The Planck Constant and the Origin of Mass Due to a Higher Order Casimir Effect
C. Baumgärtel · M. Tajmar
Abstract and summary · read the original at the source
In one page
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.
Why it matters hereChapter 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.
What it claims
01Modelling 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
Published and peer-reviewed02The 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
Published and peer-reviewed03Taking 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
Published and peer-reviewed04With 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
Published and peer-reviewed05In 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
Published and peer-reviewed06The 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
What to watch
Read it · abstract
Abstract
The Planck constant is one of the most important constants in nature, as it describes the world governed by quantum mechanics. However, it cannot be derived from other natural constants. We present a model from which it is possible to derive this constant without any free parameters. This is done utilizing the force between two oscillating electric dipoles described by an extension of Weber electrodynamics, based on a gravitational model by Assis. This leads not only to gravitational forces between the particles but also to a newly found Casimir-type attraction. We can use these forces to calculate the maximum point mass of this model which is equal to the Planck mass and derive the quantum of action. The result hints to a connection of quantum effects like the Casimir force and the Planck constant with gravitational ones and the origin of mass itself.
The way in
https://doi.org/10.1166/jap.2018.1402Licence checked directly. The author copy in TU Dresden’s Qucosa repository carries the rightsstatements.org ‘In Copyright’ statement, and no Creative Commons statement appears in the article or on the publisher page, so this page carries the summary, the claims and the authors’ own abstract and sends the reader to the source. Published as Journal of Advanced Physics 7(1), 135–140 (2018), by C. Baumgärtel and M. Tajmar of the Institute of Aerospace Engineering, Technische Universität Dresden; the author manuscript is dated 31 May 2018. The summary, the claims and the locators below were written from the full author text, read from the Qucosa copy at the persistent identifier above.
How 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
Where it sits in the curriculum