Vacuum State - Virtual Particles

Virtual Particles

The presence of virtual particles can be rigorously based upon the non-commutation of the quantized electromagnetic fields. Non-commutation means that although the average values of the fields vanish in a quantum vacuum, their variances do not. The term "vacuum fluctuations" refers to the variance of the field strength in the minimal energy state, and is described picturesquely as evidence of "virtual particles".

It is sometimes attempted to provide an intuitive picture of virtual particles based upon the Heisenberg energy-time uncertainty principle:

(with ΔE and Δt being the energy and time variations respectively; ΔE is the accuracy in the measurement of energy and Δt is the time taken in the measurement, and ħ is the Planck constant divided by 2π) arguing along the lines that the short lifetime of virtual particles allows the "borrowing" of large energies from the vacuum and thus permits particle generation for short times.

Although the phenomenon of virtual particles is accepted, this interpretation of the energy-time uncertainty relation is not universal. One issue is the use of an uncertainty relation limiting measurement accuracy as though a time uncertainty Δt determines a "budget" for borrowing energy ΔE. Another issue is the meaning of "time" in this relation, because energy and time (unlike position q and momentum p, for example) do not satisfy a canonical commutation relation (such as = i ħ). Various schemes have been advanced to construct an observable that has some kind of time interpretation, and yet does satisfy a canonical commutation relation with energy. The very many approaches to the energy-time uncertainty principle are a long and continuing subject.