For all I've read about Quantum Field Theory I've never seen the concept of the living vacuum accredited to someone in particular. Given the importance of this very application of the uncertainty principle that always seemed rather strange to me.


The "living vaccuum" was obvious to everyone by 1930, it didn't require a discoverer. Perhaps you should credit Dirac, perhaps Jordan, perhaps Fock, perhaps Fermi, perhaps Heisenberg, perhaps Bohr/Rosenfeld, perhaps Klein, who knows.

I would credit Heisenberg, Kramers, and Schrodinger, for the development of stationary state perturbation theory. The Kramers Heisenberg ideas allowed for virtual atomic transitions, between absorption and emission of light, and Schrodinger's perturbation theory allowed you to calculate the properties of eigenstates from these virtual states.

Once the quantum field theory was formulated by Heisenberg, Jordan, Dirac and others, the stationary states were clearly fixed particle occupation number states, and virtual states became virtual particles automatically, without any need for discovery, because the idea of virtual states was already understood.

One major motivation for the quantum field concept came from the Klein paradox--- the Dirac equation, if interpreted as a single particle equation, is inconsistent because it allows transmission and reflection coefficients to add up to more than one. This violates the basic ideas of probability. Oscar Klein was a major unsung player in the development of early quantum field theory.

Aside from fluctuating virtual particles, there are other concepts of dynamical vacuum which are different, and which are associated with different people:

  • The Dirac sea: this picture of positrons as electron-holes in the filled relativistic negative energy band is very physical, and due to Dirac alone.
  • Spontaneous symmetry breaking in vacuum by condensates: This idea is probably best attributed to the elder Heisenberg, who believed that these models will explain all of physics from a fundamental Fermi field. The notion of spontaneous symmetry breaking is already present in Heisenberg's analysis of a spreading S-wave of a charged particle in a bubble chamber, the particle makes a track, even through it's wave description is superficially spherically symmetric. Heisenberg's particular theory of everything doesn't work, but the idea of spontaneous symmetry breaking was made into a correct theory by Nambu, who discovered the quark chiral condensate breaks approximate chiral symmetry, and made a model of this with Jona-Lasinio.
  • Higgs mechanism: This is due to Brout and Englert, also Higgs and Hagen, Geralnik, Kibble. This idea is that the Nambu condensate can be charged and therefore superconducting.
  • QCD glue condensates: this is probably best attributed to Shifman,Vainshtein and Zakharov. The idea of a glue condensate was floating around at the time, but they gave a way to quantitate the amount of glue.
  • Dual superconductor model of confinement: This idea is due to several people, but t'Hooft is most notable. Seiberg/Witten theory made it respectable by giving quantitative exactly solvable models where you can understand the mechanism qualitatively.

There are also failed dynamical vacuum models

  • Lumineferous Ether: The 19th century idea is that there are mechanical stresses in a material filling space which are responsible for electric and magnetic fields.
  • Vortex atoms: Kelvin's idea that atoms are vortices in ether-flow.
  • Teleparallel gravity: Right after developing General Relativity, Einstein postulated the notion of teleparallelism, a field which would tell you which direction is which at far away points. This breaks general coordinate invariance, and I don't know this theory, but it wasn't taken seriously by people, including Einstein. I think this is just one of the things he had in the back of his head from the many years working on GR, and he wanted to get it out. This theory is a kind of ether, and sometimes people say "Einstein embraced the ether later in life", they are talking about teleparallel ether, which (I presume, I didn't read it) is relativistically invariant and has no relation to the lumineferous ether.

Uncertainty principle for pairs $x$ and $p$ or $E$ and $t$ data written for a physical particle has nothing to do with virtual pair production.

The "presence of higher states" in a given state has a limited and certain meaning and it is not due to fluctuations.

Let us consider an exact ground state $\psi_0$. It is often unknown as analytical formula. It is searched by the perturbation theory and is obtained in a spectral form like this one:

$$\Psi_0=e^{-iE_0 t/\hbar}\sum_{n\ge 0}C_{0n}\psi_n^{(0)}\quad (1)$$

This spectral decomposition is not a quantum mechanical superposition of states at all! All higher approximate states $\psi_n^{(0)},\: n>0$ are non observable in the exact state $\psi_0$; they are just dumb numbers to correct inexact value $\psi_0^{(0)}$ to get the exact one, the latter being still the ground state. No experiment can find an excited state, exact or approximate, in the ground state, even virtually (vacuum is a ground state). But in the formula (1) the approximate higher states are "present". This leads to an erroneous confusion that in the ground state one may "find" higher states for short period due to uncertainty relationship. No, they are not virtual states.

Note, the spectral expansions like (1) for other exact states ($n>0$) are involved in real calculations where exist observable exact states $\psi_n,\:n>0$ which bring their own $\psi_{n'}^{(0)}$ because of being expanded in the spectral series too. In that case, those approximate $\psi_n^{(0)},\:n>0$ may be called observable since $\psi_n\approx C_{nn}\psi_n^{(0)}$.

Again, in any particular state $n$ $$\psi_n=\sum_{n'} C_{nn'}\psi_n^{(0)}=C_{nn}\psi_n^{(0)}+\sum_{n'\ne n} C_{nn'}\psi_n^{(0)}\quad (2)$$ there are no other observable states $n'\ne n$, it should be clear. It is a state with a certain energy an nothing else can be found in it.

The only observable states in a general state $\Psi$ are those that are involved in the quantum mechanical superposition of exact states with their own energetic exponentials:

$$\Psi=\sum_n A_n\psi_n e^{-iE_n t/\hbar}\quad (3)$$

Often some higher observable states are just forbidden in this superposition by the energy conservation law, which valid, for example, in collisions. On the other hand, there is no limit on $n$ in the dumb spectral decompositions like (1) and (2). In perturbative calculations the observable states mix with dumb ones. But if you analyze examples carefully, you will find that the all "virtual states" are always the approximate functions $\psi_{n'}^{0}$ (corrections to $\psi_n^{0}$ injected from (2) to (3)) and never the exact states, in the regular perturbation theory or in the Feynman diagrams, whatever. This fact shows their true origin (1)-(2).

P.S. For those who did not get the point: there are no virtual states, as a matter of fact.

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    $\begingroup$ That doesn't really address the history aspect of the question... $\endgroup$ – Simon Nov 27 '11 at 1:56

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