I'm having some trouble reconciling the following facts: 1) that kinetic energy depends on v _squared_, 2) at the same time energy is conserved in all reference frames, and 3) reference frames transform linearly in v in classical mechanics (galileo transform). I've basically been able to boil down my confusion to the following thought experiment: A "train" weighing 1 kg moving at 10 m/s slows down to 1m/s by braking. In the frame of the railroad tracks it loses 10^2 - 1^2 = 99 joules of kinetic energy which presumably is all transferred into the railroad tracks in the form of heat. On the other hand, in the frame of a person walking 1m/s along the side of the train, it slowed down from 9m/s to 0 m/s, losing 9^2 - 0 = 81 joules of energy into heat in the tracks. This can't both be right - all observers should be able to agree on how much thermal energy the track has!! The only thing I can think of so far is that perhaps the idea of the "thermal energy" of an object only applies in a frame where that object is stationary. However I do not find this explanation satisfactory since an object should conduct heat to it's surroundings at a rate proportional to the temperature difference regardless of whether it is stationary or moving.