# How do quantum fluctuations make up vacuum energy? [duplicate]

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Quantum fluctuations are thought to be the reason why we have energy even if there is nothing in a region of space. My question is if quantum fluctuations give back what they got from nothing using Heisenberg's uncertainty principle $\Delta Ε \cdot \Delta t \geq \frac{h}{2}$, how do they result in a sum of energy $> 0$?

An answer that I came up with, though don't know if correct is: if you freeze time then you will catch quantum fluctuations in the in-between phase when they have not returned their energy back. And if you add all those in a region of space such as a cubic then the sum ends up being $10^{113}\text{ J/m}^3$ although the observed cosmological constant is $1.5 \cdot 10^{-9}\text{ J/m}^3$, but that's the cosmological constant problem a completely different topic.

Also when the 2 particles remerge don't they emit photons? If so photons have energy $E=hf$. But if quantum fluctuations emit photons in the end and photons have energy then how is the energy given back?

Don't be afraid to include math to your answer especially if math makes your answer more correct and complete.