## No full-text available

To read the full-text of this research,

you can request a copy directly from the author.

In the article by Haisch, Rueda and Puthoff 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.

To read the full-text of this research,

you can request a copy directly from the author.

... The quantum potential of the vacuum makes the 3D quantum vacuum a fundamentally nonlocal manifold. Equations (32) and (35) mean that, both in the relativistic and non-relativistic domains, the quantum potential -both regarding the processes of creation and regarding the processes of annihilation -has a non-local instantaneous action. In sum, the non-local connection between RS processes derives from the instantaneous action of the quantum potential guiding the evolution of the occurring of the processes of creation or annihilation of quanta (corresponding to opportune changes of the quantum vacuum energy density) in the different regions of the 3D quantum vacuum. ...

... As regards the model proposed by Haisch, Rueda, and Puthoff in [28], it must be emphasized, however, that the explanation of inertia as an "electromagnetic resistance arising from the known spectral distortion of the zero-point field in accelerated frames" has been criticized recently by Levin, who claims that this result contains errors due to incorrect physical and mathematical assumptions associated with taking a nonrelativistic approach in the calculation of the magnetic Lorentz force [35]. According to Levin's research, 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, and, moreover, the high-frequency approximation taken into consideration by the three authors is not justified. ...

A unification model where matter is a structure of energy of a three-dimensional quantum vacuum and diminishes its energy density is proposed. Mass and gravity are carried by variable energy density of the three-dimensional quantum vacuum. Electric field and magnetic field are carried by regions of polarized quantum vacuum generated by appropriate oscillations depending on fluctuations of the quantum vacuum energy density. The quantum behavior of matter derives directly from elementary energy fluctuations of the three-dimensional quantum vacuum. Dark energy is itself energy of the three-dimensional quantum vacuum. K e y w o r d s: space-time, time, three-dimensional quantum vacuum, mass, gravity, electromagnetic field, quantum physics, dark energy.

... In the case of the quartic anharmonic oscillator, Pesquera and Claverie showed that SED disagrees with quantum mechanics [16]. Additionally, the results claimed in [17][18][19] were shown to be wrong due to improper relativistic approximation [20]. While these theoretical analyses are documented in detail, it may be useful to use numerical simulation as an independent check in order to establish the validity range of SED, which is one of the objectives of our work. ...

... Therefore, all sampling methods for the allowed wave vectors k become equivalent, and the summation approaches the integral. This is consistent with the fact that no volume factor is involved in the vacuum field integral, as shown in (1)), and (21) can be used for both sampling methods to calculate the volume factor in (20) and (28): ...

Stochastic electrodynamics (SED) predicts a Gaussian probability distribution for a classical
harmonic oscillator in the vacuum field. This probability distribution is identical to that of the
ground state quantum harmonic oscillator. Thus, the Heisenberg minimum uncertainty relation
is recovered in SED. To understand the dynamics that give rise to the uncertainty relation and
the Gaussian probability distribution, we perform a numerical simulation and follow the motion of
the oscillator. The dynamical information obtained through the simulation provides insight to the
connection between the classic double-peak probability distribution and the Gaussian probability
distribution. A main objective for SED research is to establish to what extent the results of quantum
mechanics can be obtained. The present simulation method can be applied to other physical systems,
and it may assist in evaluating the validity range of SED.

... The second criterion has far reaching consequences to the understanding of whole Physics. Though it is non-violence of force law, but this refutes the applyingconcepts of first inertial law of motion that will be self-demolished with the emergent of second criterion whatever and however inertia is privileged as a fundamental entity with the causative factors explained as-inertia in fact is a consequence of electromagnetic interactions of accelerating matter (typically charged) with a quantum mechanical vacuum fluctuation electromagnetic field based on Lorentz force [56], is full of doubts [57,58] (supporting the Machian type of Inertia) and the result of errors [59]. These kinds of investigations along with Mach's version are not exactly addressed to the question of Newtonian causative inertia of rest and motion rather the study of how the mimics of field-effect come into the resistance of applied force. ...

A new type of relative (based not on Relativity) acceleration in relation to the central angle subtension around any static Gravitational mass, a quite different but in combination of central force exertion phenomenon that is based on same Newton's Universal Law of Gravitation (in terms of gravity $\mathbf{g}$) has been derived mathematically within the Classical regime, without actually violating the Newton's second law of motion but suggesting to reconsider in the applications of first law and thematically supporting and remaining as a counterpart to Relational Mechanics, primarily reviving the Aristotelian concept of \textquoteleft natural' and \textquoteleft violent' motions. Achievement of such paradigm became possible through the validation of ${(V^2/r)}$ as a real corresponding factor for both tangential $(V^2/r)\tilde{\theta}$ and inward centripetal $-(V^2/r)\tilde{r}$ accelerations in a circular motion within the uniform magnitude of tangential velocity, ${V}$. $(V^2/r)\tilde{\theta}$, being a new terminology has shown a vital role for such validation, obtained by differentiating the centripetal acceleration with respect to $\theta$. For a general case, an absurd but reforming result as a next new acceleration component, $-{d(V^2/r)\tilde{r}}/{d\theta}$ reduced equivalently to $(Vv/r)cos\psi\tilde{r}$ acting towards the center along with $\mathbf{g}$, and $(v^2/r)\tilde{\theta}$ acting tangentially appears to be presented with $v$ being any arbitrary instant velocity magnitude coupled to both radial and tangential accelerations. This helped in the identification of the net applied acceleration into scalar form, quadratically for two and three (taking circular motion as an example) dimensions obtained by applying the \textit{Resolution of Vector}. The concept of tangential motion has been revised with its impact as a basis on the proclamation of choosing alternative mode of the force law contradicting on it basic presumptions and applications, with elegant prediction of existence of extra (exactly doubled) gravitational pull (that demanded to replace dark matter) as an alternative MOND, simple discussion on supporting the pioneer anomaly as of gravitational origin, as major outputs. And possible other applications are discussed, theoretically only.

... The force they derived from this model was F = −Γw 2 c a/2πc 2 where Γ is the Abraham-Lorentz damping constant of the parton being oscillated, w c is the Compton scale of the parton below which the oscillations of the zero-point field have no effect on it, is the reduced Planck's constant, a is the acceleration and c is the speed of light. However, although their derived force looks like inertia, their derivation was complex, required the imposition of a high frequency cutoff to avoid infinite energy, and has been criticised on relativistic, and other, grounds, by, for example, Levin (2009). ...

The property of inertia has never been fully explained. A model for inertia
(MiHsC or quantised inertia) has been suggested that assumes that 1) inertia is
due to Unruh radiation and 2) this radiation is subject to a Hubble-scale
Casimir effect. This model has no adjustable parameters and predicts the cosmic
acceleration, and galaxy rotation without dark matter, suggesting that Unruh
radiation indeed causes inertia, but the exact mechanism by which it does this
has not been specified. The mechanism suggested here is that when an object
accelerates, for example to the right, a dynamical (Rindler) event horizon
forms to its left, reducing the Unruh radiation on that side by a Rindler-scale
Casimir effect whereas the radiation on the other side is only slightly reduced
by a Hubble-scale Casimir effect. This produces an imbalance in the radiation
pressure on the object, and a net force that always opposes acceleration, like
inertia. A formula for inertia is derived, and an experimental test is
suggested.

... Investigations of rotation are mostly based on the ideas developed for a linear acceleration through a vacuum [1] - [9]. For example, in [1], the authors write: "... in the Rindler case, a set of uniformly accelerated particle detectors ... will give zero response in the Rindler vacuum state, and will give a consistent thermal response to the Minkowski vacuum state." ...

We show that, for a detector rotating in a random classical zero-point electromagnetic or massless scalar field at zero temperature, thermal effects exist. The rotating reference system is constructed as an infinite set of Frenet-Seret tetrads so that the detector is at rest in a tetrad at each proper time. Frequency spectrum of correlation functions contains the Planck thermal factor with temperature $T_{rot} = \frac{\hbar \Omega}{2 \pi k_B} $. The energy density the rotating detector observes is proportional to the sum of energy densities of Planck's spectrum at the temperature $T_{rot}$ and zero-point radiation. The proportionality factor is $2/3 (4 \gamma^2 -1)$ for an EMF and $2/9 (4 \gamma^2 -1)$ for a MSF, where $\gamma = (1 - (\frac{\Omega r}{c})^2)^{-1/2}$, and r is a rotation radius. The origin of these thermal effects is the periodicity of the correlation functions and their discrete spectrum, both following rotation with angular velocity $\Omega$. The thermal energy can also be interpreted as a source of a vacuum force (VF) applied to the rotating detector from the vacuum field. The VF depends on the size of neither the charge nor the mass, like the force in the Casimir model for a charged particle, but, contrary to the last one, VF is attractive and directed to the center of the circular orbit. VF infinitely grows in magnitude with orbit radius. The orbits with a radius greater than $c/ \Omega$ do not exist because the returning VF becomes infinite. On the uttermost orbit with the radius $c / \Omega$, a linear velocity of the rotating particle would have become c. The VF becomes very small and proportional to radius when r is very small. Such VF dependence on radius, at large and small radii, can be associated respectively with so called confinement and asymptotic freedom, known in quantum chromodynamics, and provide a new explanation for them.

The origin of inertia of macroscopic bodies has never been thoroughly elucidated. In this paper we provide a new explanation based on the following assumptions: (i) we can think of any body as being composed by resonant parts of Planck size, (ii) inertia arises from the interaction among these elementary constituents and quantum fluctuations. In compliance with such prescription, we propose two frameworks within which inertia can be modeled. The first one relies on the direct application of Heisenberg Uncertainty Principle to the fluctuations nearby a body, the other involves the asymmetric (Casimir-like) damping of the radiation experienced by an accelerated object due to the appearance of a Rindler horizon. Consistency between the two approaches is then discussed.

The fundamental nature of intrinsic inertia has been interrogated within the conventional basis, relating the Landau’s (1976) extraction of Galilean frame with no ambiguity made on Machian type.

The classical derivation of the black body radiation (BBR) spectrum by Boyer was based on an equilibrium mechanism such that in the absence of thermal radiation particles in a container can gain kinetic energy from the random electromagnetic zero point field (ZPF) radiation. Their loss of that energy was to be by means of their collisions with the walls of the container. Theoretically, energy dissipation through collisions with the walls might lead to a divergent kinetic energy value for the particles. This is because the box can be taken large enough to minimize the collisions probability, and that can lead to a particle's indefinite growth in energy. Furthermore, a derivation of a general phenomenon such as the BBR should be possible without relying on the walls boundary of a box. Therefore, a new boundary condition is proposed here which is related to relativistic effects. It is shown that with the new boundary condition one may still recover the BBR spectrum. A discussion is presented that shows how the new boundary condition is indeed responsible for energy dissipations.

Stochastic electrodynamics (SED) without spin, denoted as pure SED, has been discussed and seriously considered in the literature
for several decades because it accounts for important aspects of quantum mechanics (QM). SED is based on the introduction
of the nonrenormalized, electromagnetic stochastic zero-point field (ZPF), but neglects the Lorentz force due to the radiation
random magnetic field Br. In addition to that rather basic limitation, other drawbacks remain, as well: i) SED fails when
there are nonlinear forces; ii) it is not possible to derive the Schrödinger equation in general; iii) it predicts broad spectra
for rarefied gases instead of the observed narrow spectral lines; iv) it does not explain double-slit electron diffraction
patterns. We show in this short review that all of those drawbacks, and mainly the first most basic one, can be overcome in
principle by introducing spin into stochastic electrodynamics (SEDS). Moreover, this modification of the theory also explains
four observed effects that are otherwise so far unexplainable by QED, i.e., 1) the physical origin of the ZPF, and its natural
upper cutoff; 2) an anomaly in experimental studies of the neutrino rest mass; 3) the origin and quantitative treatment of
1/f noise; and 4) the high-energy tail (∼ 1021 eV) of cosmic rays. We review the theoretical and experimental situation regarding these things and go on to propose a double-slit
electron diffraction experiment that is aimed at discriminating between QM and SEDS. We show that, in the context of this
experiment, for the case of an electron beam focused on just one of the slits, no interference pattern due to the other slit
is predicted by QM, while this is not the case for SEDS. A second experiment that could discriminate between QED and SEDS
regards a transversely large electron beam including both slits obtained in an insulating wall, where the ZPF is reduced but
not vanished. The interference pattern according to SEDS should be somewhat modified with respect to QED’s.

High order terms in the electromagnetic multipole development expose a
stabilizing mechanism for the atomic orbitals in the presence of the
ZPF-background. Boyer and Puthoff set forward the idea that for the Bohr orbits
in the hydrogen atom, radiation losses could be compensated by absorption from
a background of zero point vacuum fluctuations. This balance is, on average
over the orbit, a necessary condition for stationarity of the movement, and
imposes a relation on the pair $R_{0}$ (orbital radius), $\omega_{0}$ (orbital
angular velocity). That relation is simply what we have for long known as
angular momentum quantization. Taking into account the stochastic nature of the
ZPF, we have to realize that nothing, however, has been said yet on how could
this balance be attained on a quasi instantaneous basis, in other words, how
could the orbit accommodate the instantaneous excess or defect of energy so as
to keep constant the (at least average) values of its parameters ($R_{0}$,
$\omega_{0}$). Using classical electromagnetism, we explore some high order
interactions between realistic particles, exposing a mechanism (a feedback loop
between variables) that makes that stability possible. Puthoff's work led
necessarily to the quantization of angular momentum: "if stable orbits exist...
then their angular momentum must be quantized"; now, too, we are able to do a
much stronger statement: "the equations of the system, in the presence of ZPF
background, lead necessarily to a discrete set of stable orbits".

Under the hypothesis that ordinary matter is ultimately made of subelementary constitutive primary charged entities or partons'' bound in the manner of traditional elementary Planck oscillators (a time-honored classical technique), it is shown that a heretofore uninvestigated Lorentz force (specifically, the magnetic component of the Lorentz force) arises in any accelerated reference frame from the interaction of the partons with the vacuum electromagnetic zero-point field (ZPF). Partons, though asymptotically free at the highest frequencies, are endowed with a sufficiently large bare mass'' to allow interactions with the ZPF at very high frequencies up to the Planck frequencies. This Lorentz force, though originating at the subelementary parton level, appears to produce an opposition to the acceleration of material objects at a macroscopic level having the correct characteristics to account for the property of inertia. We thus propose the interpretation that inertia is an electromagnetic resistance arising from the known spectral distortion of the ZPF in accelerated frames. The proposed concept also suggests a physically rigorous version of Mach's principle. Moreover, some preliminary independent corroboration is suggested for ideas proposed by Sakharov (Dokl. Akad. Nauk SSSR 177, 70 (1968) [Sov. Phys. Dokl. 12, 1040 (1968)]) and further explored by one of us [H. E. Puthoff, Phys. Rev. A 39, 2333 (1989)] concerning a ZPF-based model of Newtonian gravity, and for the equivalence of inertial and gravitational mass as dictated by the principle of equivalence.

We present an approach to the origin of inertia involving the electromagnetic component of the quantum vacuum and propose this as an alternative to Mach's principle. Preliminary analysis of the momentum flux of the classical 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 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 covariant form yields a simple result that may be interpreted as a contribution to inertial mass. Our approach is related by the principle of equivalence to Sakharov's conjecture 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.

Newton's Second Law defines inertial mass as the ratio of the applied force on an object to the responding acceleration of the object (viz., F=ma). Objects that exhibit finite accelerations under finite forces are described as being "massive'' and this mass has usually been considered to be an innate property of the particles composing the object. However mass itself is never directly measured. It is inertia, the reaction of the object to impressed forces, that is measured. We show that the effects of inertia are equally well explained as a consequence of the vacuum fields acting on massless particles travelling in geodesic motion. In this approach, the vacuum fields in the particle's history define the curvature of the particle's spacetime. The metric describing this curvature implies a transformation to Minkowski spacetime, which we call the Connective transformation. Application of the Connective transformation produces the usual effects of inertia when observed in Minkowski spacetime, including hyperbolic motion in a static electric field (above the vacuum) and uniform motion following an impulse. In the case of the electromagnetic vacuum fields, the motion of the massless charge is a helical motion that can be equated to the particle spin of quantum theory. This spin has the properties expected from quantum theory, being undetermined until "measured'' by applying a field, and then being found in either a spin up or spin down state. Furthermore, the zitterbewegung of the charge is at the speed of light, again in agreement with quantum theory. Connectivity also allows for pair creation as the Connective transformation can transform positive time intervals in the particle spacetime to negative time intervals in Minkowski spacetime.

Motivated by recent works on the origin of inertial mass, we revisit the relationship between the mass of charged particles and zero-point electromagnetic fields. To this end we first introduce a simple model comprising a scalar field coupled to stochastic or thermal electromagnetic fields. Then we check if it is possible to start from a zero bare mass in the renormalization process and express the finite physical mass in terms of a cut-off. In scalar QED this is indeed possible, except for the problem that all conceivable cut-offs correspond to very large masses. For spin-1/2 particles (QED with fermions) the relation between bare mass and renormalized mass is compatible with the observed electron mass and with a finite cut-off, but only if the bare mass is not zero; for any value of the cut-off the radiative correction is very small.

A possible connection between the electromagnetic quantum vacuum and inertia was first published by Haisch, Rueda and Puthoff (1994). If correct, this would imply that mass may be an electromagnetic phenomenon and thus in principle subject to modification, with possible technological implications for propulsion. A multiyear NASA-funded study at the Lockheed Martin Advanced Technology Center further developed this concept, resulting in an independent theoretical validation of the fundamental approach (Rueda and Haisch, 1998ab). Distortion of the quantum vacuum in accelerated reference frames results in a force that appears to account for inertia. We have now shown that the same effect occurs in a region of curved spacetime, thus elucidating the origin of the principle of equivalence (Rueda, Haisch and Tung, 2001). A further connection with general relativity has been drawn by Nickisch and Mollere (2002): zero-point fluctuations give rise to spacetime micro-curvature effects yielding a complementary perspective on the origin of inertia. Numerical simulations of this effect demonstrate the manner in which a massless fundamental particle, e.g. an electron, acquires inertial properties; this also shows the apparent origin of particle spin along lines originally proposed by Schroedinger. Finally, we suggest that the heavier leptons (muon and tau) may be explainable as spatial-harmonic resonances of the (fundamental) electron. They would carry the same overall charge, but with the charge now having spatially lobed structure, each lobe of which would respond to higher frequency components of the electromagnetic quantum vacuum, thereby increasing the inertia and thus manifesting a heavier mass. Comment: 10 pages, 4 figures, AIP Conf. Proc., Space Technology and Applications International Forum (STAIF-2003)

Why does {\bf F} equal m{\bf a} in Newton's equation of motion? How does a gravitational field produce a force? Why are inertial mass and gravitational mass the same? It appears that all three of these seemingly axiomatic foundational questions have an answer involving an identical physical process: interaction between the electromagnetic quantum vacuum and the fundamental charged particles (quarks and electrons) constituting matter. All three of these effects and equalities can be traced back to the appearance of a specific asymmetry in the otherwise uniform and isotropic electromagnetic quantum vacuum. This asymmetry gives rise to a non-zero Poynting vector from the perspective of an accelerating object. We call the resulting energy-momentum flux the {\it Rindler flux}. The key insight is that the asymmetry in an accelerating reference frame in flat spacetime is identical to that in a stationary reference frame (one that is not falling) in curved spacetime. Therefore the same Rindler flux that creates inertial reaction forces also creates weight. All of this is consistent with the conceptualizaton and formalism of general relativity. What this view adds to physics is insight into a specific physical process creating identical inertial and gravitational forces from which springs the weak principle of equivalence. What this view hints at in terms of advanced propulsion technology is the possibility that by locally modifying either the electromagnetic quantum vacuum and/or its interaction with matter, inertial and gravitational forces could be modified.

The possibility of an extrinsic origin for inertial reaction forces has recently seen increased attention in the physical literature. Among theories of extrinsic inertia, the two considered by the current work are (1) the hypothesis that inertia is a result of gravitational interactions, and (2) the hypothesis that inertial reaction forces arise from the interaction of material particles with local fluctuations of the quantum vacuum. A recent article supporting the former and criticizing the latter is shown to contain substantial errors.

The question of the cause of inertial reaction forces and the validity of Mach's principle are investigated. A recent claim that the cause of inertial reaction forces can be attributed to an interaction of the electrical charge of elementary particles with the hypothetical quantum mechanical zero-point fluctuation electromagnetic field is shown to be untenable. It fails to correspond to reality because the coupling of electric charge to the electromagnetic field cannot be made to mimic plausibly the universal coupling of gravity and inertia to the stress-energy-momentum (i.e., matter) tensor. The gravitational explanation of the origin of inertial forces is then briefly laid out, and various important features of it explored in the last half-century are addressed.

This article presents a general analysis of some aspects of the interaction of classical particles with the classical electromagnetic zero-point field (cemzpf). The analysis provides a possible observational test for stochastic electrodynamics (SED). A convergence form factor derived semiclassically supports the narrow linewidth and related approximations of SED by introducing a typically sharp frequency cutoff. An extended classical charge monopole can then be shown to perform a simple jiggling motion under the influence of the cemzpf. Besides this motion (same as polarizable particles), monopolar particles also display a random walk in velocity space which leads them to ever-increasing translational kinetic energies. Hence, classical particles under the influence of the cemzpf display a conspicuous behavior because of the following well-known interrelated results: First, no velocity-dependent forces exist for classical particles moving exclusively through the cemzpf. Second, both monopolar and polarizable particles in SED are predicted to perform a random walk in velocity space due to the action of this field. Only collisions may provide a stopping mechanism. An analysis of the work of Boyer and others concerning particle collisions with walls, suggests the idea that collisions transfer energy from an unconfined gas of mutually colliding particles to the random field. Using this, a Fokker-Planck model for an unconfined gas of mutually colliding classical particles is constructed. It displays a universal equilibrium energy spectrum E-const for the gas particles under the cemzpf as seen from any point fixed to co-moving coordinates. Primary cosmic rays have such an energy distribution. This motivated the proposal of a zero-point field (zpf) cosmic-ray acceleration mechanism in a previous work. Such a proposal requires a careful examination. However, methodologically speaking, one should first examine the alternative possibility that the behavior predicted in SED for classical particles does not occur in nature. If that would happen to be the case, then SED and the cemzpf concept should be critically revised. That the cemzpf concept may apparently lead to difficulties, is seen by presenting a paradoxical example where a monopolar particle moving through the cemzpf is predicted to suffer an enormous frictional force due to the surrounding zpf. The prediction obviously violates the Lorentz invariance of the cemzpf energy density spectrum. But the paradox is easily resolved by realizing the improper ultrarelativistic behavior of the Lorentz-Dirac equation which is used in the example. Extreme care must then be exerted in the use of the equations of motion of classical charged particles when moving under the influence of a zpf. The search for internal contradictions in SED, not related with the well-known renormalization and other difficulties of classical electrodynamics, has so far been unsuccessful. This and several points of rigor here and elsewhere included, are enough to indicate that the conspicuous behavior of classical particles discussed here is correctly predicted from the assumptions of SED. It is therefore proposed that this predicted behavior may serve as an observational test for the validity of SED.

The thermal effects of acceleration found by Davies and Unruh within quantum field theory are shown to exist within random classical radiation. The two-field correlation functions for random classical radiation are used as the basis for investigating the spectrum of radiation observed at an accelerating point detector. An observer with proper acceleration a relative to the Lorentz-invariant spectrum of random classical scalar zero-point radiation finds a spectrum identical with that given by Planck's law for scalar thermal radiation where the temperature is related to the acceleration by T=ℏa/2πck. An observer with proper acceleration a relative to the Lorentz-invariant spectrum of random classical electromagnetic radiation finds a stationary radiation spectrum which is not Planck's spectrum. Rather, the observed spectrum in the electromagnetic case contains a term agreeing with Planck's electromagnetic spectrum plus an additional term. This spectrum for the electromagnetic case appears in the work of Candelas and Deutsch for an accelerating mirror and corresponds to thermal radiation in the non-Minkowskian space-time of the accelerating observer. The calculations reported here involve an entirely classical point of view, but are shown to have immediate connections with quantum field theory.

In 1976 Unruh showed that a scalar quantum particle in a box accelerating through the vacuum of scalar quantum field theory responded as though it were in a thermal bath at temperature T=ℏa/2πck. Here we show an analogous result within classical electromagnetic theory. A classical electric dipole oscillator accelerating through classical electromagnetic zero-point radiation responds just as would a dipole oscillator in an inertial frame in classical thermal radiation with Planck's spectrum at temperature T=ℏa/2πck. In an earlier work it was shown that the electromagnetic field correlation functions for an observer accelerating through classical electromagnetic zero-point radiation correspond to a spectrum different from Planck's. The same spectrum is found in the quantum analysis of a vector field where the departure from Planckian form is assigned to the change in the number of normal modes associated with the event horizon of the accelerating observer. The present work shows that the relativistic radiation reaction for an accelerating classical charge contains a term which exactly compensates the departure of the electromagnetic spectrum from Planckian form so as to bring the oscillator's behavior into precise agreement with the usual Planckian thermal form.

In previous work it has been shown that the electromagnetic quantum vacuum, or electromagnetic zero-point field, makes a contribution to the inertial reaction force on an accelerated object. We show that the result for inertial mass can be extended to passive gravitational mass. As a consequence the weak equivalence principle, which equates inertial to passive gravitational mass, appears to be explainable. This in turn leads to a straightforward derivation of the classical Newtonian gravitational force. We call the inertia and gravitation connection with the vacuum fields the quantum vacuum inertia hypothesis. To date only the electromagnetic field has been considered. It remains to extend the hypothesis to the effects of the vacuum fields of the other interactions. We propose an idealized experiment involving a cavity resonator which, in principle, would test the hypothesis for the simple case in which only electromagnetic interactions are involved. This test also suggests a basis for the free parameter η(ν) which we have previously defined to parametrize the interaction between charge and the electromagnetic zero-point field contributing to the inertial mass of a particle or object.

Even when the Higgs particle is finally detected, it will continue to be a legitimate question to ask whether the inertia of matter as a reaction force opposing acceleration is an intrinsic or extrinsic property of matter. General relativity specifies which geodesic path a free particle will follow, but geometrodynamics has no mechanism for generating a reaction force for deviation from geodesic motion. We discuss a different approach involving the electromagnetic zero-point field (ZPF) of the quantum vacuum. It has been found that certain asymmetries arise in the ZPF as perceived from an accelerating reference frame. In such a frame the Poynting vector and momentum flux of the ZPF become non-zero. Scattering of this quantum radiation by the quarks and electrons in matter can result in an acceleration-dependent reaction force. Both the ordinary and the relativistic forms of Newton's second law, the equation of motion, can be derived from the electrodynamics of such ZPF-particle interactions. Conjectural arguments are given why this interaction should take place in a resonance at the Compton frequency, and how this could simultaneously provide a physical basis for the de Broglie wavelength of a moving particle. This affords a suggestive perspective on a deep connection between electrodynamics, the origin of inertia and the quantum wave nature of matter. Comment: Annalen der Physik, in press