This thread is probably overdue and see this blogpost
. While many of us might be taught that the total amount of energy in an isolated system remains the same, it's doesn't seem to be something we intuitively assume based on everyday experience. Consider the need for vehicles, aircraft and vessels to use energy to keep moving, from that, one who hasn't studied science might conclude that energy can just vanish. And according to that blogpost and this one
, energy is not conserved. In fact the reason we have to believe that energy is
conserved (in spite of everyday experience, even, to my knowledge, among engineers) is the time translation invariance. And Emmy Nöther showed that conservation of energy implies symmetry, and for there to be symmetry, either it is coincidence, or there must be intrinsic certainty (with no mixed states). Nöther's theorem was discovered before the uncertainty principle.