Editing Virtual particle (section)

== Vacuums ==
{{Main article|Quantum fluctuation|QED vacuum|QCD vacuum|Vacuum state}}

In formal terms, a particle is considered to be an [[eigenstate]] of the [[particle number operator]] ''a''<sup>†</sup>''a'', where ''a'' is the particle [[annihilation operator]] and ''a''<sup>†</sup> the particle [[creation operator]] (sometimes collectively called [[ladder operator]]s). In many cases, the particle number operator does not [[commutator|commute]] with the [[Hamiltonian (quantum mechanics)|Hamiltonian]] for the system. This implies the number of particles in an area of space is not a well-defined quantity but, like other quantum [[observable]]s, is represented by a [[probability distribution]]. Since these particles are not certain to exist, they are called ''virtual particles'' or ''vacuum fluctuations'' of [[vacuum energy]].  In a certain sense, they can be understood to be a manifestation of the [[Uncertainty principle#Robertson.E2.80.93Schr.C3.B6dinger uncertainty relations|time-energy uncertainty principle]] in a vacuum.<ref>{{cite book|last1=Raymond|first1=David J.|title=A radically modern approach to introductory physics: volume 2: four forces|date=2012|publisher=New Mexico Tech Press|location=Socorro, NM|isbn=978-0-98303-946-4|pages=252&ndash;254|url=http://kestrel.nmt.edu/~raymond/books/radphys/book2/book2.html#x1-2100014.7}}</ref>

An important example of the "presence" of virtual particles in a vacuum is the [[Casimir effect]].<ref>{{cite journal|last1=Choi|first1=Charles Q.|title=A vacuum can yield flashes of light|journal=Nature|date=13 February 2013|doi=10.1038/nature.2013.12430|s2cid=124394711|url=http://www.nature.com/news/a-vacuum-can-yield-flashes-of-light-1.12430|access-date=2 August 2015|doi-access=free}}</ref> Here, the explanation of the effect requires that the total energy of all of the virtual particles in a vacuum can be added together. Thus, although the virtual particles themselves are not directly observable in the laboratory, they do leave an observable effect: Their [[zero-point energy]] results in forces acting on suitably arranged metal plates or [[dielectric]]s.<ref>{{cite journal|last1=Lambrecht|first1=Astrid|title=The Casimir effect: a force from nothing|journal=Physics World|date=September 2002|volume=15|issue=9|pages=29&ndash;32|doi=10.1088/2058-7058/15/9/29}}</ref>  On the other hand, the Casimir effect can be interpreted as the [[Casimir effect#Relativistic van der Waals force|relativistic van der Waals force]].<ref>{{cite journal|last1=Jaffe|first1=R. L.|title=Casimir effect and the quantum vacuum|journal=Physical Review D|date=12 July 2005|volume=72|issue=2|pages=021301|doi=10.1103/PhysRevD.72.021301|arxiv = hep-th/0503158 |bibcode = 2005PhRvD..72b1301J |s2cid=13171179}}</ref>