Fibonacci Sequence In Theoretical Physics

[write4u]

I believe the Fibonacci Sequence is ubiquitous in nature due to natural selection of growth pattern efficiency.

The Fibonacci Sequence has very practical survival utility; It affords maximum use of space for collection of sunlight and petal and seed placement.

a) it forms a perfectly balanced structure in vertical growth. Almost all vertical growing organisms utilize the FS . Branch growth in trees follow almost always the FS.

http://www.eniscuola.net/wp-content/uploads/2016/07/fillotassi_en.jpg

b) it is the most efficient distribution format in plant petal growth and seed distribution. Daisies almost always have FS sequential petal growth. Pine cone seeds are arranged in FS.  Sunflowers seed are arranged in FS sequences.

Flowers

The Fibonacci sequence can be seen in two different places in flowers. The most visible place is the petals of a flower. Several flowers have petals that are numbers of the fibonacci sequence. Lilies have 3 petals, buttercups have 5 petals, and daisies have 34 petals, for example. Scientists have theorized that petals that fit the Fibonacci sequence absorb more sunlight, among other uses.

https://www.mensaforkids.org/teach/lesson-plans/fabulous-fibonacci/

http://www.eniscuola.net/en/2016/06/27/the-numbers-of-nature-the-fibonacci-sequence/

https://interestingengineering.com/mother-natures-favorite-number-sequence-the-fibonacci

Edited February 10, 2021 by write4u

[write4u]

I also believe the Fibonacci Sequence offers the perfect self-referential mathematical information processing function, a form of quasi intelligent mathematical information processing. Consciousness is not required for functionality. These are fundamental and simple mathematical guiding equations for most growth functions, similar to a pure exponential growth function. i.e. 2, 4, 8, 16, 32, 64, .....etc.

There are several similar regular patterns like the Fibonacci Sequence, such as  2, 2, 4, 6, 10, 16, 26 ........etc.....and 1, 3, 4, 7, 11, 18.......etc.  

I am confident these regular self-referential patterns evolve over time via natural selection, dependent on the mathematical growth pattern allowed by environmental conditions. They are part of the tendency for symmetry in nature.

https://scholarworks.smith.edu/cgi/viewcontent.cgi?article=1029&context=mth_facpubs

 

Edited February 10, 2021 by write4u

[Fenmachsa]

On 3/8/2011 at 3:01 PM, Don Blazys said:

Quoting onionsoflove:

Physicists are indeed discovering relationships between patterns

found in number theory and patterns found at the quantum level. Here:

 

http://www.physorg.com/news182095224.htmldrift boss

 

is but one example (which happens to involve the Fibonacci Sequence and

the Golden Ratio of which you speak.) What really impresses me here is

how clever some of these physicists are about inventing, developing and

manufacturing the gadgets required to make these incredible measurements.

 

Don.

In theoretical physics calculations involving the speed of light, c, if you're stuck with miles per hour, multiply by the golden ratio. Amazing link.

[pascal2]

The sequence of dimensions utilized in String Theory (starting with the Holographic model) is also apparently every other doubled Fibonacci number- so 2, 4, 10, 26.  Recently I discovered another relationship from an entirely different area that might be related. One can model the charges of the Standard Model fermions using a cube embedded in a reference plane along a body diagonal which runs through the cube's center and two diametrically opposed vertices. Then you rotate the cube along this diagonal so that one vertex subtends an angle of arctan(sqrt27) with reference to the plane. If you do this then the length of the normals from the plane to the vertices (sines or cosines) parallels the magnitudes of the fermion charges, and the direction of the normals to the vertices (half above the plane, and half below) parallel the polarities of the charges (plus or minus). 

Anyway, I found that if you divide the reciprocal of the Fine Structure Constant (137.035999...) by the angle mentioned above (which comes to 79.10660535... degrees) the result is almost exactly the square root of 3 (1.732 and change), with the difference being much less than 1%. But in the early, high energy universe, the Fine Structure Constant's reciprocal was lower, closer to 127. If you use 128, and divide by arctan(sqrt27) then the result is almost exactly the Golden Ratio, 1.618033989.... The difference here from the actual value of the latter is also much less than 1%.

Jess Tauber

[OceanBreeze]

8 hours ago, pascal2 said:

The sequence of dimensions utilized in String Theory (starting with the Holographic model) is also apparently every other doubled Fibonacci number- so 2, 4, 10, 26.  Recently I discovered another relationship from an entirely different area that might be related. One can model the charges of the Standard Model fermions using a cube embedded in a reference plane along a body diagonal which runs through the cube's center and two diametrically opposed vertices. Then you rotate the cube along this diagonal so that one vertex subtends an angle of arctan(sqrt27) with reference to the plane. If you do this then the length of the normals from the plane to the vertices (sines or cosines) parallels the magnitudes of the fermion charges, and the direction of the normals to the vertices (half above the plane, and half below) parallel the polarities of the charges (plus or minus). 

Anyway, I found that if you divide the reciprocal of the Fine Structure Constant (137.035999...) by the angle mentioned above (which comes to 79.10660535... degrees) the result is almost exactly the square root of 3 (1.732 and change), with the difference being much less than 1%. But in the early, high energy universe, the Fine Structure Constant's reciprocal was lower, closer to 127. If you use 128, and divide by arctan(sqrt27) then the result is almost exactly the Golden Ratio, 1.618033989.... The difference here from the actual value of the latter is also much less than 1%.

Jess Tauber

While interesting, I suspect you can find all sorts of numerical relationships using arbitrary number units such as degrees but I fail to see where such numerical relationships have any significance.

If you find similar relationships using all-natural units, such as radians, and the dimensionless fundamental physical constants, such as the fine structure constant, I think that would be far more meaningful.

But even the significance of such relationships with all-natural units can be dubious because we have to rely on the CODATA Internationally recommended values of the Fundamental Physical Constants which depend on the unit system used to express them.