# Zero Point Energy and Zero Point Field http://www.calphysics.org/zpe.html :
Quantum physics predicts the existence of an underlying sea of zero-point energy at every point in the universe. This is different from the cosmic microwave background and is also referred to as the electromagnetic quantum vacuum since it is the lowest state of otherwise empty space. This energy is so enormous that most physicists believe that even though zero-point energy seems to be an inescapable consequence of elementary quantum theory, it cannot be physically real, and so is subtracted away in calculations.
A minority of physicists accept it as real energy which we cannot directly sense since it is the same everywhere, even inside our bodies and measuring devices. From this perspective, the ordinary world of matter and energy is like a foam atop the quantum vacuum sea. It does not matter to a ship how deep the ocean is below it. If the zero-point energy is real, there is the possibility that it can be tapped as a source of power or be harnassed to generate a propulsive force for space travel.
The propellor or the jet engine of an aircraft push air backwards to propel the aircraft forward. A ship or boat propellor does the same thing with water. On Earth there is always air or water available to push against. But a rocket in space has nothing to push against, and so it needs to carry propellant to eject in place of air or water. The fundamental problem is that a deep space rocket would have to start out with all the propellant it will ever need. This quickly results in the need to carry more and more propellant just to propel the propellant. The breakthrough one wishes for deep space travel is to overcome the need to carry propellant at all. How can one generate a propulsive force without carrying and ejecting propellant?
There is a force associated with the electromagnetic quantum vacuum: the Casimir force. This force is an attraction between parallel metallic plates that has now been well measured and can be attributed to a minutely tiny imbalance in the zero-point energy in the cavity between versus the region outside the plates. This is not useful for propulsion since it symmetrically pulls on the plates. However if some asymmetric variation of the Casimir force could be identified one could in effect sail through space as if propelled by a kind of quantum fluctuation wind. This is pure speculation.
The other requirement for space travel is energy. A thought experiment published by physicist Robert Forward in 1984 demonstrated how the Casimir force could in principle be used to extract energy from the quantum vacuum (Phys. Rev. B, 30, 1700, 1984 http://www.calphysics.org/articles/Forward1984.pdf ). Theoretical studies in the early 1990s (Phys. Rev. E, 48, 1562, 1993 http://www.calphysics.org/articles/CP93.pdf ) verified that this was not contradictory to the laws of thermodynamics (since the zero-point energy is different from a thermal reservoir of heat). Unfortunately the Forward process cannot be cycled to yield a continuous extraction of energy. A Casimir engine would be one whose cylinders could only fire once, after which the engine become useless.
# ORIGIN OF ZERO-POINT ENERGY :
The basis of zero-point energy is the Heisenberg uncertainty principle, one of the fundamental laws of quantum physics. According to this principle, the more precisely one measures the position of a moving particle, such as an electron, the less exact the best possible measurement of momentum (mass times velocity) will be, and vice versa. The least possible uncertainty of position times momentum is specified by Planck’s constant, h. A parallel uncertainty exists between measurements involving time and energy. This minimum uncertainty is not due to any correctable flaws in measurement, but rather reflects an intrinsic quantum fuzziness in the very nature of energy and matter.
A useful calculational tool in physics is the ideal harmonic oscillator: a hypothetical mass on a perfect spring moving back and forth. The Heisenberg uncertainty principle dictates that such an ideal harmonic oscillator — one small enough to be subject to quantum laws — can never come entirely to rest, since that would be a state of exactly zero energy, which is forbidden. In this case the average minimum energy is one-half h times the frequency, hf/2.
Radio waves, light, X-rays, and gamma rays are all forms of electromagnetic radiation. Classically, electromagnetic radiation can be pictured as waves flowing through space at the speed of light. The waves are not waves of anything substantive, but are in fact ripples in a state of a field. These waves do carry energy, and each wave has a specific direction, frequency and polarization state. This is called a “propagating mode of the electromagnetic field.”
Each mode is subject to the Heisenberg uncertainty principle. To understand the meaning of this, the theory of electromagnetic radiation is quantized by treating each mode as an equivalent harmonic oscillator. From this analogy, every mode of the field must have hf/2 as its average minimum energy. That is a tiny amount of energy, but the number of modes is enormous, and indeed increases as the square of the frequency. The product of the tiny energy per mode times the huge spatial density of modes yields a very high theoretical energy density per cubic centimeter.
From this line of reasoning, quantum physics predicts that all of space must be filled with electromagnetic zero-point fluctuations (also called the zero-point field) creating an universal sea of zero-point energy. The density of this energy depends critically on where in frequency the zero-point fluctuations cease. Since space itself is thought to break up into a kind of quantum foam at a tiny distance scale called the Planck scale (10-33 cm), it is argued that the zero point fluctuations must cease at a corresponding Planck frequency (1043 Hz). If that is the case, the zero-point energy density would be 110 orders of magnitude greater than the radiant energy at the center of the Sun.
# CONNECTION TO INERTIA AND GRAVITATION :
When a passenger in an airplane feels pushed against his seat as the airplane accelerates down the runway, or when a driver feels pushed to the left when her car makes a sharp turn to the right, what is doing the pushing? Since the time of Newton, this has been attributed to an innate property of matter called inertia. In 1994 a process was discovered whereby the zero-point fluctuations could be the source of the push one feels when changing speed or direction, both being forms of acceleration. The zero-point fluctuations could be the underlying cause of inertia. If that is the case, then we are actually sensing the zero-point energy with every move we make (see origin of inertia http://www.calphysics.org/inertia.html ).
The principle of equivalence would require an analogous connection for gravitation. Einstein’s general relativity successfully accounts for the motions of freely-falling objects on geodesics (the “shortest” distance between two points in curved spacetime), but does not provide a mechanism for generating a gravitational force for objects when they are forced to deviate from geodesic tracks. It has been found that an object undergoing acceleration or one held fixed in a gravitational field would experience the same kind of asymmetric pattern in the zero-point field giving rise to such a reaction force. The weight you measure on a scale would therefore be due to zero-point energy (see gravitation http://www.calphysics.org/gravitation.html ).
The possibility that electromagnetic zero-point energy may be involved in the production of inertial and gravitational forces opens the possibility that both inertia and gravitation might someday be controlled and manipulated. This could have a profound impact on propulsion and space travel.
# Primary Articles (see Scientific Articles http://www.calphysics.org/sci_articles.html for additional articles)
– Gravity and the Quantum Vacuum Inertia Hypothesis http://www.calphysics.org/articles/gravity_arxiv.pdf
Alfonso Rueda & Bernard Haisch, Annalen der Physik, Vol. 14, No. 8, 479-498 (2005).
– Analysis of Orbital Decay Time for the Classical Hydrogen Atom Interacting with Circularly Polarized Electromagnetic Radiation http://www.calphysics.org/articles/ColeHydrogenPRE.pdf
Daniel C. Cole & Yi Zou, Physical Review E, 69, 016601, (2004).
– Inertial mass and the quantum vacuum fields http://xxx.arxiv.org/abs/gr-qc/0009036
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 http://www.calphysics.org/articles/Cole_Rueda_Danley.pdf
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 http://xxx.arxiv.org/abs/gr-qc/0002069
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 http://xxx.arxiv.org/abs/gr-qc/9906084
B. Haisch & A. Rueda, Physics Letters A, 268, 224, (2000).
– Contribution to inertial mass by reaction of the vacuum to accelerated motion http://xxx.arxiv.org/abs/physics/9802030
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 http://xxx.arxiv.org/abs/physics/9802031
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” http://www.calphysics.org/articles/zpf_apj.pdf
B. Haisch & A. Rueda, Astrophysical Journal, 488, 563, (1997).
– Quantum and classical statistics of the electromagnetic zero-point-field http://www.calphysics.org/articles/PRA96.pdf
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 http://adsbit.harvard.edu/cgi-bin/nph-iarticle_query?1995ApJ%2E%2E%2E445%2E%2E%2E%2E7R&nosetcookie=1Vacuum Zero-Point-Field Pressure
A. Rueda, B. Haisch & D.C. Cole, Astrophysical Journal, Vol. 445, pp. 7-16 (1995).
– Inertia as a zero-point-field Lorentz force http://www.calphysics.org/articles/PRA94.pdf
B. Haisch, A. Rueda & H.E. Puthoff, Physical Review A, Vol. 49, No. 2, pp. 678-694 (1994).
# Questions and Answers about the Origin of Inertia and the Zero-Point Field http://www.calphysics.org/questions.html :
NOTE — This section attempts to elucidate the possible connection between inertia and the zero-point field and its implications via straightforward questions and answers. This results in considerable oversimplification especially since research to date has been limited to the assumptions of stochastic electrodynamics. Our research colleagues are urged to base their professional judgments not on these questions and answers, but rather on the published papers http://www.calphysics.org/sci_articles.html and the goal of the Calphysics Institute to explore whether these concepts can be reformulated and validated within the more comprehensive disciplines of modern quantum field theory, string and brane theory, quantum gravity, supersymmetry etc. The SED and ZPF perspective presented below must be viewed as a potentially fruitful set of interrelated concepts bearing on some foundational problems in physics, but concepts that remain to be proven. The testing, examination and, if promising, development of these concepts is the mission of the Calphysics Institute.
# What is the zero-point field or zero-point fluctuations (ZPF)? What is its relationship to the quantum vacuum?
In the view of modern physics, the vacuum is far from empty. Take away all particles and all electromagnetic radiation and you will have an apparently empty region of space at a temperature of absolute zero. But in fact this “vacuum” will still be full of energies and particle pairs (such as positrons and electrons): the electromagnetic zero-point field, the zero-point fields of the weak and strong interactions, and the Dirac sea of negative energy particle pairs. All of these energies and particles are collectively referred to as the quantum vacuum (making the vacuum in reality a plenum). Our work so far has involved only one component of the quantum vacuum: the electromagnetic zero-point field or zero-point fluctuations. (Henceforth, unless stated otherwise, ZPF refers only to the electromagnetic ZPF.) The ZPF was a hypothesis put forward by Max Planck in 1911, and was developed by him and Walther Nernst between 1911 and 1916. In 1947 the effect of the ZPF was directly demonstrated by Willis Lamb, in a famous experiment, which Lamb himself has described as “a proof that the vacuum does not exist” (i.e. that the “vacuum” is a “plenum”). The Casimir effect, predicted in the following year and subsequently verified, is another direct demonstration of the ZPF’s reality.
# But where does the ZPF come from?
Imagine an oscillator, such as a pendulum. Unless you keep putting in energy to keep it going, any swinging pendulum will eventually come to rest as a result of friction. But things are different in the quantum realm. The Heisenberg uncertainty relation would forbid a quantum pendulum from ever coming completely to rest. There is a minimum energy that you cannot take away according to quantum laws. Like a pendulum, light and other forms of electromagnetic radiation consist of oscillations: in this case oscillations of electric and magnetic fields. Every direction, every frequency and each polarization state of the electromagnetic field thus has a minimum energy, thanks to the Heisenberg uncertainty relation. Add up all of these “modes of the field” and you have the electromagnetic ZPF.
# But wouldn’t this argument yield an infinite ZPF? Surely there has to be a cutoff somewhere.
At higher and higher energies the electromagnetic and the weak interactions become the same electroweak interaction. At very high frequencies (i.e. high energies) the ZPF therefore ceases to be a purely electromagnetic field. Rather than a cutoff there would be a gradual transition from a purely electromagnetic ZPF to an electroweak ZPF. At even higher energies this would unify with a gluon-related zero-point field. Indeed the governing equations become increasingly non-linear and there is the likelihood that, just as with the Planck function, this will lead to quenching of the divergence. Thus at higher and higher energies the relevant physics changes and so it would be incorrect to think (or worry) about infinite electromagnetic energy in the ZPF. Collectively, however, when all fields are counted, the ensemble of their vacua still presents a problem of divergence that needs to be addressed.
# Is the ZPF a kind of ether? Does it violate special relativity?
No, not at all. The ZPF as used in stochastic electrodynamics is nothing other than electromagnetic waves, a form of light. This makes the ZPF by definition consistent with special relativity, because special relativity is based on light propagation. The frequency-cubed spectrum of the ZPF renders it Lorentz invariant. Therefore it is nothing like the 19th century ether concept.
# Your article Beyond E=mc2 http://www.calphysics.org/haisch/sciences.html is subtitled “A First Glimpse of a Universe Without Mass.” But what does this mean? How can there be no mass?
A goal of modern quantum field theory is to eliminate mass as a primary property of matter, so we are pursuing a mainstream objective of contemporary physics. For example, it is believed that the sum of the masses of the 3 quarks constituting protons or neutrons is only 2 or 3 percent of the inertial mass of those protons or neutrons. Most of the mass is attributed to the energy associated with quark motions and gluon fields, but precisely how this energy translates into the property of mass through a Higgs field is not easy to understand (see two recent articles by F. Wilczek in Physics Today, Nov. 1999 and Jan. 2000 for an overview). Our semi-classical approach is quite different and at this point involves purely classical electrodynamics plus a real electromagnetic ZPF that has exactly the same energy density spectrum as the quantum electromagnetic ZPF. We have found that when an object is forced to accelerate, it will see the ZPF to be asymmetric, or in other words, distorted. Due to this distortion the accelerating object will see a zero-point flux of energy and momentum coming at it, whereas ordinarily, when the object is not being accelerated, the ZPF is perfectly uniform and symmetric. A key result of our analysis is that these fluxes prove to be proportional to the acceleration of the object, i.e. the more rapid the acceleration, the more the ZPF is distorted. Material objects consist of charged quarks and electrons, which will tend to scatter any oncoming electromagnetic flux. When all the quarks and electrons in an object scatter the distorted ZPF passing through, the object will experience a kind of drag force. We are proposing that this might be what the inertia reaction force really is… the drag force due to being accelerated through the vacuum fields. In this view, objects would not intrinsically resist being accelerated; objects would not possess mass. Mass would really be just a way of characterizing the resistance due to the ZPF molasses (or in the future more general case, the quantum vacuum molasses) that kicks in upon acceleration. Of course the limitation that we are only, so far, considering the electromagnetic ZPF means that what we have found may be only a part of the story. The electromagnetic ZPF may contribute to inertia but still not account for all the mass.
[NOTE: In the Standard Model attempt to obtain, in John Wheeler’s quote, “mass without mass,” the issue of inertia appears to be left out of the picture. As Wilsczek states: “Most of the mass of ordinary matter, for sure, is the pure energy of moving quarks and gluons. The remainder, a quantitatively small but qualitatively crucial remainder — it includes the mass of electrons — is all ascribed to the confounding influence of a pervasive medium, the Higgs field condensate.” An explanation of proton and neutron masses in terms of the energies of quark motions and gluon fields is fine, but falls short of offering any insight on inertia itself. One is no closer to an understanding of how this energy somehow acquires the property of resistance to acceleration known as inertia. The modern Standard Model explanation of mass is satisfied if it can balance the calculated energies with the measured masses but merely equating energy and mass does not explain inertia. The quantum vacuum-inertia hypothesis addresses the deeper issue of what inertia might actually be, viz. a force originating in quantum vacuum distortions that makes matter resist acceleration.]
# But if there is no mass, what happens to the concepts of momentum and kinetic energy?
So long as an object is in uniform motion, its momentum and kinetic energy are purely hypothetical, abstract properties. Indeed their values depend on the relative motion of you and the object, and so the momentum and kinetic energy you calculate for a moving object can take on any value you like by changing your own motion. Real effects only arise when you change the velocity of an object, such as when two billiard balls collide. When you change the velocity, i.e. accelerate, that is when the ZPF distortion appears and then forces arise which behave like the inertia of mass. Momentum and kinetic energy of material objects in motion are thus useful mathematical bookkeeping tools that will tell you what to expect when you change velocity, such as in a collision, but real measureable forces only arise when that change of velocity occurs. Note that we do attribute momentum and energy to the electromagnetic zero-point field. Indeed, the change in momentum of an object in a collision can be attributed to the momentum flux of the ZPF.
# What are the implications for gravity? After all, the principle of equivalence dictates that inertial mass and gravitational mass must be same.
General relativity (GR) attributes gravitation to spacetime curvature. Modern attempts to reconcile quantum physics with GR take a different approach, treating gravity as an exchange of gravitons in flat spacetime (analagous to the treatment of electromagnetism as exchange of virtual photons). A non-geometric (i.e. flat spacetime) approach to gravity is legitimate in quantum gravity. Similarly another non-geometric approach would be to assume that the dielectric properties of space itself may change in the presence of matter: this can be called the polarizable vacuum (PV) approach to gravity. Propagation of light in the presence of matter would deviate from straight lines due to variable refraction of space itself, and other GR effects such as the slowing down of light (as judged by a distant observer) in a gravitational potential would also occur. But of course it is the propagation of light from which we infer that spacetime is curved in the first place. This raises the interesting possibility that GR may be successful and yet not because spacetime is really curved: rather because the point-to-point changes in the dielectric (refractive) properties of space in the presence of matter create the illusion of geometrical curvature. A PV type of model does not directly relate gravitation to the ZPF (or to the more general quantum vacuum) but it does appear to provide a theoretical framework conducive to developing the conjecture of Sakharov that it is changes in the ZPF that create gravitational forces (although it also has the drawback of apparently being at odds with the existence of black holes).
# But isn’t the energy density of the ZPF so high that it would have an enormous gravitational effect, just like a huge cosmological constant?
Not necessarily. If gravitation derives from the ZPF (and possibly the other quantum vacua) and changing dielectric properties of space, then the energy of the ZPF cannot gravitate. Gravitation would consist of minute changes in the ZPF in the presence of matter in analogy to the minute changes in the ZPF that an accelerating particle experiences. Indeed, one would be able to derive the principle of equivalence if we had a complete quantum vacuum-based theory of inertia and gravitation (including possibly the weak and strong interaction zero-point fields). But certainly the ZPF would not act on itself to gravitate; that would be impossible in this picture. The argument about a huge cosmological constant arising if you take the ZPF literally misses the point that a self-consistent ZPF basis for both inertia and gravitation would necessarily preclude this.
# Returning to inertial mass, how could a neutral particle interact with the electromagnetic vacuum? Wouldn’t your theory predict neutral particles to be massless, and if so, what about the recent neutrino mass determination?
The neutron would be no problem: it consists of 3 charged quarks (the sum of electric charges cancelling) and the interactions with the ZPF almost surely take place at the level of the individual quarks. But if the neutrino is truly neutral, not consisting of any smaller charged particles, then indeed the electromagnetic ZPF inertia hypothesis could not yield a mass. But recall that there are two other zero-point fields: those associated with the weak and strong interactions. 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. (It is worth keeping in mind, though, that while there is now considerable indirect evidence that neutrinos possess mass, even the recent Super-Kamiokande measurements are not direct measurements of neutrino mass.)
# What does the quantum vacuum-inertia hypothesis have to say about the mass in the E=mc2 relationship?
The customary intepretation is that one kind of thing, energy, can change into a completely different kind of thing, mass, and vice versa… almost like magic. The ZPF perspective offers a very different view, which is not of course tantamount to proof. There is an extremely rapid particle quantum fluctuation that can be attributed to the perturbations of the ZPF. This was named Zitterbewegung (German for quivering motion) by Schroedinger, and in a model proposed by Dirac the fluctuations of this Zitterbewegung happen at the speed of light, c. In his 1989 attempt to develop the Sakharov conjecture connecting the quantum vacuum and gravitation, Puthoff suggested (as others had speculated previously as well) that the kinetic energy associated with the ZPF-driven Zitterbewegung is what provides the energy for the E=mc2 relation. The real stuff is the energy, E, and as with inertial mass, it is only our (obstinate) habit of believing that matter must possess mass that leads to our insisting that there must exist a right hand side to this equation, namely mc2. In reality (perhaps) there is no mass, just the energy, E, that the quantum vacuum gives in the form of Zitterbewegung in the same way that there is no inertial mass, just the force that the quantum vacuum gives when an object accelerates. In a sense this does away with the need for a veritably magical transmutation of energy into matter or matter into energy. In this view we never get energy by destroying matter. We get energy by liberating some or all of the kinetic energy that the quantum vacuum puts into the Zitterbewegung of what are really massless quarks and electrons. Rest mass would really be ZPF energy (or more generally quantum vacuum energy) associated with a particle via Zitterbewegung (almost certainly at a resonance). This approach to rest mass is very suggestive, but of course needs a great deal more work.
# Doesn’t General Relativity (GR) already provide an origin for inertia?
Einstein formulated GR by assuming that the force you feel standing still in a gravitational field, say at the surface of the Earth, is indistinguishable from the force you would feel if you were accelerating, say in a rocket steadily increasing its speed at one gee. (Actually this is only true for a point. Tidal effects can distinguish acceleration from gravitation at other than a single point.) This is the “principle of equivalence” and is tantamount to assuming that inertial mass and gravitational mass are equal. The consequence of this is that all objects fall at the same rate (an experiment attributed, perhaps apocryphally, to Galileo at the Leaning Tower of Pisa). But note that the principle of equivalence is an assumption, not an explanation. Assuming that a one-gee gravitational force and a one-gee inertial force are equal may be a true representation of reality, but is different from explaining how the forces originate. The mathematical formulation of GR represents spacetime as curved due to the presence of matter and is called geometrodynamics because it explains the dynamics (motions) of objects in terms of four-dimentional geometry. Here is a crucial point that is not widely understood: Geometrodynamics merely tells you what path (called a geodesic) that a freely moving object will follow. But if you constrain an object to follow some different path (or not to move at all) geometrodynamics does not tell you how or why a force arises. Geometrodynamics leaves it up to the concept of inertia to generate such a force. Logically you wind up having to assume that a force arises because when you deviate from a geodesic you are accelerating, but that is exactly what you are trying to explain in the first place: Why does a force arise when you accelerate? Geometrodynamics explains the motion of unconstrained objects, but has no mechanism to generate forces for constrained objects. It leaves it to inertia to provide that force, but this merely takes us in a logical full circle. For a more detailed explanation of this see Dobyns, Rueda and Haisch (2000).
# What is this new interpretation of the de Broglie wavelength of a moving particle that you are proposing?
Our Poynting-vector approach to inertia (the 1998 Rueda and Haisch papers) strongly suggests that the interactions between the ZPF and charged fundamental particles (quarks and electrons) take place at specific frequencies or resonances. Consider the electron. Where in frequency would such a resonance be? On reading articles by Hunter, by Kracklauer and chapter 12 in the monograph by de la Pena and Cetto, we discovered a very similar resonance concept, call it the de Broglie resonance, that might explain the wave-like properties of a moving particle. In the 1920’s de Broglie proposed that just as a wave of light can sometimes act like a particle (a photon) depending on the measurement you make, so too can a particle sometimes behave like a wave. He postulated that the wavelength of a moving particle would be h/p, where h is Planck’s constant and p the momentum. This was confirmed for the electron in a famous 1927 experiment by Davisson and Germer. But how does a particle acquire such wavelike attributes? This has remained a fundamental mystery of quantum physics, and the usual reply is effectively: “Don’t ask such questions. It’s just a law of nature.” But de Broglie made a second, less well known proposal. If you combine the E=mc2 and the E=hf equations (where f is frequency), you can calculate a frequency known as the Compton frequency. de Broglie believed that this Compton frequency reflected, in the case of the electron (quarks were not yet discovered), some kind of fundamental intrinsic oscillation or circulation of charge associated with the particle. However this presumed oscillation can also be interpreted instead as being externally driven, where the external driving agent is the ZPF (see chap. 12 of de la Pena and Cetto). Now comes a very intriguing result. One can easily show that if the electron really does oscillate at the Compton frequency in its own rest frame, when you view the electron from a moving frame there is a beat frequency superimposed on this oscillation due to the Doppler shift. It turns out that this beat frequency proves to be exactly the de Broglie wavelength of a moving electron. So our conjecture is that the resonance that is involved in giving the electron inertia is the very same resonance as the one that gives the electron its apparent wave properties when in motion. It is a very appealing picture suggesting a connection not only between electrodynamics and mass, but between electrodynamics and quantum mechanics: the ZPF drives the electron to undergo some kind oscillation at the Compton frequency and this is where and how the inertia-generating interaction takes place and where and how the de Broglie wavelength originates due to Doppler shifts (for details see Haisch and Rueda (2000)
# See also: