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We often say that the conservation of the energy could be violated by a quantity $\Delta E$ but only within a precise interval of time $\Delta t$, dictated by the Heisenberg principle ($\Delta t \lesssim h/\Delta E$). But in the Heisenberg principle it seems that the $\Delta t$ should be greater, not lesser, than this: $$ \Delta t \cdot \Delta E > h/4\pi.$$ How could I explain all this in plain words to my students?

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    $\begingroup$ Hi Curiousprof. The energy time uncertainty principle is widely misrepresented in popular science books, and it leads to misunderstands like the one you ask about here. See the question I've linked for what it actually means. $\endgroup$ – John Rennie Feb 16 at 11:54
  • $\begingroup$ who says? this $\Delta t \lesssim h/\Delta E$) has the wrong direction of inequality. $\endgroup$ – anna v Feb 16 at 14:16
  • $\begingroup$ Thank you John! Very useful texts. $\endgroup$ – Curiousprof Feb 16 at 14:34