Re: Space-time interval...

On 2024-08-12 09:27:04 +0000, Richard Hachel said:

What is the space-time interval?
To describe it, mathematically, and not semantically,
 because it may be an abstract construction requiring a complex number, we use the formula ds²=dl²-dt².
 That doesn't make the "thing" much clearer.

In an orthogonal isometric coordinate system ds² = dt²-dx²-dy²-dz².
If ds² = 0 the line element is light-like. If ds² > 0 the line element
is time-like and √(ds²) is proper time. If ds² < 0 the line element
is space-like and √(-ds²) is proper distance.
Although the formula refers to a particular coordinate system any other
orthogonal isometric coordinate system can be used instead and ds² is
the same.
--
Mikko