I found a webpage that just kind of mentions the uncertainty principle lightly but doesn't really go into detail as to why we need it in the first place when considering quantum fluctuations and particles/anti-particles.
I want to understand why we care about this equation as it is related to the creation and annihilation of virtual particles.
I would guess that it helps us answer the question: "Well, if these particles are being created and destroyed in a really small time interval, then we can estimate that the energy they create must be relatively large." But then this just gives me another question: in the full time interval (from $t_i$ to $t_f$), wouldn't $\Delta E=0$?
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