Historical research guide · 0613 · 2018
The Planck Constant and the Origin of Mass Due to a Higher Order Casimir Effect
C. Baumgärtel · M. Tajmar
In one minute
Christof Baumgärtel and Martin Tajmar, at TU Dresden’s Institute of Aerospace Engineering, go after a constant nobody has ever derived. Planck’s constant is measured, superbly well, but it has never been built out of anything else. Their route builds it. They model a massive particle as a tiny oscillating electric dipole, and let two such dipoles pull on each other through Weber electrodynamics — an eighteen-forties force law, extended by André Assis, in which the force between charges depends on their separation and on how fast that separation is changing. Expand that force in orders of speed and three familiar effects drop out of one calculation: a first-order term falling as one over distance to the fourth, which behaves exactly like the Casimir force; a second-order term that behaves like gravity; a third-order term that behaves like inertia. Matching the Casimir term to the ordinary Casimir pressure fixes the last free coefficient, and Planck’s constant comes out within seven percent of the measured value, with nothing left to tune.
Connection
Chapter 3 holds that mass, inertia and gravity are effects of the vacuum rather than fundamental properties handed down from nowhere, and this is one of the sharpest published attempts to put the arithmetic on the page — all three falling out of a single dipole interaction, anchored to the same Casimir force chapter 2 is built on.
From the source
Modelling a massive particle as an oscillating electric dipole and computing the interaction of two such dipoles through an extended Weber force yields three effects from one expansion: a Casimir-type attraction at the first-order alpha term, gravitational attraction at the second-order beta term, and inertial effects at the third-order gamma term.Section 3, the summary list of first, second and third order effects
The newly found first-order term falls as one over the fourth power of separation, the Casimir force’s own distance law, which the authors identify as a Casimir-type attraction arising naturally out of dipole-dipole interaction rather than being inserted by hand.Section 3, discussion following Equation 24; Equation 30
Taking the ratio of the model’s Casimir pressure to the standard Casimir pressure fixes the previously unknown coefficient beta at approximately 0.07739 — calculated for the first time rather than assumed, with alpha already known to be one half from electromagnetism.Section 3, Equations 32 to 35
With beta fixed, Planck’s constant follows as fifty n squared e squared divided by pi times the vacuum permittivity times the speed of light, giving 0.9291 times the measured value of h and using no free parameters at all.Section 3, Equations 36 and 37; Section 4, conclusion
In this model mass requires at least one vibrating dipole, so a single charge on a string is massless, and the maximum point mass the model permits is the Planck mass — which is what lets the quantum of action be read off.Section 3, the vibrating-string interpretation and Equations 28 and 29
The authors read the result as a real connection between electrodynamics, gravitation, quantum theory and the origin of mass, all linked through the Planck constant — a reading that further bench tests able to separate Weber-force predictions from Maxwell-Lorentz ones would settle.Section 1, introduction on Weber-versus-Maxwell experiments; Section 4, conclusion
The way in
https://doi.org/10.1166/jap.2018.1402How to cite it
C. Baumgärtel, M. Tajmar (2018) The Planck Constant and the Origin of Mass Due to a Higher Order Casimir Effect doi:10.1166/jap.2018.1402