World Science Scholars
29.8 Invariants
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In ordinary geometry, a circle is the collection of all points that are the same distance from, say, the origin. What is the corresponding geometrical concept for a collection of points that are the same invariant interval from the origin?
In ordinary geometry, the usual “invariant” 𝛥𝑥²+𝛥𝑦² has an immediate interpretation: the distance between two points. Can you explain again the interpretation of the invariant interval −𝒄²𝛥𝑡²+𝛥𝑥² in special relativity?
In a spacetime diagram how do I figure out the spacing between tick marks along the axis of a moving frame relative to those of the stationary frame?
Couldn’t you also prove that all observers agree on the invariant interval using hyperbolic trig identities?

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