In formal terms, a particle is considered to be an eigenstate of the particle number operator a a, where a is the particle annihilation operator and a the particle creation operator (sometimes collectively called ladder operators). In many cases, the particle number operator does not commute with the 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 observables, 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 time-energy uncertainty principle in a vacuum.