The Origin of Inertia

It is suggested that inertia is a fundamental property that has not been properly addressed by quantum field theory or superstring theory. The acquisition of mass-energy via a Higgs field may still require a mechanism to generate an inertial reaction force upon acceleration. Even when a Higgs particle is finally detected one may still need a mechanism for giving the Higgs-induced mass the property of inertia. The following discussion and articles are based on research carried out so far using only the techniques of stochastic electrodynamics. A goal of the Calphysics Institute is to explore whether these concepts can be reformulated, validated and generalized within the more comprehensive discipline of modern quantum field theory and superstring theory.

The Higgs Field

The Higgs field was first proposed in 1964 and is still a key element of the Standard Model of particle physics; it is needed to confer the property of mass on the fundamental particles. In the theory, all particles are intrinsically massless until acted upon by the Higgs field. The quantum of the Higgs field is the Higgs boson. Attempts to detect the Higgs boson, and therefore to verify the Higgs field as the mass-generating mechanism of the Standard Model, have been unsuccessful. The current best hope is on the forthcoming Large Hadron Collider at CERN scheduled to go on line in 2007.

Even if the Higgs field is experimentally discovered, however, that will still not explain the origin of inertial mass of ordinary matter. The Higgs field applies only to the electro-weak sector of the Standard Model. The mass of ordinary matter is overwhelmingly due to the protons and neutrons in the nuclei of atoms. Protons and neutrons are comprised of the two lightest quarks: the up and down quarks. The rest masses of their constituent quarks (approx. 0.005 and 0.010 GeV/c² for the up and down quarks respectively) which could be attributed to the Higgs field comprise only about one percent of the masses of the protons and neutrons (0.938 and 0.940 GeV/c² respectively). The remainder of the proton and neutron masses would have to be attributed to contributions from the gluon field strong interaction energies plus smaller electromagnetic and weak fields contributions which would not be affected by a Higgs field. The origin of inertial mass of ordinary matter is thus a wide open question.

The following description of the Higgs mass-generating process was published by M. J. G. Veldman (Scientific American, Nov. 1986).

"The way particles are thought to acquire mass in their interactions with the Higgs field is somewhat analogous to the way pieces of blotting paper absorb ink. In such an analogy the pieces of paper represent individual particles and the ink represents energy, or mass. Just as pieces of paper of different sizes and thicknesses soak up varying amounts of ink, different particles 'soak up' varying amounts of energy or mass. The observed mass of a particle depends on the particle's 'energy absorbing' ability, and on the strength of the Higgs field in space."

This is basically a transfer of energy from a field to a particle. Note that this does not address a deeper question: why does the energy "soaked up" from the Higgs field resist acceleration? Perhaps that is not a legitimate question. Perhaps mass and energy intrinsically possess the property of inertia and that is the end of the story. On the other hand, we have found a very intriguing interaction with the electromagnetic quantum vacuum that appears to provide just this property of resistance to acceleration that defines inertia.

The SED-based Hypothesis for Inertia

In 1994, using a semi-classical technique in physics known as Stochastic Electrodynamics (SED), B. Haisch, A. Rueda and H. Puthoff published the hypothesis that inertia may originate in interactions between the electromagnetic zero-point field of the quantum vacuum and the quarks and electrons constituting matter (Phys. Rev. A, 49, 678, 1994). This SED analysis suggested that Newton's equation of motion (F=ma), heretofore regarded as a postulate of physics, might be derivable from Maxwell's equations as applied to the electromagnetic zero-point field.

This led to a NASA-funded study beginning in 1996 at the Lockheed Martin Advanced Technology Center in Palo Alto and the California State University in Long Beach. That study found the more general result that the relativistic equation of motion could be derived from consideration of the Poynting vector of the zero-point field in accelerated reference frames, again within the context (and limitations) of SED.

It is well known that an accelerating observer will experience a bath of radiation resulting from the quantum vacuum which mimics that of a heat bath, the so-called Davies-Unruh effect. This was discovered shortly after, and in connection with, a 1974 paper by Hawking proposing quantum evaporation of very low mass black holes. For an accelerated object moving through the vacuum the zero-point field will yield a non-zero Poynting vector. Scattering of this radiation by the quarks and electrons constituting matter would result in an acceleration-dependent reaction force that would appear to be the origin of inertia of matter (Rueda and Haisch, Physics Letters A, 240, 115, 1998; Foundations of Physics, 28, 1057, 1998). In the subrelativistic case this inertia reaction force is exactly newtonian and in the relativistic case it exactly reproduces the well known relativistic extension of Newton's Law. Both the ordinary, F=ma, and the relativistic form of Newton's equation of motion may be derived from Maxwell's equations as applied to the electromagnetic zero-point field. We expect to be able to extend this analysis in the future to more general versions of the quantum vacuum than just the electromagnetic one. Indeed, it is quite possible that what we have shown is how the electromagnetic ZPF contributes to inertia, but this may not be the whole story.

A Resonance Frequency and the de Broglie Wavelength

The approach used in the NASA study also suggested that there should be a specific resonance frequency for the particle-ZPF interaction giving rise to inertia. We have found that if, for the case of the electron, the inertia-generating resonance is at the Compton frequency, then such a resonance, driven by the zero-point fluctuations, could simultaneously account for both the inertial mass of the electron and its de Broglie wavelength when in motion as first measured by Davisson and Germer in 1927 (Physics Letters A, 268, 224, 2000, cf. also chapter 12 of de la Pena and Cetto, "The Quantum Dice: An Introduction to Stochastic Electrodynamics, Kluwer Academic Publishers). The de Broglie wavelength of an electron placed in motion appears to be related to Doppler shifts of Compton-frequency oscillations associated with Zitterbewegung. This provides a very suggestive perspective on a connection between electrodynamics and the quantum wave nature of matter, again limited by the validity of SED theory in this domain.

Casimir Effects and the Quantum Vacuum Energy

There is growing interest in the nature of, and possibly even the manipulation of, the quantum vacuum. The vacuum stress predicted by Casimir in 1948 between conducting plates due to modification of the electromagnetic zero-point fluctuations has been confirmed by experiments. Agreement with theory at the five percent level has been obtained in a micron-range cavity (Lamoreaux, Phy. Rev. Lett., 78,  5, 1997; see also Lamoreaux, 1999). Thermodynamic analysis has also shown that it is apparently possible, in principle, to extract energy from the quantum vacuum. More specifically, no violation of thermodynamics appears to result from such a process involving the ZPF. Although numerous unsubstantiated claims of ZPF energy tapping gadgets may be found on the internet, no one has yet devised any radically new means to extract such energy on a practical scale. Only a very minute and impractical level may be achieved using Casimir plates (which is nonetheless important as a proof of principle; see for example the article ``Extracting electrical energy from the vacuum by cohesion of charged foliated conductors'' by Robert Forward, Phys. Rev. B, 30, 1700, 1984; for more recent theoretical analyses see Cole, 1999, Amer. Inst. Physics Conf. Proc. No. 458, 960, 1999 and Cole & Puthoff, Phys. Rev. E, 48, 1562, 1993).

Objections

The major objection raised against these concepts is that the ZPF must not be taken literally. According to general relativity theory, the energy density of the ZPF would generate an enormous spacetime curvature, akin to a huge cosmological constant. This is, of course, true in the standard interpretation of mass-energy. However one has to be careful to maintain self-consistency when comparing theoretical models: the quantum vacuum-inertia concept implies, via the principle of equivalence, that gravitation must also have a connection to the ZPF (along lines conjectured by Sakharov in 1968). If that is the case, then the ZPF cannot gravitate, because gravitation would involve the interaction of the ZPF with fundamental particles, not with itself. The energy density of the ZPF could then no longer be naively equated to a source of gravitation. Such an electromagnetically-based theory of gravitation has only undergone a preliminary development, but it does appear that in the weak field approximation the general relativistic curvature of spacetime can be mimicked by a vacuum having variable dielectric properties in the presence of matter (as conjectured by Wilson, Dicke, Puthoff and others). This raises the tantalizing question of whether spacetime is actually physically non-Euclidean or whether our measurements of curvature merely reflect light propagation through a polarizable medium (the vacuum itself). This possibility is, admittedly, unlikely given the strong evidence in astrophysics for the existence of black holes. Since the assumed curvature of spacetime is measured (by definition) via light propagation, there might be no way to distinguish one from the other: curved spacetime vs. light propagation with a dielectrically-modified speed-of-light. (We note that Einstein himself spent many years looking for an electromagnetic basis for gravitation, albeit unsuccessfully. Moreover modern attempts to quantize gravity treat gravitation as just another fundamental force in flat spacetime in which the exchange of gravitons parallels the exchange of virtual photons as a representation of the electromagnetic force.)

Another objection involves the neutrino. If, unlike the neutron which consists of three quarks whose charges cancel, the neutrino is truly a neutral particle, it could have no electromagnetically originating mass. It was announced in 1998 that the Super-Kamiokande neutrino observatory had, at last, succeeded in measuring a mass for the neutrino. But bear in mind that the Super-Kamiokande measurements did not directly measure the property of inertial mass. What was measured was the ratio of two types of neutrino (the mu neutrino and the tau neutrino) created by cosmic rays. The ratios of these two types is different as measured in an upward and a downward direction. The neutrinos coming from below the detectors have passed through the earth, and it is thought that during that passage there has been an oscillation of one type into the other. Only half as many mu neutrinos are coming up through the earth as are coming down through the atmosphere. In the current Standard Model of particle physics, such an oscillation between the two types of neutrinos implies a theoretical mass. To call this a measured mass is somewhat misleading; it is a mass based on a specific interpretation from the Standard Model not a direct measurement of inertial mass (and the quantum vacuum-inertia concept of mass proposes specifically that mass is a quite different thing than the concept of mass in the Standard Model). However there is a more likely resolution. There are two other vacuum fields: those associated with the weak and strong interactions (see Questions). The neutrino is governed by the weak interaction, and it is possible that a similar kind of ZPF-particle interaction creates inertial mass for the neutrino but now involving the ZPF of the weak interaction. At present this is pure conjecture. No theoretical work has been done on this problem. In either case, it is prudent to be open to the possibility that certain areas of standard theory may benefit from a fundamental reinterpretation of mass which would resolve these apparent conflicts.

While the standard-theory arguments about the cosmological constant and the mass of the neutrino may prove in the long run to be valid, they must be kept in context. The quantum vacuum-inertia concept appears at this time to be self-consistent with a real, necessarily non-gravitating ZPF and with a neutral neutrino. Of course other objections may well arise and much work remains to be done to test this potentially revolutionary perspective on the origin of mass and the wave-nature of particles.

Stochastic Electrodynamics and Quantum Field Theory

The zero-point field of stochastic electrodynamics (SED) is similar to the quantum fluctuations one finds in modern quantum field theory (QFT). But the random SED electromagnetic fields and the quantum field fluctuations are far from identical, and the mathematical techniques are radically different. SED uses classical electrodynamics, whereas QFT represents the fluctuations as creation and annihilation operators acting on the vacuum. Modern QFT is an amazingly accurate description of nature. In Feynman's popular-level book "QED" for example he presents, in the Introduction, the example of agreement between theory and prediction to 12 significant figures for the magnetic moment of the electron. The challenge is therefore to see whether the possibly significant connection between the ZPF of SED and the inertia of matter can be successfully translated into the more sophisticated and precise formulation of QFT. Can quantum field theory yield an analogous interpretation of inertia and how would this relate to the Higgs field? Indeed, 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.

For an independent evaluation of these concepts see the Report
Zero-Point Fields, Gravitation and New Physics
by Prof. Paul Wesson

Primary Articles (see Scientific Articles for additional articles)

Gravity and the Quantum Vacuum Inertia Hypothesis
Alfonso Rueda & Bernard Haisch, Annalen der Physik, Vol. 14, No. 8, 479-498 (2005).

Review of Experimental Concepts for Studying the Quantum Vacuum Fields
E. W. Davis, V. L. Teofilo, B. Haisch, H. E. Puthoff, L. J. Nickisch, A. Rueda and D. C. Cole, Space Technology and Applications International Forum (STAIF 2006), p. 1390 (2006).

Analysis of Orbital Decay Time for the Classical Hydrogen Atom Interacting with Circularly Polarized Electromagnetic Radiation
Daniel C. Cole & Yi Zou, Physical Review E, 69, 016601, (2004).

Inertial mass and the quantum vacuum fields
Bernard Haisch, Alfonso Rueda & York Dobyns, Annalen der Physik, Vol. 10, No. 5, 393-414 (2001).

Stochastic nonrelativistic approach to gravity as originating from vacuum zero-point field van der Waals forces
Daniel C. Cole, Alfonso Rueda, Konn Danley, Physical Review A, 63, 054101, (2001).

The Case for Inertia as a Vacuum Effect: a Reply to Woodward & Mahood
Y. Dobyns, A. Rueda & B.Haisch, Foundations of Physics, Vol. 30, No. 1, 59 (2000).

On the relation between a zero-point-field-induced inertial effect and the Einstein-de Broglie formula
B. Haisch & A. Rueda, Physics Letters A, 268, 224, (2000).

Contribution to inertial mass by reaction of the vacuum to accelerated motion
A. Rueda & B. Haisch, Foundations of Physics, Vol. 28, No. 7, pp. 1057-1108 (1998).

Inertial mass as reaction of the vacuum to acccelerated motion
A. Rueda & B. Haisch, Physics Letters A, vol. 240, No. 3, pp. 115-126, (1998).

Reply to Michel's "Comment on Zero-Point Fluctuations and the Cosmological Constant"
B. Haisch & A. Rueda, Astrophysical Journal, 488, 563, (1997).

Quantum and classical statistics of the electromagnetic zero-point-field
M. Ibison & B. Haisch, Physical Review A, 54, pp. 2737-2744, (1996).

Vacuum Zero-Point Field Pressure Instability in Astrophysical Plasmas and the Formation of Cosmic Voids
A. Rueda, B. Haisch & D.C. Cole, Astrophysical Journal, Vol. 445, pp. 7-16 (1995).

Inertia as a zero-point-field Lorentz force
B. Haisch, A. Rueda & H.E. Puthoff, Physical Review A, Vol. 49, No. 2, pp. 678-694 (1994).