I'm reading Peter Atkins' book, Galileo's Finger, and in the chapter on energy, he makes the points that the conservation of momentum stems from the shape of space (that it's smooth and not lumpy) and that the conservation of energy stems from the shape of time (that it's smooth and not lumpy). I'm not totally clear on how the shape of spacetime leads to the conservation laws. Could someone elucidate the relationship, in layman's terms?
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