Re: Space-time interval...

Am Donnerstag000015, 15.08.2024 um 11:26 schrieb Mikko:

On 2024-08-13 13:10:33 +0000, Richard Hachel said:
 

Le 13/08/2024 à 13:38, Mikko a écrit :
>

In an orthogonal isometric coordinate system ds² = dt²-dx²-dy²-dz².

>
 Not really.
>
 ds² = dx²+dy²+dz²-dt²

 Both sign conventions are used. It doesn't matter as long as one knows
which one is used. The information content is the same anyway.
 If you represent vectors and position defferences with quaternions then
the real part of the square of the quaternion is ds² according to the
sign convetion that I used. But quaternions are rarely used in this
context so that is not important.

Yes, becaause quaternions are the wrong construct, but quite close.
The 'real deal' is something called 'complex four-vectors' (aka 'Bi-quaternions').
This construct seems to mimic spacetime in the correct way.
It could be understood as certain type of 'geometric algebra', with such bi-quaternions as 'elements' and so called 'Pauli algebra' as conncetion.
A guy named Jonathan Scott had written about this construct and how to use it in the context of SRT (and others).
I took the idea and enhanced it to 'structured spacetime'.
My concept assumes, that spacetime of GR is real and composed from elements, which behave like bi-quaternions.
This idea works without particles as real lasting entities, but regards matter as internal structure of spacetime.
(This spacetime could also be called 'active vacuum', 'relativistic ether' or similar.)
The main idea is, that the background (spacetime, 'active vacuum') acts like a real physical system, which has internal structure, to which matter (and we ourself) belong.
I have written kind of 'book' about this idea, which can be found here:
https://docs.google.com/presentation/d/1Ur3_giuk2l439fxUa8QHX4wTDxBEaM6lOlgVUa0cFU4/edit?usp=sharing
TH
...