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- TL;DR Summary
- space time interval is defined as ds^2=(cdt)^2-(dx^2+dy^2+dz^2) but where does this equation come from?

While not having a professional physics background I was still interested in knowing more about special and general relativity. Therefore I was trying to find out where the space time interval was coming from in relation to the speed of light. Of course this is the first point to start I believe.

But in most explanations about special relativity it turned out that the spacetime interval was presented as something basic but without referring to where it exactly comes from. So for me that looked like making too much steps at a time and missing some fundamental steps in between especially where the minus sign comes from.

Therefore starting from scratch I tried to understand it starting from the speed of light being constant and the comparison between 2 reference frames with constant speed difference.

Then I could immediately see that pythagoras holds making the square of the distance (dx^2+dy^2+dz^2) + ds^2=(cdt)^2 where ds^2 is the distance that the light moves in 1 second as seen by each observer in its own reference frame. But the observer looking to the other reference frame sees the light passing over a longer distance therefore the light seems to go slower from his perspective.

so it this where it comes from?

But in most explanations about special relativity it turned out that the spacetime interval was presented as something basic but without referring to where it exactly comes from. So for me that looked like making too much steps at a time and missing some fundamental steps in between especially where the minus sign comes from.

Therefore starting from scratch I tried to understand it starting from the speed of light being constant and the comparison between 2 reference frames with constant speed difference.

Then I could immediately see that pythagoras holds making the square of the distance (dx^2+dy^2+dz^2) + ds^2=(cdt)^2 where ds^2 is the distance that the light moves in 1 second as seen by each observer in its own reference frame. But the observer looking to the other reference frame sees the light passing over a longer distance therefore the light seems to go slower from his perspective.

so it this where it comes from?