Sakharov's induced gravity: a modern perspective
Matt Visser
Summary and citation · read the original at the source · arXiv assumed-1991-2003 licence, not a Creative Commons grant
Na jednej stronie
Sakharov's 1967 note was three pages and four formulas, and Visser's article is the piece that made it usable again: it translates the idea into modern language and sorts the versions of it now in circulation. The framework is set out in five steps. Take a Lorentzian manifold; assume nothing about how its geometry moves, leaving it free to flap in the breeze; do not quantise gravity, but quantise everything else; work out the one-loop effective action for the matter fields on that background; and read off what it contains. It contains, uninvited, a cosmological-constant term, an Einstein-Hilbert term and curvature-squared terms. Visser then shows that this single calculation supports four quite different research programmes depending on what you demand of it — Sakharov's own demand of one-loop dominance, Pauli's of one-loop finiteness, Frolov and Fursaev's of one-loop calculability, and plain renormalizability's of calculable one-loop changes. Each imposes its own constraints on what particles may exist, and he gives the coefficients in a table.
Dlaczego ma tu znaczenieChapter 3 rests on the claim that gravity can be induced rather than fundamental, and this is where that claim is stated in language a reader can follow and check. It also supplies the chapter's sharpest line: whatever view you take of the four programmes, even if Einstein gravity is not there at zero loops, it is automatically generated at one loop.
Co twierdzi
01The basic idea is that gravity is not fundamental in the sense of particle physics: general relativity emerges from quantum field theory in roughly the same sense that hydrodynamics or continuum elasticity theory emerges from molecular physics.Abstract; Section 1, Introduction
Published and peer-reviewed02The central observation is a calculation, not a conjecture. Quantise matter on a classical curved background and the one-loop effective action automatically contains a cosmological-constant term, a term proportional to the curvature scalar — the Einstein-Hilbert action — and curvature-squared terms.Section 1, Eqs. 1 and 2
Settled physics03The same one-loop formulae support four different programmes, and the difference between them is what each demands: Sakharov demands one-loop dominance, Pauli one-loop finiteness, Frolov and Fursaev one-loop calculability, and ordinary renormalizability demands only that certain differences be calculable.Section 2, close; Sections 4 to 7; Section 9, Summary and Discussion
Published and peer-reviewed04On Sakharov's own reading — set every tree-level constant to zero, let one-loop physics dominate, take dimensionless numbers of order one and cut off at the Planck scale — the reciprocal of Newton's constant is given by the square of the cutoff multiplied by a supertrace over the particle spectrum. That conjectured link between Newton's constant and particle physics is what drew the attention, and Visser notes over 260 citations as of February 2002.Section 4, Eq. 29
What to watch05The finiteness route puts hard constraints on what matter may exist. Pauli's conditions are a forerunner of supersymmetry and are not satisfied by the standard model, and Visser carries Pauli's own verdict on them: these requirements are so extensive that it is rather improbable that they are satisfied in reality.Section 5, Steps 1 to 3, with Table 1; the quoted Pauli remark at the close of Section 5
Published and peer-reviewed06The conclusion all four routes share is the one that matters for an emergent-gravity programme: even if Einstein gravity is not there at zero loops, it will automatically be generated at one loop — so deriving the inverse square law is not the hard step for a candidate theory of quantum gravity, and gravity was never quantised anywhere in the argument.Section 9, Summary and Discussion
Published and peer-reviewed
Droga do źródła
https://arxiv.org/abs/gr-qc/0204062SOURCE READ IN FULL. The complete 17-page preprint 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 journal version is held by World Scientific. This sheet therefore carries a summary, the results and short quotations, and sends the reader to the free original. Written at Washington University in Saint Louis; the paper notes Visser's move to Victoria University of Wellington from July 2002.
Jak cytować
Matt Visser (2002) Sakharov's induced gravity: a modern perspective. doi:10.1142/S0217732302006886
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