If we map as a continuous motion an ionising electron (beginning its journey at n=1) in an H atom, a specific hyperbolic spiral appears (see animation). When we solve this spiral formula, we find that at regular intervals the spiral angles will cancel to give integer values (360°=4r, 360+120°=9r, 360+180°=16r, 360+216°=25r ... 720°=∞ ... formulas below).
As the orbital levels corresponding to the principal quantum number n^2 (4, 9, 16, 25 ...) naturally occur via this spiral geometry, then at those points where the angles cancel to give integers (360°, 360+120°, 360+180°, 360+216° ...) we can use the spiral perimeter (r = Bohr radius) to derive the transition frequency for that integer (n^2) level ......, the question then becomes, could quantization in the atom have geometrical origins?
https://en.wikiversity.org/wiki/Fine-structure_constant_(spiral)
In the animation the radius is mapped (during ionization), as the electron reaches each integer level, it completes 1 orbit (for illustration) then continues outward (actual velocity will become slower as radius increases).
https://en.wikiversity.org/wiki/Fine-structure_constant_(spiral)#/media/File:Alpha-hyperbolic-spiral.gif
Does your one-dimension static equation recognize three-dimension, color, taste, smells, temperature, pressure.....?
Reading this might help.
Article Intelligent Atom
Hi Sydney,
Thanks for the remarks.
For the Planck unit geometries you mentioned, I have moved the formulas to these wiki pages
https://en.wikiversity.org/wiki/Physical_constant_(anomaly)
https://en.wikiversity.org/wiki/Planck_units_(geometrical)
https://en.wikiversity.org/wiki/Electron_(mathematical)
To my mind, these anomalies in the dimensioned physical constants can only be explained by a simulation universe, would be interested in your thoughts on the subject.
I read the article by Fotini. He takes as a fundamental premise that quantum theories represent the base level, in my modeling the Planck scale is the base level, the quantum and macro levels emerge from this level, so you cannot apply quantum math to the Planck scale, rather the reverse. Indeed we should be talking about Planck mechanics, furthermore for me the Planck scale is discrete and so the math is quite simple, this is because there is no time dimension and so there is nothing to integrate.
I suggested (wiki sites) that at this Planck level the Planck units are geometrical objects that embed their function, the function time is embedded in the object T, the function length is embedded in the object L ... and so we can build the universe Lego-style. An apple has mass because embedded in the apple are these mass objects ... and so I am modeling the Planck scale using geometry.
I wrote a gravity simulation program that treats orbiting objects as the sum, averaged over time, of individual rotating particle to particle orbital pairs, this is because at the Planck scale planets, as we know them, don’t exist. When I used the electron and proton as my orbiting pair example, I got this spiral..., where the angles collapse to give the n levels, the perimeter gives the transition frequency. Weird. We write the n levels as n = 1, 2, 3... with (2)n^2 as the number of electrons that can fit, the spiral suggests that the n levels are 1, 4, 9 16 ...
https://en.wikiversity.org/wiki/Quantum_gravity_(Planck)#Atomic_orbitals
In summary, where Fotini sees the universe as a quantum computer, I see it as a Planck computer with the source code using geometry. Electrons orbit protons due to geometrical imperatives and so on ...
Cheers,
Malcolm
- Badges
- Science topic
- Similar topics
- Biological Science
- Molecular Biology
- Biomolecules
- Nucleic Acids
- RNA