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I was brooding some more about the frames of reference thing and maybe beginning to see where the paradox lies. Thing is [perhaps] that the observer in the car is non-accelerated only up to the moment of impact: we can't use him to assess KE after that moment with the same cavalier abandon that prevailed beforehand. [Especially since he'll have a headache.] Thus it is not legitimate to say: "from car 1's POV, KE before = 2mv2, KE after = 0 + 0, therefore KE dissipated into crunch = 2mv2". Which would be very troubling since it would appear to let us distinguish between states of rest/uniform motion by Physics.
What we can say instead is that from the point of view of a non-accelerated observer *travelling initially with car 1*, the KE before = 2mv2 and the KE after = 1/2 2m (-v)2 = mv2 so the KE going into the impact process = 2mv2 - mv2 = mv2. Which agrees with the observer on the roadside! So maybe the old geezer with the mop of white hair and the century's most iconic formula was right after all. I'm sufficiently encouraged to copy this email to my tormentor in Jordanstown and see if it allays his apprehensions. Hi Colin!

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