## Golden Ratio Discovered In a Quantum World 191

FiReaNGeL writes

*"Scientists have for the first time observed a nanoscale symmetry hidden in solid state matter. 'In order to study these nanoscale quantum effects, the researchers have focused on the magnetic material cobalt niobate. It consists of linked magnetic atoms, which form chains just like a very thin bar magnet, but only one atom wide.' By artificially introducing more quantum uncertainty, the researchers observed that the chain acts like a nanoscale guitar string. The first two notes show a perfect relationship with each other. Their frequencies (pitch) are in the ratio of 1.618, which is the golden ratio famous from art and architecture. The observed resonant states in cobalt niobate are a dramatic laboratory illustration of the way in which mathematical theories developed for particle physics may find application in nanoscale science and ultimately in future technology."*
## Re:Summary wrong (Score:3, Informative)

It's an irrational number...

## Art and Architecture? (Score:5, Informative)

...the golden ratio famous from art and architecture...

As a (former) mathematician, I would like to point out that the ratio really comes from elementary (pun intended; read on to find out more) geometry. The ancient Greeks played around with it quite a lot and Euclid mentioned it (more or less) in his Elements [clarku.edu]. The Greeks weren't interested in this because of art or how pretty it was, but because they were particularly crazy about geometry (nearly all of their mathematics was derived from it) and some seemed to think that the universe could be understood through geometry alone. Anyway, it is just the fairly simple ratio of lengths of two lines such that the ratio between the larger and the smaller is the same as the ratio of them both added and the larger, or algebraically;

(a + b)/a = a / b = phi

This can then be trivially rearranged into phi^2 - phi - 1 = 0, and then that has the one positive solution; phi = [1 + sqrt(5)]/2 (the negative solution being [1 - sqrt(5)]/2 = - 0.618... but negative lengths and ratios tend to prove problematic). As usual, Wikipedia has more information. [wikipedia.org]

While it is quite interesting to see it appear in a quantum mechanical setting, it isn't particularly shocking (to me). The number is the result of a fairly simple equation (as shown above) which is why it seems to appear so frequently in nature. While I didn't get this far in my studies of quantum theories, it wouldn't surprise me if, once the mathematicians have a chance to look into this, the reason behind this appearance of phi is found to be rather trivial.

However, I am not a physicist, or an expert in this field, so I may be completely wrong.

## Re:Looking for god's finger prints? Here it is. (Score:3, Informative)

You might have a point if the golden ratio were an entirely arbitrary number and not one derived from a simple geometric relation [wikimedia.org]. Pointing to the golden ratio as evidence for the existence of god is like pointing to occurrences of pi in nature, or the Fibonacci sequence. It isn't god's fingerprints, it's math's fingerprints.

## Re:Summary wrong (Score:5, Informative)

Oh there's been some speculation about possible 'deeper' significances of Planck length,

as well as other Planck units. But as far as we KNOW, they have no significance at all.

They're just a set of units, convenient to eliminate a bunch of constants from equations.

(There are other sets as well, e.g. Atomic units, depending on which kind of equation you're working with)

But nowhere anywhere in current quantum theory is there 'no such thing' as a circle, or anything else.

Circles have a diameter of Pi times the radius in QM just as anywhere else.

## Re:Summary wrong (Score:1, Informative)

moron moderators don't even know what an irrational number is?

anyway, the real golden ratio is half of one plus the square root of five.

## Re:Summary wrong (Score:3, Informative)

Incorrect. The plank length is the smallest region in space that can theoretically be measured. A photon with a short enough wavelength to take a measurement of anything shorter than the plank length will collapse upon its self as a newly formed black hole. It is the fundamental limit to known physics and is effectively the granularity of space its self.

## Re:Summary wrong (Score:2, Informative)

A measurement cannot have such great precision that the inaccuracy in the measurement is shorter than the plank length.

## Re:Looking for god's finger prints? Here it is. (Score:5, Informative)

Einstein:

"God doesn't play dice"

Stephen Hawking:

"Not only does He play dice, He does it with his hands behind his back"

## Re:Looking for god's finger prints? Here it is. (Score:3, Informative)

just to nitpick (I like irony): Fibonacci sequence IS a golden ratio in its essence; more specifically Fib(n+1)/Fib(n) -> golden_ratio :)

## For those who want to hear it. (Score:5, Informative)

For those of you that want to hear what this ratios sounds like, it's 833 cents [mal-2.com], or a minor sixth plus 33 cents. This happens to be the interval used to form the aptly named Bohlen 833 cents (or A12) scale. [wikipedia.org]

Mal-2

## Re:Looking for god's finger prints? Here it is. (Score:5, Informative)

That's actually not quantum mechanics but rather the Copenhagen

interpretationof QM.QM doesn't actually tell us much on whether the universe is deterministic or not, because:

A) The time-evolution of the wave-function itself is deterministic.

and

B) Because it's a philosophical question Science will never be able to answer.

You can always simply deny that it's the ultimate theory of Reality and then add a metaphysical layer explaining why it only 'appears' to be random. Or non-random.

## Re:Summary wrong (Score:5, Informative)

"The whole concept of Planck length dictates minimum distances, angles and such, and objects have granularity"You have been misinformed but it's a common misconception. The Plank length is the base unit for a system of units derived from physical constants, geometries smaller than the PL are where GR theory stops working and QM takes over. That the dividing line between our two best models of the universe should be expressable using nothing but physical constants is quite remarkable and it's probably telling us something we don't yet comprehend. Or as Heisenberg is alleged to have put it; "more fascinating than watching a monkey shit a grandfather clock." [cracked.com]

## Re:Summary wrong (Score:4, Informative)

I never said that smaller length scales couldn't exist, just that they could not effectively be distinguished through measurement according to our current knowledge of physics. The restriction may be sidestepped if gravity acts in a different manner at such extremely small length scales than it does it larger scales. A smaller value for G would effectively decrease the size of the plank scale as an example. However, at the current time, physics as we know it does not allow for measurements to be made that are of greater precision.

## Re:Summary wrong (Score:5, Informative)

You are mistaken. There is no fundamental limit (at least, according to known theory) on the precision of a measurement of the position. The only limit is on how well you can simultaneously measure the position and the momentum. The "plank length" is nothing more than a convenient choice of units.

http://en.wikipedia.org/wiki/Planck_length [wikipedia.org]

## Re:Summary wrong (Score:4, Informative)

I wish there was more geometry in the mathematics syllabus.

## Re:Golden ratio? Just like Dan Brown said? (Score:2, Informative)

They found Mary's grave, and Dan Brown was right, she had a kid by Jesus, only they'd stayed in Jerusalem and both Jesus and their son are buried with her. The son was named Judas.

http://mideast.blogs.time.com/2007/02/23/jesus_tales_from_the_crypt/ [time.com]

## Re:Summary wrong (Score:4, Informative)

## Re:Summary wrong (Score:2, Informative)

Wrong.

Depends on parsing. He could've meant (half of one) plus (the square root of five) or half of (one plus the square root of five), the latter being the correct value of phi as you stated.