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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.

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    $\begingroup$ 1. Please define what you mean by "quantum fluctuations". For different definitions, your first sentence is either trivially true, obviously false, or simply meaningless. 2. That there is an energy-time uncertainty principle that can be applied like this is a persistent, but false, myth, see this question and its accepted answer 3. What are "the 2 particles" you are talking about in the third paragraph? $\endgroup$
    – ACuriousMind ♦
    Commented Sep 10, 2017 at 16:01
  • $\begingroup$ By quantum fluctuations I mean virtual particles popping in and out of existence due to Heisenberg's uncertainty principle $\endgroup$
    – Bill
    Commented Sep 10, 2017 at 16:04
  • $\begingroup$ By 2 particles I was thinking about a simple case of quantum fluctuations such as an electron and a position appearing from nothing and then colliding $\endgroup$
    – Bill
    Commented Sep 10, 2017 at 16:12
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    $\begingroup$ That's a pop-sci phrase that doesn't actually mean anything in actual quantum field theory, see e.g. physics.stackexchange.com/q/162845/50583, physics.stackexchange.com/q/185110/50583. As for the validity of the uncertainty principle, see the question I linked in my first comment $\endgroup$
    – ACuriousMind ♦
    Commented Sep 10, 2017 at 16:12
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    $\begingroup$ Possible duplicate of Are vacuum fluctuations really happening all the time? $\endgroup$
    – John Rennie
    Commented Sep 10, 2017 at 16:31

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