calculation".
With the electric field, ... well you can't put it in a 4-vector, you must use something more weird that is a 4x4-matrix.
Three partially correct answers of the same question:
1) Nobody decided it. It is just how the universe is.
2) You have the formulas where the space-something appear, and you randomly try propose to replace something with things you know, like mass, time, color, ... It is actually more easy, because using the units you know that something must be measured in seconds, so it discards a lot of possibilities.
3) You have the "classic" formulas where space appears https://en.wikipedia.org/wiki/Lorentz_transformation that were actually discovered almost 20 years before the work of Einstein. And you rewrite them in the equivalent of the "vectorial" notation. In the usual space it is like replacing (x,y,z) with a big X and never looking inside X. If you try it, the only way you can success is if you group (ct,x,y,z).
The trick is to look carefully at the calculation and try to think what you can arrange it to be able to rewrite the calculation in the correct form.
For example with momentum, you look carefully and realize you must add energy as the fourth component.
If you choose to group space and time, and you choose to group momentum and energy, then you must use the same choose in all the formulas. You can not choose a different grouping for each formula.
But sometimes it is not so easy. With speed you realize that it is too bad to be fixed, and you must define another speed-like-thing and then give another formula that transform the "real speed that you measure in a lab" and the "abstract speed-like-thing that you use in the calculation".
With the electric field, ... well you can't put it in a 4-vector, you must use something more weird that is a 4x4-matrix.