In quantum field theory, such as quantum electrodynamics (QED), the vacuum is not truly empty but rather a complex and dynamic medium filled with virtual particles constantly fluctuating in and out of existence. These virtual particles can include electron-positron pairs, among others.
According to quantum theory, these virtual particles can temporarily borrow energy from the vacuum and manifest as real particles before annihilating each other and returning the borrowed energy. This phenomenon is known as vacuum fluctuations or vacuum polarization.
In the case of an electron-positron pair, the probability of their existence in a given volume of the vacuum is not constant but depends on the energy and duration of their appearance. The precise calculation of these probabilities is highly complex and requires advanced mathematical techniques.
However, it is important to note that these virtual particles are not directly observable in the usual sense. Their effects can be indirectly detected and measured through various experimental phenomena, such as the Lamb shift and the Casimir effect, which arise from the influence of vacuum fluctuations on the behavior of real particles.
So, while quantum theory allows for the temporary appearance of electron-positron pairs in the vacuum, it does not provide a simple probability for their existence in a particular volume like a liter. The calculations involved are intricate and require sophisticated mathematical tools to determine the likelihood of such events.