The energy-time uncertainty principle, given by, $$\Delta E\Delta t\geq\frac{\hbar}{2},$$

can be used to explain the existence of virtual particles which violate the law of conservation of energy. That is, the smaller the uncertainty in time, $\Delta t$, the greater $\Delta E$ that is needed to ensure that this relation holds. My question however is this: What is stopping both the uncertainty in time and the uncertainty in energy being large simultaneously?

From what I can tell, a simultaneously large $\Delta t$ and $\Delta E$ would not violate this relation, so why do virtual particles have such short lifetimes?



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