What's the physical reason that all (inertial) observers agree on the value of the spacetime interval $$ds^2 = (c dt)^2 - dx^2 - dy^2 -dz^2 \, ?$$
What would be the physical implications if different (inertial) observers wouldn't find different values of $ds^2$, analogous to how they find different time intervals and different distances?
EDIT: none of the linked questions (to which this question supposedly is a duplicate) explain why a constant speed of light implies that all observers agree on the value of the spacetime interval.
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