Quantum fluctuations are part of quantum field theory, a method of calculating and predicting the behavior of elementary particles. At present it is the basic underlying level of nature, out of which classical field theories emerge in a mathematically continuous and provable manner.
These calculations involve summations of a series of integrals over the variables describing an elementary particle interaction or decay, or even a stable state. The organization of this series expansion was greatly facilitated by the invention of Feynman diagrams which gave an iconic representation with fixed rules that could be translated one to one into the necessary integrals of the diminishing power series for calculating interactions,
Here is a first order diagram, i.e. dominating the total value for electron electron scattering:
In this diagram, only the incoming and outgoing electrons are real, i.e. are described by a four vector whose "length" is the exact mass of the electron. Internal lines are off mass shell, and under the final integration implied by the diagram, take continuous values for the mass that are not connected with the mass of the exchanged particle, in this case the virtual photon can have a mass, but it is a gimmick of the mathematical representation. Energy and momentum are conserved by the incoming and outgoing real electrons.
To get better and better accuracy in the calculation, higher order Feynman graphs have to be added and calculated. In this higher order graphs loops of virtual particle antiparticle appear , and their inclusion in the sums was important in getting correct values for experimental numbers, like the measurable Lamb shift.
In this Feynman diagram:
a single loop is introduced of a particle antiparticle pair, and can be used to correct the crossection for better accuracy. The diagram is higher order because there are more electromagnetic vertices. The important thing is to note tha there is always a line for loops connecting with a real particle, which bring in energy and momentum, and the total input and output energy and momentum are conserved. Virtual particles between real ones do not affect this conservation law, because the integration takes care of it.
The moral of the story is that vacuum fluctuations in order exist at all need an incoming real energy and momentum vertex. This is demonstrated for the Casimir effect , showing that the "shorthand" of "vacuum fluctuations" are dependent on real energy input and output interactions:
When the plates were idealized as perfect conductors, assumptions
were made about the properties of the materials and the strength of the QED coupling α , that obscure the fact that the Casimir force originates in the forces between charged particles in the metal plates.
In a near vacuum, quantum effects can cause short-lived particles to appear. When they disappear, on average no extra energy remains in the universe, so on average, the total amount of energy in the universe is conserved.
The word "near vacuum" is necessary to give an input energy and momentum conserving vertex to any vacuum fluctuations . In a complete vacuum there can be no loops affecting the four dimensional space.