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Obviously I am misunderstanding how an interval of space- time can be invariant under coordinate transformations. The following elementary (but obviously incorrect) calculation will illustrate my difficulty.

Alice is leaving her two boyfriends, Bob and Charlie. Bob sees Alice going at a constant velocity of 3/5 the speed of light away from him, so after a second, Bob measures Alice’s space-time change as (using the (+,-,-,-) convention) (9.0 x 10^{16}m^{2}- 5.4 x 10^{16}m^{2}= 3.6 x 10^{16}m.

Charlie also sees Alice going away from him at a constant velocity, but at 4/5 the speed of light, so after a second, Charlie measures Alice’s space-time change as

9 x 10^{16}m^{2}- 7.2 x 10^{16}m^{2}= 1.8 x 10^{16}m.

I would be grateful for corrections.

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# Invariance of spacetime intervals

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