Golden ratios in quantum mechanics?

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Discussion Overview

The discussion explores the potential presence of golden ratios in quantum mechanics, specifically in relation to the standard model, string theory, and quantum gravity. Participants examine whether these ratios manifest in fundamental symmetries and theories within quantum physics.

Discussion Character

  • Exploratory, Debate/contested, Conceptual clarification

Main Points Raised

  • One participant questions the existence of golden ratios in quantum mechanics, suggesting that nature seems to favor two-fold symmetry, with the ratio of 1.414... being more common.
  • Another participant mentions the Fibonacci anyon model, indicating that golden ratios appear in relation to the quantum dimension of anyons, though the physical relevance is debated.
  • A different participant references an article discussing the golden ratio's appearance in neutrino theory, implying a possible connection but not elaborating on its significance.
  • One participant raises the question of whether golden ratios are less significant in the microverse compared to the macroverse, suggesting a potential disparity in their relevance across scales.

Areas of Agreement / Disagreement

Participants express differing views on the relevance and occurrence of golden ratios in quantum mechanics, with no consensus reached on their significance or presence in various theories.

Contextual Notes

Some claims depend on specific interpretations of symmetry and the definitions of physical examples, and the discussion does not resolve the implications of golden ratios in quantum theories.

Loren Booda
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Do golden ratios appear in quantum mechanics - such as with the standard model, string theory or quantum gravity?
 
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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.
 
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...
 
Is it true that golden ratios do not play as significant a part in the microverse as they play in the macroverse?
 

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