Contribution to Inertial Mass by Reaction of the Vacuum to Accelerated Motion
Alfonso Rueda · Bernhard Haisch
Abstract and summary · read the original at the source
In one page
This is the long version of the argument Alfonso Rueda and Bernhard Haisch made in 1998: what pushes back when you push an object is the vacuum itself. Quantum physics says empty space is filled with a restless electromagnetic sea, the zero-point field. Sit still in it and it looks the same in every direction, so nothing pushes. Accelerate, and Rueda and Haisch show — using nothing but the standard relativistic transformations of electric and magnetic fields — that the field’s flow of energy and momentum becomes lopsided in the object’s own volume, and that the imbalance points backwards, in exact proportion to the acceleration. An object that scatters even a fraction of that flow therefore feels a resisting force. Newton’s f equals m a drops out, and so does the fully relativistic four-force. Their formula for inertial mass is striking in its plainness: it is the slice of vacuum energy inside the object’s own volume that the object actually interacts with. The authors present it as a descendant of Sakharov’s idea that gravity, too, is induced by the vacuum.
Why it matters hereChapter three rests on this: inertia and gravity read as effects of the zero-point field rather than brute properties of matter. And because the paper writes mass as a coupling strength — how strongly a body interacts with the field it sits in — chapter eight can ask the engineering question that follows, whether that coupling is something a machine could ever tune.
What it claims
01The zero-point field’s momentum density vanishes for an observer at rest or in uniform motion, but in an accelerated frame the standard relativistic transformations of the electric and magnetic fields make it non-zero and directed against the acceleration — no model of the particle is used anywhere in the derivation.Sec. V, paragraphs following Eq. (24); Eqs. (25)–(27)
Published and peer-reviewed02Identifying the rate of change of that vacuum momentum with a force gives an opposing force exactly proportional to the acceleration, which the authors propose is the inertia reaction force itself; by Newton’s third law the accelerating agent must supply f equals m a.Sec. V, Eqs. (28) and (29); Sec. VI, opening paragraph
Published and peer-reviewed03The coefficient that emerges has the dimensions of mass and a plain reading: inertial mass is the fraction of the zero-point radiation energy enclosed within the object’s proper volume that actually interacts with it, set by a frequency-dependent coupling coefficient between zero and one.Sec. V, Eq. (30) and the paragraph interpreting it
Published and peer-reviewed04The result is not merely Newtonian: the same construction returns the special-relativistic momentum and the correct four-force, and a fully covariant version of the calculation removes the stray factor of four-thirds that the non-covariant route leaves behind.Sec. VI, Eqs. (31)–(33); Appendix D
Published and peer-reviewed05The derivation is carried out for uniformly accelerated (hyperbolic) motion; the authors argue it extends to arbitrary motion because the result is memoryless, and name the calculation that would confirm it — circular motion at constant angular velocity.Sec. VII, Eq. (34) and closing paragraph
What to watch06Only the electromagnetic vacuum is treated here; Rueda and Haisch propose that the zero-point fluctuations of the weak and strong fields should oppose accelerated motion in the same way, so that inertia can be accounted for by the fields already established rather than by an added mass-giving field.Sec. VIII, ‘Outlook and Closing Remarks’, second and third paragraphs
What to watch
Read it · abstract
Abstract
We present an approach to understanding the origin of inertia involving the electromagnetic component of the quantum vacuum and propose this as a step toward an alternative to Mach’s principle. Preliminary analysis of the momentum flux of the classical electromagnetic zero-point radiation impinging on accelerated objects as viewed by an inertial observer suggests that the resistance to acceleration attributed to inertia may be at least in part a force of opposition originating in the vacuum. This analysis avoids the ad hoc modeling of particle-field interaction dynamics used previously by Haisch, Rueda and Puthoff (Phys. Rev. A 49, 678, 1994) to derive a similar result. This present approach is not dependent upon what happens at the particle point, but on how an external observer assesses the kinematical characteristics of the zero-point radiation impinging on the accelerated object. A relativistic form of the equation of motion results from the present analysis. Its manifestly covariant form yields a simple result that may be interpreted as a contribution to inertial mass. We note that our approach is related by the principle of equivalence to Sakharov’s conjecture (Sov. Phys. Dokl. 12, 1040, 1968) of a connection between Einstein action and the vacuum. The argument presented may thus be construed as a descendant of Sakharov’s conjecture by which we attempt to attribute a mass-giving property to the electromagnetic component — and possibly other components — of the vacuum. In this view the physical momentum of an object is related to the radiative momentum flux of the vacuum instantaneously contained in the characteristic proper volume of the object. The interaction process between the accelerated object and the vacuum (akin to absorption or scattering of electromagnetic radiation) appears to generate a physical resistance (reaction force) to acceleration suggestive of what has been historically known as inertia.
Alfonso Rueda and Bernhard Haisch. Foundations of Physics 28 (1998) 1057–1108. Author version: arXiv:physics/9802030.
(Abstract only. The author version is free to read on arXiv — see the rights note for why the full text is not reproduced here, and for the two companion sheets in this library.)
The way in
https://doi.org/10.1023/A:1018893903079Licence checked directly. Published as Foundations of Physics 28, 1057–1108 (1998); the Crossref record for the DOI carries only Springer Nature’s text-and-data-mining terms. The author version is free to read on arXiv as physics/9802030, posted 17 February 1998, and that record carries the arXiv assumed-1991-2003 licence, which grants arXiv distribution and nothing further — checked on the arXiv abstract page on 2026-09-08, where no Creative Commons statement appears, and none appears in the text either. So this sheet carries the summary, the claims and the authors’ own abstract and sends the reader to the source. The claims below were written from the arXiv text and the locators use its section, equation and appendix numbering. Rueda writes from the Department of Electrical Engineering at California State University, Long Beach; Haisch from the Solar and Astrophysics Laboratory at Lockheed Martin, Palo Alto, and the Max-Planck-Institut für Extraterrestrische Physik, Garching. Its companion, the short Physics Letters A statement of the same derivation, is on this site as stm-532ddcda6d; the NASA final report in which Haisch and Rueda gather the whole four-year programme is at /library/stm-93cf38cc58.
How to cite it
Alfonso Rueda, Bernhard Haisch (1998) Contribution to Inertial Mass by Reaction of the Vacuum to Accelerated Motion. doi:10.1023/A:1018893903079
Where it sits in the curriculum
Inertia and gravity from the vacuumWhat the vacuum isInertial mass reduction and transmedium craftThe unified picture