Do virtual particles take energy from the fabric space and when they annihilate in the split second they distribute that energy back to space, therefore abiding by the law for the conservation of energy?
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$\begingroup$ Possible duplicate of Are vacuum fluctuations really happening all the time? $\endgroup$– John RennieCommented Aug 7, 2019 at 14:29
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$\begingroup$ Possibly also of interest: Why do many people say that virtual particles do not conserve energy? $\endgroup$– John RennieCommented Aug 7, 2019 at 14:31
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2 Answers
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They do not actually violate conservation of energy. They are called "virtual" for a reason -- they are part of a larger mathematical calculation, and to think of them as actual particles with physical energies is incorrect.
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When you include interactions, "empty space" defined as a space absent of particles, is not actually an energy eigenstate. That means that the universe in that case does not have a definite energy. This state can then evolve, through mechanisms similar to optical squeezing, with particle-antiparticle pairs forming and disappearing, but with the expectation value of the energy $\langle \Psi | H |\Psi\rangle$ staying constant.
So no: no violation of energy conservation (but it might misleadingly look like it in the basis of the free Hamiltonian, for very short times $t\ll\hbar/m c^2$).
answered Aug 7, 2019 at 14:12