Historical research guide · 0778 · 2009
Inertia as a zero-point-field force: Critical analysis of the Haisch-Rueda-Puthoff inertia theory
Yefim S. Levin
In one minute
In 1994 Haisch, Rueda and Puthoff proposed that resistance to acceleration arises from a vacuum reaction. Yefim Levin worked through that calculation and reports in Physical Review A that it does not follow as written. His objections are technical: the correlation function implicitly used for zero-point radiation in an accelerating detector is not the correct non-relativistic limit; the force retains the motion’s entire history, so the calculation cannot be non-relativistic; and the calculated component is zero with Boyer’s exact correlation function. Levin says he tried to repair the theory but could not. His paper does not analyse Haisch and Rueda’s later derivation, which takes another route.
Connection
Chapter 3 rests on the proposition that inertia is a vacuum effect, and a site that teaches that proposition has to teach where the argument is load-bearing and where it is still being worked out. Levin marks the exact technical joint the 1994 derivation turns on — and, better, names the open question that would settle it: which correlation function actually describes zero-point radiation seen by a uniformly accelerated detector. Chapter 1 gets a clean worked example of how a claim of this size is examined in the literature.
From the source
The analysis is scoped to one calculation. Levin examines the magnetic Lorentz force on a small uniformly accelerated oscillator as computed in Haisch, Rueda and Puthoff’s 1994 Physical Review A paper. He records that Haisch and Rueda’s 1998 Foundations of Physics analysis, which the authors say avoids the ad hoc modelling of particle-field interaction dynamics used in 1994, is not considered in his work — so the later derivation of the same conclusion is untouched by this paper.Section I, Introduction, page 012114-1
Levin identifies two assumptions carrying the 1994 result: first, that a non-relativistic approximation of the zero-point-field correlation function exists; second, that in the force integral the contributions of the integrand for large differences in time are damped and can be ignored.Abstract, page 012114-1
His central result: the force exerted on even a slowly moving accelerated oscillator remembers the entire history of the accelerated motion, including times when its velocity could have any large value. The force is therefore fundamentally a relativistic one, and computed with Boyer’s exact correlation function Levin finds it equal to zero — so on his reading this component of the Lorentz force does not produce inertia.Abstract; Section II C, pages 012114-2 to 012114-6
A separate arithmetic point about the sign. The arctangent in the 1994 force expression is bounded between minus and plus one half of pi, so for small positive values of its argument the limit is plus one half of pi, which makes the resulting force positive; the 1994 paper selects the negative sign, which is the sign that reads as inertia. Levin argues the sign should have been an outcome, not a choice.Section II A, equations 6 and 7, page 012114-2
Levin states his own motive in the paper: the aim was not only to correct algebra but to see whether the ideas could be better implemented so as to save the main claim that the zero-point field can resist the motion of an accelerated oscillator. He reports that he did not succeed in that attempt, and adds that it is very instructive to thoroughly examine the mathematical model.Section II A, page 012114-2
The open question the paper leaves on the bench is sharper than its verdict. Two different correlation functions for the zero-point electromagnetic field measured by a uniformly accelerated detector are in circulation: Boyer’s, which is not singular when the two times coincide and gives zero force, and Cole’s, which is singular there and gives a non-zero force with both magnetic and electric components, interpreted there as mass corrections long known from QED analysis. Levin writes that this has no explanation at present, and that distinguishing the two could provide additional insight into the problem. Settle that, and the 1994 calculation settles with it.Section II D, Closing remarks, page 012114-6
The way in
https://doi.org/10.1103/PhysRevA.79.012114How to cite it
Yefim S. Levin (2009) Inertia as a zero-point-field force: Critical analysis of the Haisch-Rueda-Puthoff inertia theory doi:10.1103/PhysRevA.79.012114