PHYSICS OF THE ZERO-POINT FIELD - IMPLICATIONS FOR INERTIA, GRAVITATION AND MASS.pdf - Megacollection - Tom Bearden - Onfi

PHYSICS OF THE ZERO-POINT FIELD:

IMPLICATIONS FOR INERTIA, GRAVITATION AND MASS

BERNHARD HAISCH

Lockheed Martin Solar and Astrophysics Laboratory

Dept. 91-30, Bldg. 252, 3251 Hanover St., Palo Alto, CA 94304

email: haisch@sag.space.lockheed.com

ALFONSO RUEDA

Department of Electrical Engineering, California State University

Long Beach, CA 90840

email: arueda@csulb.edu

H. E. PUTHOFF

Institute for Advanced Studies at Austin

4030 Braker Lane, Suite 300, Austin, TX 78759

email: putho®@aol.com

Speculations in Science and Technology , Vol. 20, pp. 99{114, 1997

(preprint version)

Abstract

Previous studies of the physics of a classical electromagnetic zero-point ¯eld (ZPF) have implicated it as a

possible basis for a number of quantum phenomena. Recent work implies that the ZPF may play an even

more signi¯cant role as the source of inertia and gravitation of matter. Furthermore, this close link between

electromagnetism and inertia suggests that it may be fruitful to investigate to what extent the fundamental

physical process of electromagnetic radiation by accelerated charged particles could be interpreted as scattering

of ambient ZPF radiation. This could also bear upon the origin of radiation reaction and on the existence of the

same Planck function underlying both thermal emission and the acceleration-dependent Davies-Unruh e®ect.

If these ¯ndings are substantiated by further investigations, a paradigm shift would be necessitated in physics.

An overview of these concepts is presented thereby outlining a research agenda which could ultimately lead to

revolutionary technologies.

Keywords: zero-point ¯eld; ZPF; stochastic electrodynamics; quantum electrodynamics; quantum vacuum;

inertia; gravitation; dark matter; mass; relativity

Introduction and Overview

In 1901 Planck was successful in deriving a closed mathematical expression that ¯t the then recent measurement

of the spectral distribution of thermal radiation by hypothesizing a quantization of the average energy per mode

of oscillation [1]. This new formulation avoided the so-called ultraviolet catastrophe , the unphysical prediction

of classical theory readily derivable from energy equipartition that the blackbody spectrum should diverge to

in¯nity as º 3 . Planck derived the well-known blackbody function,

½ ( º;T ) dº =

c 3 µ hº

¶ dº;

(1)

e hº=kT

in which the º 3 catastrophe is overcome by the exponential denominator resulting from his substitution of

discrete for continuous energy intervals. The expression is factored here to show the two components of density

of modes (i.e. number of degrees of freedom per unit volume) times the thermal energy per mode in the frequency

interval dº . As discussed in detail in Kuhn's monograph Black Body Theory and the Quantum Discontinuity:

1894{1912 [2], Planck himself remained skeptical of the physical signi¯cance of his mathematical assumption

and of his apparently new constant, h , for over a decade. In 1913 Bohr [3] made quantization of atomic energy

levels a postulate, thereby laying a foundation for quantum physics based upon Planck's unit of quantization.

That same year Einstein and Stern published a paper [4] studying the interaction of matter with radiation

using classical physics and a model of simple dipole oscillators to represent charged particles. They remarked

8 ¼º 2

that if, for some reason, such a dipole oscillator had a zero-point energy, i.e. an irreducible energy even at T =0,

of hº , the Planck formula for the radiation spectrum would result without the need to invoke quantization. a In

1916 Nernst published an article [6] in which he proposed that the Universe might actually contain enormous

amounts of such zero-point radiation. In fact, the existence of such a zero-point ¯eld (ZPF) had been ¯rst

envisaged by Planck around 1910 when he formulated his so-called second theory: namely an attempt to

derive the blackbody spectral formula with a weaker quantization assumption. It was Nernst who captured the

paramount thermodynamic implications and relevance of such a sea of background radiation and became the

main proponent of this concept. Both Planck and Nernst used the correct (1 = 2) hº form for the average energy

of the zero-point electromagnetic °uctuations instead of the hº value assumed later by Einstein and Stern; the

hº assumption is correct for the sum of interacting harmonic oscillators plus the energy of the electromagnetic

¯elds. The electromagnetic blackbody spectrum including ZPF would then be:

½ ( º;T ) dº =

c 3 µ hº

+ hº

¶ dº:

(2)

e hº=kT

While this once again appears to result in a º 3 ultraviolet catastrophe, that is not the case because this

component now refers not to measurable excess radiation from a heated object, rather to a uniform, isotropic

background radiation ¯eld that cannot be directly measured because of its homogeneity. This approach to

understanding the blackbody spectrum was not developed further thereafter, and was in fact essentially forgotten

for the next ¯fty years. What happened instead was that with the success of quantum mechanics, and then

quantum electrodynamics, the generalization and existence of an equivalent to the ZPF, the quantum vacuum,

was taken to be a consequence of quantum laws. In other words, a quantum version of the ZPF became an

accepted part of physics whose existence was interpreted as being due to quantum laws.

In recent years there has been a growing interest in reviving the original semi-classical approach and

exploring its rami¯cations. The motive until recently, besides gaining intuitive insights and calculational ease,

has been to see to what extent various quantum phenomena could be explained solely on the basis of classical

physics with a random perturbing radiation ¯eld | the ZPF | providing quantum-like °uctuations. This

would (again) reverse the cause and e®ect of ZPF vis-a-vis quantum physics. This area of physics is known

as Stochastic Electrodynamics , SED. For a recent short but still comprehensive review see [7] which also gives

valuable references to other older but thorough reviews. SED is also discussed in the monograph by Milonni

[8]. The general idea that the origin of quantization was to be found in some classical stochastic subquantum

background was very much in the air among the founders of modern physics [9]. In 1966, Nelson published a

seminal paper [10] stating:

We shall attempt to show in this paper that the radical departure from classical physics produced by

the introduction of quantum mechanics forty years ago was unnecessary. An entirely classical derivation

and interpretation of the Schrodinger equation will be given, following a line of thought which is a

natural development of reasoning used in statistical mechanics and in the theory of Brownian motion.

Examining the Heisenberg uncertainly principle Boyer [11] showed that for the harmonic oscillator the

°uctuations caused by the ZPF on the positions of particles are exactly in agreement with quantum theory.

Recently Rueda [12] has arrived at the Schrodinger equation, albeit in a restrictive context that invokes a

ZPF-induced Brownian-motion model.

The most optimistic outcome of the SED approach would be to demonstrate that classical physics plus

a classical electromagnetic ZPF could successfully replicate all quantum phenomena, a situation which would

undermine some of the present ontological basis of quantum physics. While successful up to a point, SED has

not yet achieved this.

As dramatic as a substitution for quantum physics would be on the part of SED, recent studies have

identi¯ed even more profound roles that the ZPF may play in the foundation of physical laws, the constitution

of matter, and the structure of the Universe.

(1) The inertia of matter may be due to a Lorentz force-like electromagnetic interaction between charge at the

quark or fundamental lepton level and the ZPF [13, HRP].

(2) There appears to be an analogous electromagnetic vacuum origin for gravitation | as there would neces-

sarily be from the principle of equivalence | an idea originally proposed by Sakharov [14] [15]. It needs

a Several such derivations of the blackbody function using classical physics with a real zero-point ¯eld but

without quantization have been published by Boyer; cf. [5] and references therein.

8 ¼º 2

to be shown that this can be made mathematically equivalent to curved space-time. The approach that

Einstein took in 1911 [16] (with later corrections [17]) involving a speed of light which is dependent on

gravitational potential, c (©), suggests a promising avenue.

(3) Matter and the concept of mass would appear to be secondary phenomena arising out of charge-ZPF

interactions: energy, charge and electromagnetic ¯elds being primary.

(4) The creation of electromagnetic radiation by accelerated charge may possibly be interpretable as scattering

of ambient ZPF radiation. In stationary frames the scattering of ZPF radiation by a dipole is an equilibrium

process [18]; the asymmetry in the scattering process when an accelerated dipole is viewed from a stationary

laboratory frame would appear to be the source of what is customarily interpreted as radiation emitted by

accelerated charge (see pp. 114{120 of [19]).

(5) In the ideal case of the Bohr atom, the stability of the ground state of the hydrogen atom can be attributed

to energy absorption from the ZPF rather than Bohr's postulated quantum prohibition [11] [20].

(6) Spontaneous emission can be interpreted at least in part (one half of it to be precise) as emission stimulated

by the background ZPF. As McCrea has argued [21], this places the ZPF in the role of a kind of universal

clock governing seemingly spontaneous phenomena.

(7) Even within general relativity, non-gravitational accelerations require a frame of rest that is absolute in

either the Newtonian or the Machian sense [22][23][24]. However owing to special relativity, such a frame

cannot be absolute with respect to uniform rectilinear motions. This seemingly impossible requirement is

actually met by the ZPF. Owing to its º 3 spectrum it has a Lorentz invariant energy density spectrum, yet

acquires certain asymmetries as viewed from an accelerating frame ::: which leads, among other things,we

think, to inertia, thus providing a quantitative, modern version of Mach's principle [HRP].

(8) The structure of the Universe on the largest scale | voids and sheets | can be attributed to the ZPF via

an Einstein-Hopf type acceleration process [25][26][27]. The same acceleration process may also underlie

cosmic rays [5][28].

The objective of this paper is not to establish the veracity of these paradigm-shifting possibilities; some

are clearly speculative at this time, e.g. in the case of (8), caveats exist concerning the Einstein-Hopf process.

A recent evaluation of this appears in a review published by de la Pena and Cetto after acceptance of this

paper [29]. Our goal is to present an overview of reasonably justi¯ed conclusions concerning the ZPF based

upon published work and to extrapolate to new research programs that may come about, clearly identifying

speculations as such. The intellectual and perhaps even technological rewards that would be forthcoming should

such a research agenda succeed may attract innovative scientists to examine these possibilities in su±cient detail

so that in a few years we may know whether this approach has been an intoxicating but illusory deadend or the

path to a new paradigm for the next millenium.

If the ZPF is real, why is it not detectable?

The most universal real radiation ¯eld we are familiar with today is the cosmic microwave background

(CMB). While the NASA COBE measurements, published in 1992, ¯nally found minute inhomogeneities, to

high precision the CMB can be considered as quite uniform and isotropic, yet readily detectable. That being

the case, why is the ZPF not equally evident? The ratio of the two is simply the ratio of the two terms in eqn.

(2) taking T =2 : 73 K. At the 53 GHz-frequency middle band of the COBE Di®erential Microwave Radiometer

this ratio would be ½ ZPF =½ CMB =0 : 77. Even more dramatically, in the optical spectrum, eqn. (2) predicts

that the ZPF should be about two orders of magnitude brighter than the Sun. Why are we not blinded by the

ZPF?

To ¯rst order, in the absence of special conditions (discussed below), the ZPF is isotropic and homogeneous

in its spatial distribution. This must be the case even inside matter due to the characteristics of the ZPF

that dipole transitions absorb and re-emit this isotropic, º 3 radiation without change in spatial or spectral

distribution [11][18]. Therefore matter that might ordinarily be considered opaque to radiation of a given

frequency e®ectively passes on the ZPF radiation without attenuation, i.e. the radiation may be absorbed and

re-emitted many times, but the net e®ect is nil. In such fashion the ZPF resists direct observation. Only

deviations \above" the ZPF are measurable.

To second order, however, the presence of the ZPF can be registered indirectly, not on the basis of absorption

and reemission, but rather by correlation or interference e®ects. In the case of closely-spaced atoms or molecules,

for example, the absorption and reemission of the ZPF radiation results in the generation of secondary short-

range ¯elds (even at temperatures of absolute zero) that, because of their correlating e®ects, result in short-range

attractive forces: the so-called van der Waals forces. Similarly, in a macroscopic version of the same phenomenon,

a unique attractive quantum force (the Casimir force) between dielectric or conducting plates can be shown to

exist on the basis that absorption and reemission of the ZPF radiation by the plates results in interference and

cancellation of certain electromagnetic modes between the plates. The result is an imbalance in the associated

ZPF radiation pressures interior and exterior to the plates, hence a net force of attraction between the plates;

a close parallel can be drawn between this phenomenon and the familiar concept of radiation pressure [30a].

Again, the ZPF background is inferred from its consequences rather than from direct observation. Indeed, at

a deeper level, the various phenomena listed above in (1) through (8) can all be taken as con¯rmation and

perhaps even as indirect \observations of the ZPF" in the sense that their elucidation is most parsimonious in

terms of the ZPF interpretation.

Inertia and Mach's Principle

= ma

? Newton's equation of motion is a good starting point for discussion. Consider a slight variation of it. Some

of the largest scale motions in the Universe involve extremely small accelerations: The v 2 =r acceleration of the

Sun around the Milky Way galaxy amounts to a

10 kpc).

This is typical of rotational accelerations in outer galactic regions. Accelerations of galaxies within clusters are

on a similar scale. Such small accelerations would be extremely di±cult to create and measure in a laboratory,

and to that extent, the F = ma relation is terra incognita in this regime. Without implying any judgement

as to the validity of the proposal, we note that an alternate explanation to the existence of dark matter as a

cause of non-Keplerian galactic rotation curves, etc., involves hypothesizing a non-linear F = ma relationship

for accelerations in this regime [30b]. The point is not to promote this particular hypothesis, merely to point

to a conceivable application for a more complex view of inertia. b

10 ¡ 8

cm s ¡ 2

(taking v

250 km/s and r

A discussion of Mach's principle could ¯ll volumes [31]; it was an important consideration for Einstein

in his development of general relativity (GR) [17] [32], and while he initially thought that GR incorporated

Mach's principle, a GR-solution for a universe devoid of matter was discovered by Einstein himself [33], and a

solution for a rotating universe by Godel, both demonstrating that Mach's principle was not compatible with

GR. Mach argued that all motions must be relative. That being the case, whether one chooses for purposes

of analysis a rotating earth or a stationary earth and a counter-rotating universe should not matter. But

what would be the origin of centrifugal force in the latter view, deforming the shape of the earth to make it

equivalent to the rotating-earth perspective. Mach proposed that the solution lies in the circumstance that the

local property of inertia of any material object is caused by the surrounding matter. In this way a rotating

universe could conceivably induce an equivalent of centrifugal force in a stationary earth. This view would also

be consistent with the idea that it should not make sense to allow a measurable perception of rotation (again

from centrifugal or Coriolis forces) if an object were rotating in an empty universe, i.e. rotating with respect to

what? In Mach's view such rotation would be an absurdity, and without the presence of other matter available

to create inertia the conundrum is avoided. The only long-range force available being gravitation, a Machian

inertia must somehow be related to gravity. A preliminary Newtonian model of this was proposed by Sciama

¡ R V ( ½=r ) dV , while inertia arises via the

next higher extension, a vector potential, A =

on a cosmological distance scale would predominate in the origin of (local) inertia. No entirely satisfactory

formulation of Mach's principle has been developed [34]. Moreover, asymmetries such as those measured by the

NASA Cosmic Background Explorer, the mass-asymmetry due to our location in the Milky Way, etc., do not

give rise to a measurable asymmetry in inertia, i.e. mass is not a vector quantity. Remarkable upper limits can

be placed on this thanks to the Hughes-Drever experiments: ¢ m=m

10 ¡ 20

[35] whereas Sciama's approach

[33] would predict ¢ m=m

10 ¡ 7

due to the Milky Way.

The concept developed by us [HRP] is di®erent. Inertia does result from something external: not other

matter but the ZPF, with the e®ect, at the ¯rst level of the analysis at least, being entirely local. In HRP we

b Should the ZPF inertia theory result in a prediction of a non-linear inertia in the regime hypothesized by

Milgrom, this would of course be a plus for the theory resolving a major astrophysical puzzle | the nature of

dark matter | in a quite unexpected way.

That matter should have the property of inertia is so fundamental to our conception of physical reality

that it is di±cult to imagine how matter could not have such an innate property. How could one have a stable,

solid (including liquid and gas in this context) reality without inertia? Put another way, how could F

analyzed the forces on a Planck oscillator when subject to acceleration using the methods of SED. Analytically,

we set a point-charge (termed a parton: this could represent a quark or an electron for example) into harmonic

motion driven by the random °uctuations of the ZPF. These °uctuations are perfectly symmetrical in stationary

or uniform-motion frames. It was discovered by Davies [36] and by Unruh [37] that acceleration-dependent terms

arise in the spectral energy density of the ZPF (cf. equation 3 of HRP). One of these is a pseudo-Planckian

component of the ZPF involving an acceleration-temperature (cf. equation 2 of HRP), a very small term under

ordinary accelerations. The other term is an acceleration-squared modi¯cation of the spectral energy density.

In HRP we investigate this term. Following the technique of Einstein and Hopf and the identical con¯guration

used by Boyer [38] to derive the Davies-Unruh e®ect in the context of SED, we investigated the heretofore

unexplored v

a . The Lorentz force

resists acceleration in a linear way. We interpret the inertial resistance to acceleration of matter to be this

electromagnetic Lorentz force; inertia would thus be electromagnetic in origin . This is, in e®ect, a derivation

of F = ma from the electrodynamics of ZPF-charged particle interactions. The inertial mass, m i , is then a

function of electrodynamic parameters,

B ZP >

m i =

¡ h! c

2 ¼c 2

(3)

200 di®erence between an electron and a muon in spite of

their identical charge. For a composite particle such as a proton (made of uud quarks) or neutron (made of udd

quarks) the inertia-producing interactions would take place with the individual quarks; at very high frequencies

quarks would oscillate essentially independently given the nature of the strong interaction, so-called asymptotic

freedom (\At close range, jostling around inside a proton, quarks barely notice one another's presence and act

like independent particles." [39]); di®erences in the sign of the charge would only change the phase of the

oscillations giving rise to the Lorentz force, not the direction, thus making the e®ect on the individual quarks

in a nucleon additive.

The HRP analysis has been criticized for using an Abraham-Lorentz-Dirac (ALD) equation of motion as a

basis, the argument being that we are \using Newton's law to derive Newton's law." This is not the case since

the ALD equation is phenomenologically invoked as an SED resource solely to bring about oscillations in a plane

with the Lorentz force arising independently out of the magnetic component of the ZPF in a perpendicularly-

accelerating direction. Other justi¯ed criticisms involve the use of an ideal parton to represent charged matter

and general mathematical complexity.

All of these problems will be addressed and hopefully swept aside by a new approach in which one considers

solely the time evolution of the momentum-°ux derived from the Poynting vector of the ZPF in a uniformly

accelerating coordinate system [40][41]. This new analysis does not concern itself with particle-ZPF interactions

other than to assume that ZPF radiation can be scattered by charged matter. Using entirely straightfor-

ward Lorentz transformations of the electromagnetic ¯eld one can derive the analogous result to HRP: viz, an

acceleration-dependent resistance originating in such scattering of radiation. Moreover this analysis has the

merit of not only being analytically simpler than HRP, but also of being relativistic, i.e. one can derive the

relativistic form of Newton's law in this fashion:

= d

=d¿ , the well-known four-vector form applicable to

particles accelerated to high speeds.

Gravitation

All experiments and observations to date are consistent with predictions of general relativity. The math-

ematical treatment of gravitation as a space-time curvature works well. However if it could be shown that a

di®erent theoretical basis can be made analytically equivalent to space-time curvature, with its prediction of

gravitational lensing, black holes, etc. this would reopen the possibility that gravitation is a force. Einstein

himself \did not think that electromagnetism and gravity should remain separate, and spend the later years of

his life searching for a theory of `electro-gravity' to complete the work begun by Maxwell" [39]. The following

B ZP force that the driven-oscillator would experience in an accelerating frame. The v are

the oscillatory motions in a plane due to the electric driving forces, E ZP , of the ZPF. The oscillator is then

forced to undergo a uniform acceleration, a , in a direction perpendicular to the plane of oscillation ; the resulting

Lorentz force after proper stochastic averaging turns out to be such that <v

where ¡ is a damping constant for the oscillations and ! c relates to a characteristic frequency of particle-ZPF

interactions. In HRP, ! c was taken to be either a ZPF cuto® frequency (the Planck frequency) or a re°ection

of the minimum parton size (the Planck length) which would translate into the same cuto® frequency. We

speculate that in more re¯ned future versions of the theory this simple ! c cut-o® parameter will actually be

replaced by a resonance frequency, ! 0 , and that di®erences in resonance are factors determining di®erences in

masses of fundamental particles, i.e. the factor of

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