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Plain "empty space" or vacuum is not empty after all. It contains small quantum fluctuations. Virtual Particles pop in and out of existence all around us. In this system, an electron and a positron appear. My first question is: How do they just appear, and after a period of time disappear?

"Empty space" is measured to have about 10^-8 ergs of energy density. But according to this video, Sean Carrol points out we estimated the energy of "empty space" would be 10^112 ergs density. Could you tell me how this was calculated? And how was "10^-8 ergs" measured?

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    $\begingroup$ "Empty space" is measured to have about 10^-8 ergs of energy. You are confusing energy and energy density. $\endgroup$
    – G. Smith
    Commented Jan 9, 2021 at 4:23
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    $\begingroup$ I will leave a detailed answer to others, but the concept of virtual particles is not as mysterious as it seems. The basic stuff that the universe is made out of isn't particles but quantum fields. When a quantum field has an excitation that obeys the energy-momentum relation from special relativity, it is called a "real particle" because it will behave "like a particle" in many ways and can exist indefinitely until it interacts with something else. When an excitation does not obey the energy-momentum relation, it does not behave like a particle and decays into other particles/fields. $\endgroup$
    – sasquires
    Commented Jan 9, 2021 at 4:42
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    $\begingroup$ The question of how we can measure the apperance/disappearance of virtual particles from a human perspective is a complex topic and is somewhat related to the question of interpretations of quantum mechanics. But everyone agrees on how to do the calculations and what the results are. For the current discussion, I'll just say the following. If you take out any human observers, then it is easy to make an analogy with classical mechanics. ... $\endgroup$
    – sasquires
    Commented Jan 9, 2021 at 4:48
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    $\begingroup$ ... Just like a moving electric charge produces a magnetic field, different types of quantum fields are constantly exciting other kinds of quantum fields, all the time. The standard model of particle physics describes all these interactions between fields. $\endgroup$
    – sasquires
    Commented Jan 9, 2021 at 4:48
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    $\begingroup$ All particles, both real and virtual, are excitations of a quantum field. In regular quantum mechanics, you take the existence of particles as a given, and then you can calculate their energy states. In quantum field theory, which is more fundamental, you take the quantum field as given and then calculate what the particles are. You'll have to get to a QFT class before that concept makes sense though. $\endgroup$
    – sasquires
    Commented Jan 9, 2021 at 4:50

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