Historical research guide · 0936 · 1989

Gravity as a zero-point-fluctuation force

Harold E. Puthoff

In one minute

Harold Puthoff develops Andrei Sakharov’s proposal that gravity can arise from vacuum fluctuations rather than from a separate fundamental force. His 1989 paper models charged point particles driven by the vacuum electromagnetic zero-point field. In the model, each particle’s vacuum-driven Zitterbewegung, or trembling motion, supplies kinetic energy identified with mass. Puthoff uses the accelerated-frame spectrum and the equivalence principle to fix a high-frequency cutoff near the Planck scale. Following Boyer’s method, he treats the interaction of two particles as a retarded van der Waals force and derives a leading inverse-square attraction. These are results inside a point-particle zero-point-field model, not direct measurements of a new gravitational mechanism. The paper links that model to mass, the gravitational constant, Mach’s principle, and a proposed electromagnetic account of gravity.

Connection

This is the fully worked version of Sakharov’s induced-gravity proposal used in Chapter 3. It puts mass, the gravitational constant, and an inverse-square attraction into one vacuum-field model. The engineering question that follows is concrete: identify a field condition that the model says changes an inertial or gravitational response, hold ordinary electromagnetic forces constant, and measure the predicted difference. Until such a measurement separates this mechanism from standard gravity, the derivation remains a research programme that readers can trace line by line.

From the source

The paper treats gravitation as an induced residual effect of zero-point fluctuations in the vacuum electromagnetic field, rather than as a separately existing fundamental force. It places the proposed mechanism in the family of van der Waals and Casimir forces, following the proposal Sakharov made in 1967.Section I, Introduction; restated at the head of Section VI, Discussion
Within the model, particle mass is derived rather than assumed. It is the expectation value of kinetic energy in the vacuum-driven trembling motion of charged point particles, an internal energy whose scale is set by the particle’s radiation-damping constant and the high-frequency cutoff of the vacuum spectrum.Section III into Section IV, the passage defining rest-mass energy from the trembling kinetic energy
The model fixes the zero-point spectrum’s cutoff frequency through the principle of equivalence rather than by a fit. An accelerated observer sees an added spectral term proportional to acceleration squared; applying the same addition near a gravitating mass yields Sakharov’s relation between the gravitational constant and a cutoff on the order of the Planck frequency.Section II, the leading terms of the accelerated-frame spectrum; Section IV, equations 39 and 40
Following Boyer’s method, the paper computes the force between two model particles as a retarded van der Waals force between correlated radiation fields. Its leading non-oscillatory term is Newton’s inverse-square law of gravitation, with no adjustable parameter inside the model.Section V, equations 56 through 62
The model gives specific accounts of familiar gravity features: its weakness follows from the inverse square of a very high cutoff frequency; its attraction follows the sign of a van der Waals force; and its single-signed charge follows from mass being positive kinetic energy. It also treats gravity as unshieldable because vacuum noise is unshieldable in the model’s dilute-particle, high-frequency cavity picture.Section VI, Discussion, second and third paragraphs
Because the construction rests on the vacuum electromagnetic zero-point field alone, Puthoff calls this form of gravitational theory an ‘already unified’ theory. If the model correctly represents the interaction, he argues, gravity need not be treated as a separate force waiting to be unified or as a separate field to be quantized.Section VI, Discussion, fourth and fifth paragraphs; and the abstract

The way in

https://doi.org/10.1103/PhysRevA.39.2333

Historical source-access record. This guide links to the original; it does not reproduce the paper text.

PUBLICATION. Physical Review A, third series, volume 39, number 5, pages 2333 to 2342, 1 March 1989. Received 14 March 1988, revised manuscript received 15 August 1988. Copyright 1989 The American Physical Society, published under the APS default licence, with no Creative Commons statement anywhere in the article, so only the abstract is reproduced here. SOURCE READ. The complete ten-page article was retrieved as a PDF from the APS harvest service at harvest.aps.org, path /v2/journals/articles/10.1103/PhysRevA.39.2333/fulltext, and read in full; the abstract below is the article’s own printed abstract, and the summary, claims and locators were written from the complete text, not from a database record. AUTHOR AFFILIATION as printed: H. E. Puthoff, Institute for Advanced Studies at Austin, Austin, Texas 78746. The given name Harold is expanded here from the author’s other publications of the same period; the article itself prints the initials H. E. Puthoff. NOTATION. The paper’s equations use characters this site cannot render safely, so relations are written out in words. The paper writes the Zitterbewegung jitter motion in italics throughout, and the scan of the running text renders that word inconsistently; it is given in its correct spelling here. LATER EXCHANGE. The paper drew a published comment and reply four years on, both confirmed in Crossref: S. Carlip, Comment on ‘Gravity as a zero-point-fluctuation force’, Physical Review A 47, pages 3452 to 3453 (DOI 10.1103/PhysRevA.47.3452), and H. E. Puthoff, Reply to ‘Comment on “Gravity as a zero-point-fluctuation force”’, Physical Review A 47, pages 3454 to 3455 (DOI 10.1103/PhysRevA.47.3454). Neither the comment nor the reply was read for this page; they are recorded here so a reader following the argument knows the exchange exists and where to find it.

How to cite it

Harold E. Puthoff (1989) Gravity as a zero-point-fluctuation force doi:10.1103/PhysRevA.39.2333

Where it sits in the curriculum

Inertia and gravity from the vacuum