The book by E. Volovik seems very complete but I was unable to read it since it requires a very technical understanding of various areas of physics.
Can anyone explain what this theory is about and how serious it is? Is it backed up by the community? Could it be verified by experiment?
Also, what other papers or books can I read to prepare for this one?
This (big) book investigates the analogy between the elementary particles (excitations of the quantum vacuum) and the quasiparticles/collective excitations in quantum liquids (in particular the superfluid He-4, bosonic, and superfluid He-3, fermionic).
Elementary particles (like electrons, neutrinos, photons...) are excitations of a more fundamental "medium", the quantum vacuum. Among the existing condensed matter systems, the superfluid A-phase of He-3 most closely represents the quantum vacuum: this phase is the outcome of a spontaneous symmetry breaking of a rather complex group, so that different Goldstone modes appear, which means "new particles" (5 for the A-phase and 4 for the B-phase, as the number of the Goldstone modes usually coincides with the dimension of the manifold of the degeneracy states, see this for more math on this aspect).
The aim of Volovik is to investigate this analogy (and not only, since a fundamental point is also played by topological defects, like quantized vortices). Quasiparticles in Helium are similar to the elementary particles, while the collective modes are analogues of photons and gravitons. The laws of physics, such as the laws of relativity (Lorentz invariance) and gauge invariance, arise when the temperature of the quantum liquid decreases (Volovik calls this "emergent" relativistic quantum field theory).
Moreover, different superfluid phases are related to different vacua with a different symmetry breaking. Here is the link with the "Universe": as the very early Universe expands (and cools down), it undergoes a sequence of symmetry breakings, see also this SE question (like the electroweak breaking). The same for quantum liquids: as they are cooled down, a superfluid (symmetry broken) phase with "new particles" (related to the symmetry breaking) appears.
Terminology note: in condensed matter, an "elementary excitation" is usually called a "quasiparticle" if it is a fermion (in particular, if it is a "dressed" atom or particle) and a "collective excitation" if it is a boson. Goldstone modes are typically regarded as "collective excitations", and are kind of similar to photons (i.e. the most famous Goldstone mode is the "phonon", a quantum of sound that has linear dispersion relation, somehow analogous to the photon).
Note on "seriousness" and "experiments": the book is not only this, and some topics there are really the personal view of the author (the Foreword of the book, written by James D. Bjorken, warns the reader against it... but the book is certainly "serious": it is widely cited and considered to be an important reference). Regarding experiments: there is a known analogy between gravity and hydrodynamics, and also experiments dedicated to recreate sonic black-holes. Several experiments aim at investigating this analogy. Moreover: the topological defects, the presence of Goldstone modes and the superfluid phases (like the A and B phases of Helium-3) described in Volovik's book are well known and experimentally studied. I suggest you to have a look at this introductory paper.
