“Is Weber-Sansbury More Energetically Probable than Bohr?”
The basic question we want to answer is whether the Weber-Sansbury planetary model of the atoms is any more or less energetically probable than the Bohr quantum model. It’s a billion dollar question. Specifically if we consider hydrogen, then the question becomes:
“Is Bohr’s planetary model of the hydrogen atom \([+1, -1]\) more probable than Sansbury-Weber’s model of \([[+2, -1], [+1, -2]]\)?
*“Is Sansbury’s prediction of the structured electron* \(e^{-}=[+1, -2]\) correct?”
The question of which states or models are more probable is effectively an energy and statistical question. It’s generally understood from thermodynamics that more probable states are those with lower potential energies (i.e. with less capacity for work).
Remark on notation: Here \([+n]\) or \([-n]\) refers to \(n\)-particle system of \(n\) equal \([\pm 1]\) charges and having sufficient energy to break through the critical radius. Therefore \([+n]\) represents an \(n\)-body molecule of identical electric particles.
For example the system \([-1, -1]\) is naturally repulsive in isolated environment, but becomes the molecule \([-2]\) only if sufficient work is done by the environment on the system. This is Weber’s amazing prediction that electrons are attractive within the critical radius and an energy \(E=\mu c^2\) is required, where \(\mu\) is the reduced inertial mass of the system.
In a system like \([[+2, -1], [+1, -2]]\), it’s possible that the system have zero net radiation (effectively isolated and stable) whilst the subsystems \([+2, -1]\) and \([+1, -2]\) undergoes a continuous exchange of radiation while maintaining a total energy balance. This is Sansbury’s insight.
Bohr’s Invention of Quantum Hypotheses
We review the history and development of physics, and we see that individuals with large personalities have a dominating influence in physics. Anybody from anywhere can be called into physics. This we learned from Manjit Kumar’s book on Quantum, and the historical biographic accounts it describes from Planck, Bohr, Einstein, etc..
It’s important to recall Niels Bohr’s statement [insert ref] that: “those who are not shocked when they first come across quantum theory cannot possibly have understood it.” This is key to the quantum hypothesis which took this author a long time to appreciate. The point is that Bohr introduced new hypotheses, totally contrary to classical physics, in attempt to “solve” the problem of the apparent stability of the hydrogen atom.
By 1894 it seems physicists found a puzzling problem: Maxwell’s electromagnetism equations imply that electric charges in bound orbits must be continuously radiating energy into the environment. The puzzle was a consequence of Maxwell’s field theory, which predicted via the Poynting vector that an accelerating particle would have nonzero energy flux. The accelerating particle would be radiating away energy via the field from the Maxwellian perspective. This implied a short lifetime for any simple electrical systems modelled after Maxwell.
Initially Rutherford’s model of the atom was static, something like J.J. Thompson’s plum pudding. But eventually the dynamic motion was considered, and this lead to the radiation instability as predicted by Larmor’s calculation. Apparently Rutherford knew this was a problem (1906 Radioactive Transformations).
There was further mechanical instability implied by Nagaota (1904 Japanese). This was naive “Saturn” model of rings. The mutual repulsion of electrons in the orbits of the planetary systems could not mutually cooperate in the ringed Saturn models.
So Bohr writing to Rutherford (1911-1912) assumes the conclusions of Newton and Maxwell, all forecasting the instability of the “planetary atom”. From here Bohr decided that *“the question of stability must therefore be treated from a different point of view* \(\ldots\).” Bohr determines that a “radical change” is needed. Looks to Planck’s quantum proposal. Bohr claims electrons are restricted to “special orbits” where they do not radiate. Bohr calls these states the so-called “stationary states”. No explanation or mechanism is provided to account for the apparent nonradiation of these stationary states.
Bohr reads John Nicholson, encounters the idea of quantized angular momentum \(L=mvr\) when particle is moving in a circular orbit. Nicholson postulated [ref] that \(L=n h\) where \(h\) is Planck’s constant. From here Bohr calculates \(E_1 / n^2 = E_n\), deducing that \(E_1 = -13.6 eV\) while \(E_2 = -13.6/4 = -3.40 eV\). Bohr also calculated that the radius of the hydrogen atom in ground state is \(5.3\) nanometers.
Next Bohr meets Hans Hansen who asks Bohr to explain the spectra of gases, the so-called absorption and emission lines (February 1913). Bohr conceives that absorption and emission are generated by electrons “jumping” between energy levels, and the radiation \(E_2 - E_1\) is equal to the emitted radiation. Bohr uses Planck-Einstein formula \(E = h \nu\) where \(\nu\) is the frequency of the emitted radiation.
Bohr introduces the instantaneous and discontinuous “jumps” or “transitions” of electrons in the orbits, and continues to believe that if the electron travels continuously between orbits, then it must accelerate and radiate continuously. [ref]
In March 1913 Bohr tries to convince Rutherford. Rutherford argues that an electron moving in a circle is an oscillating system with a frequency (i.e. the number of revolutions per second). Expect oscillating system to radiate energy at the frequency of its oscillation (Maxwell?). But the two energy levels have two frequencies, and what is the relation between these two frequencies? Moreover if there is no continuous motion between energy levels, the Rutherford asks the usual question: How does the electron “know” where to go? Which energy levels will it jump to?
Bohr eventually publishes [“On the Constitution …”] in April 1913 and released in July.
The hypotheses of Bohr’s atomic model include the assumptions that:
atomic electrons exist in discrete stable orbits;
the angular momenta are discretized following Nicholson’s formula;
electrons transition discontinuously between different energy levels, and the electron radiate and absorb photons at that energy level according to Planck-Einstein formula \(E_f - E_i = h \nu\).
Eventually the Bohr-Sommerfeld “quantum numbers” would need to be introduced [ref]. These numbers arose from the interpretation of Stern-Gerlach’s experiment, and the hypothesis of “quantum spin” was introduced by W. Pauli [ref].
Ralph Sansbury and “Classical Physics 2.0”
Here enters Ralph N. Sansbury (1938 – 2014) and the ideas introduced in his book “Faster Than Light”. Our critical review of special relativity here, and especially our proposed Fizeau-Sansbury experiment is directly influenced by our reading Sansbury’s book.
From our perspective, Sansbury’s ideas coupled with Wilhelm E. Weber’s (1804-1891) work allows for a Classical Physics 2.0 to be developed. And this is our goal.
Among Sansbury’s ideas is that “light is not something that travels at all, rather the assumed “travel time” of light (the delay between emission and reception) takes place not in the movement of photons, but in the atomic nuclei of the receiver. [ref] This leads to Sansbury’s idea of cumulative instantaneous action at a distance models.
Our goal is to develop the Weber-Sansbury planetary atomic models. We assume that atomic molecules are configurations in relatively stable orbits of \((+1)\) and \((-1)\) electrically charged particles. Our main proposition is that Weber-Sansbury force interactions are stable and substitute – as Sansbury originally proposed – for Bohr’s quantum hypotheses. That is to say, the quantum hypotheses are unnecessary and there is a return to Weber-Newtonian continuity of matter and energy.
Sansbury never explicitly applied Weber’s electrical force laws to his models. His book and papers always assumes Coulomb electrical force laws. The classicaly Coulomb law however does not have the key physical properties of Weber. With Weber force law the Nagaota critique is overturned by the appearance of a new phenomenon, namely the electrical Weber derivation of \(E=mc^2\), and the natural precession of orbits.
With Weber’s force law, the various electrical orbits inside the atom have more opportunity for “cooperation” and “coordination”. Therefore:
- Weber’s force law, especially his derivation of \(E=\mu c^2\), predicts the stability of atomic planetary orbits.
We have written here on Weber’s prediction of the critical radius \(r_c\) where repulsive electric particles obtain a negative effective mass.
Sansbury further proposes that: the apparently discrete orbits of Bohr are actually continuous and synchronized with smaller interior orbits. Thus Sansbury argues that atomic orbits cannot be stably sustained “unless they are multiples of the smaller orbits. This leads to no apparent net radiation because of a balance of forces. The discrete radii whose average frequency between transitions are the observed frequencies and spectrum of wavelengths.” [Paraphrased from Sansbury’s book]
Sansbury observes that there is no measurable difference between average frequencies during light emission and absorption, and difference frequencies as Bohr had proposed.
For example, atomic spectra are strips of light produced on a receiver source by a single heated gas source of light. The spectra are produced through a double slit. Sansbury’s explanation is that light from one edge takes slightly longer than the other edge to appear at a point on the screen. The difference in these times causes the observed interference pattern.
[To be continued – JHM]