Inertia as a zero-point-field force: Critical analysis of the Haisch-Rueda-Puthoff inertia theory

In the article by Haisch, Rueda, and Puthoff (HRP) [Phys. Rev. A 49, 678 (1994)], an explanation of inertia as an “electromagnetic resistance arising from the known spectral distortion of the zero-point field in accelerated frames” is proposed. In this paper, we show that this result is an error due to incorrect physical and mathematical assumptions associated with taking a nonrelativistic approach. At the core of HRP’s theory is a calculation of the so-called magnetic Lorentz force, which can be represented in terms of a correlation function of zero-point field (ZPF) radiation and a form factor of a small uniformly accelerated oscillator. To consider this force, the authors use a nonrelativistic approach based in fact on two main assumptions. (i) A nonrelativistic approximation of the correlation function exists. (ii) In the force integral expression, contributions of the integrand for large differences in time are damped and can be ignored. We show that their implicit nonrelativistic implementation of the correlation function is incorrect, and present as the correct expression a proper nonrelativistic limit of the exact correlation function offered earlier by Boyer. We also show that the second assumption is misguided, and the force exerted on even a slow moving accelerated oscillator “remembers” the entire history of the accelerated motion including times when its velocity could have any large value. A nonrelativistic approximation of the force leads to a contradiction. The force is fundamentally a relativistic one, which we show is equal to zero. Consequently, the interaction of the accelerated oscillator with ZPF radiation does not produce inertia, at least not for the component of the Lorentz force that HRP considered. Finally, several other calculation errors are discussed in our paper: the sign (which is of paramount importance for HRP’s theory) of HRP’s final force expression should be positive, not negative, and the high-frequency approximation used is not justified.