From Quantum Hydrodynamics to Quantum Gravity
Grigory E. Volovik
Summary and citation · read the original at the source · arXiv assumed-1991-2003 licence, not a Creative Commons grant
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Volovik's rapporteur article asks what a laboratory liquid can teach a theory of gravity, and answers it with a calculation rather than an analogy. Both hydrodynamics and general relativity are perfect classical theories, he notes, and general relativity can be viewed as a theory of hydrodynamic type in which the collective variables are the metric fields; quantised, both share deep features including quadratic divergences, and quantising hydrodynamics is a problem as old as quantising gravity. He then works Landau's quantum hydrodynamics through to the vacuum-energy question. In a liquid, the analogue of the vacuum energy density obeys the equation of state that pressure equals minus energy density — the same equation of state the cosmological constant obeys. And for an isolated liquid in equilibrium with nothing pressing on it from outside, that quantity is exactly zero, with no fine tuning anywhere in the derivation. Add matter and it is no longer zero: thermal excitations push, the vacuum pushes back, and the vacuum energy settles at one third of the matter energy density.
Pourquoi cela compte iciChapter 5's central move is that the enormous mismatch between the calculated and observed vacuum energy is not a failure of arithmetic but a sign the wrong sum was being done. This is the paper that shows what the right sum looks like in a system you can actually cool and measure, and it states the conclusion the chapter needs: the vacuum energy is naturally determined by macroscopic quantities, rather than by a huge microscopic Planck energy scale.
Ce qu'il affirme
01General relativity can be viewed as a theory of hydrodynamic type in which the collective variables are the metric fields, and at the quantum level quantum hydrodynamics and quantum gravity share many common features — both, for example, have quadratic divergences.Section 1, Introduction
Published and peer-reviewed02In a quantum liquid the analogue of the vacuum energy density obeys the equation of state that the vacuum pressure equals minus the vacuum energy density — the same relation the cosmological constant obeys in cosmology.Section 2, Eq. 3; restated in Section 4.3, Eq. 51
Published and peer-reviewed03For an equilibrium liquid in the absence of any external environment, that vacuum energy density is exactly zero, and Volovik states the generality plainly: the nullification of vacuum energy occurs for any non-disturbed equilibrium vacuum. Nothing is tuned to make it happen — it follows from the liquid being self-sustained and in equilibrium at zero external pressure.Section 2, Eq. 9 and the sentence following it; Section 2 close
Published and peer-reviewed04Add matter and the vacuum responds. Thermal phonons produce a radiation pressure that the vacuum must compensate, and the vacuum energy density settles at one third of the matter energy density — the back reaction of the vacuum to relativistic matter, obtained entirely within quantum hydrodynamics.Section 4.3, Eqs. 52 and 53
Published and peer-reviewed05The consequence Volovik draws is that the vacuum energy is naturally determined by macroscopic quantities rather than by the huge microscopic Planck energy scale — which is the point of contact with the cosmological-constant problem, since an effective theory that sums zero-point energies gives an answer many orders of magnitude too big in the liquid exactly as it does in gravity.Section 4.3, close; Section 5.2, the passage citing Weinberg's review
What to watch06A second hint is a constraint on any microscopic theory of quantum gravity: it must contain an additional parameter beyond h-bar, c and Newton's constant, giving a dimensionless number that distinguishes microscopic theories sharing the same macroscopic behaviour. Volovik quotes Bjorken on the requirement — the emergence can only work if there is an extremely small expansion parameter in the game.Section 5.2
What to watch
La porte d'entrée
https://arxiv.org/abs/gr-qc/0612134SOURCE READ IN FULL. The complete 20-page preprint, version 5, was downloaded from arXiv on 2026-09-11 and read. The arXiv record carries the assumed licence for submissions of 1991 to 2003, which grants arXiv the right to distribute the paper and nothing more — it is not an open licence — and the proceedings version is held by World Scientific. This sheet therefore carries a summary, the results and short quotations. WHY THIS SHEET EXISTS ALONGSIDE THE BOOK. The Universe in a Helium Droplet, at /library/stm-6ee45bd8be, is the monograph statement of the same programme, and it is in copyright and unreadable without a library. This paper is free, it is short, and it carries the vacuum-energy argument to a numbered equation, which is why the claims below can name one. Written at the Low Temperature Laboratory, Helsinki University of Technology, and the Landau Institute, Moscow.
Comment le citer
Grigory E. Volovik (2006) From Quantum Hydrodynamics to Quantum Gravity. doi:10.48550/arXiv.gr-qc/0612134
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