Historical research guide · 0537 · 1998
Contribution to Inertial Mass by Reaction of the Vacuum to Accelerated Motion
Alfonso Rueda · Bernhard Haisch
In one minute
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.
Connection
Chapter 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.
From the source
The 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)
Identifying 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
The 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
The 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
The 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
Only 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
The way in
https://doi.org/10.1023/A:1018893903079How 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