Origin of the de Broglie wavelength In the 1920's de Broglie proposed that just as a wave of light can sometimes act like a particle (a photon) depending on what 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 one of the major quantum mysteries. de Broglie made a second, less well known conjecture. If you combine the E=mc2 and the E=hf equations (where f is frequency), you arrive at the Compton frequency. de Broglie's conjecture was that the 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 electron. However it is now known that this presumed oscillation can also be interpreted instead as being externally driven by the zero-point fluctuations of the quantum vacuum (see chap. 12 of the monograph "The Quantum Dice" by 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 a beat frequency becomes superimposed on this oscillation due to a Doppler shift. It turns out that this beat frequency proves to be exactly the de Broglie wavelength of a moving electron. The quantum vacuum inertia hypothesis strongly suggests that the interaction between the quantum vacuum and charged fundamental particles (quarks and electrons) takes place at specific frequencies or resonances. So our conjecture is that the resonance that is involved in giving the electron inertia is the very same resonance as the one conjectured by de Broglie which in turn could give the electron its apparent wave properties when in motion via the Doppler shift effect mentioned above. It is a very appealing picture suggesting connections not only between electrodynamics and mass, but between electrodynamics and quantum mechanics: the zero-point fluctuations drive the electron to undergo some kind oscillation at the Compton frequency and this is where and how both the inertia-generating interaction takes place and the de Broglie wavelength originates due to Doppler shifts (for details see Haisch and Rueda (2000).

(1) ELECTROMAGNETIC QUANTUM VACUUM The zero-point fluctuations of the electromagnetic quantum vacuum may be approximated as a continuous flow of energy: randomly-phased plane-waves in the representation of stochastic electrodynamics (SED). Since the flow of radiation is on average the same in all directions, there is no net flux of energy or momentum as perceived by an observer in an inertial frame. However an accelerating observer will experience an asymmetry. Acceleration through the quantum vacuum results in the appearance of an electromagnetic effect -- a cousin of the well-known Unruh-Davies radiation -- whose strength is proportional to acceleration. [STATUS: SED theory well developed since 1960s. See Rueda & Haisch (1998) papers on the Poynting vector of the zero-point fluctuations on the Scientific Articles page. See also SLAC physicist Pisin Chen's proposed experiment to measure Unruh-Davies radiation using an ultra-high-intensity laser (Chen and Tajima, Phys. Rev. Lett., 83, 256, 1999).] (2) REST MASS: E=mc2 A fundamental particle may be an intrinsically massless thing of some sort (string? spacetime deformation or singularity?) which continuously interacts with the quantum vacuum. Buffeted by the zero-point fluctuations of the electromagnetic quantum vacuum, a particle exhibits Brownian-like motion which Schroedinger named "zitterbewegung" (quivering motion). A tiny bit of the quantum vacuum energy is diverted into the kinetic energy of this zitterbewegung. We suggest that this is the origin of E=mc2 for a particle. If true, there would be no physically distinct mc2. The physically real thing would be only the energy, E, associated with the zitterbewegung of the particle. In this view there is no need for any magic, mysterious conversion of mass into energy and vice versa. One could think of a particle as a localized concentration of zero-point energy which gravitates and resists acceleration for the reasons given below... no traditional "mass" needed. [STATUS: Zitterbewegung and its connection to the zero-point fluctuations is well-developed. See for example the monograph by de la Pena and Cetto: "The Quantum Dice" (Kluwer 1996). The E=mc2 interpretation needs development. See H. E. Puthoff, Phys. Rev. A, 39, 2333, 1989.] (3) INERTIAL MASS Consistent with (2), inertial mass may also not be a physically real, innate property of matter. What we traditionally (since Newton's Principia) think of as inertial mass would in reality be a resistance of the quantum vacuum to acceleration. The fundamental particles (quarks and electrons) in an accelerating object interact with the electromagnetic quantum vacuum, whereby a drag force is generated that is proportional to acceleration. This could be the origin of F=ma. We refer to this as the quantum vacuum inertia hypothesis. [STATUS: Well developed hypothesis. See numerous papers on Scientific Articles page.] (4) ACTIVE GRAVITATIONAL MASS As a consequence of (2) the greater the number of fundamental particles in a given volume of space, the greater the energy deficit of the electromagnetic quantum vacuum (since more of it is diverted into zitterbewegung). This may create an asymmetry in the energy-momentum flow of the zero-point fluctuations (in the SED representation). In other words a Newtonian gravitational field or a general relativistic curvature of spacetime produced by mass may in actuality be manifestations of a quantum vacuum energy asymmetry. [STATUS: Tentative hypothesis. Need to reconcile this in detail with general relativistic spacetime curvature produced by mass-energy. See also a recent attempt to develop the polarizable vacuum gravitation perspective.] (5) PASSIVE GRAVITATIONAL MASS A particle at a fixed distance above a gravitating body such as a planet, will experience a downward force as a consequence of (4). This would be the origin of the force which we traditionally have called weight. [STATUS: See Gravity and the Quantum Vacuum Inertia Hypothesis, Rueda & Haisch, Annalen der Physik, 2005.] (6) PRINCIPLE OF EQUIVALENCE Inertial mass and gravitational mass may be identical because they have an identical source process. Acceleration through the quantum vacuum and being held stationary in a gravitional field in which the electromagnetic quantum vacuum, being radiation, falls past on curved geodesics are, after all, identical processes. [STATUS: See Gravity and the Quantum Vacuum Inertia Hypothesis, Rueda & Haisch, Annalen der Physik, 2005.]