Golden ratios in quantum mechanics?

[Loren Booda]

Do golden ratios appear in quantum mechanics - such as with the standard model, string theory or quantum gravity?

 

[Phrak]

I don't think so, Loren--at least, not yet. However, I was very startled to see the question! Your natural tendency to think far out of the box is your talent.

In a world dominated by two fold symmetry, 1.414... to 1 is a common ratio we see occurring often. Nature seems to prefer 2:1 over any other.

0.866... is the square root of 3. We don't see it as often. Quarks seem to the the first known, fundamental 3-fold symmetry.

The golden ratio is about 5-fold symmetries. To my knowledge, there is yet to be discovered any elemental 5-fold symmetries in nature.

 

[ccesare]

It appears in relation to the quantum dimension of the (nontrivial) anyon in the Fibonacci anyon model. Whether or not you consider this a physical example is another matter...

 

[The_Duck]

I noticed an article that mentioned an appearance of the golden ratio in some neutrino theory: http://arxiv.org/abs/0705.4559

 

[Loren Booda]

Is it true that golden ratios do not play as significant a part in the microverse as they play in the macroverse?