5 ms·

Golden Ratio Discovered in Quantum World

63 points by slater 17y ago

pohl 17y ago
There's a very good Ted Talk on E8. I don't understand how the appearance of Phi suggests E8 (if someone here understands this, please explain), but the first thing that came to mind was whether Garrett Lisi knows about this news yet: http://www.youtube.com/watch?v=y-Gk_Ddhr0M http://www.youtube.com/watch?v=y-Gk_Ddhr0M http://en.wikipedia.org/wiki/E₈ http://en.wikipedia.org/wiki/E₈
- Devilboy 17y ago
  I understand that most particle physicists don't really take Lisi's work very seriously. Does this discovery lend more weight to his E8 theories?
tibbon 17y ago
I want to look into this more, but I have to wonder- if you look hard enough for a number/ratio to appear, won't you find it almost everywhere? Seems kinda like a fortune teller asking you to look for the number '3'. I am not a mathematician, so I also have no idea what I'm talking about- just gut instinct.
- pohl 17y ago
  That's a good question. I would imagine the probability to vary a great deal by what particular number one is looking for. That is, I would expect it to be very easy to find small integers, but extremely unlikely to accidentally find a very large prime number. I suspect it would be much harder to find (1 + sqrt(5)) / 2 everywhere you look than to find 3.
- snorkel 17y ago
  The value 1.618... is not as interesting as its recursive fraction form which happens to be = 1 + (1 + 1/ ( 1 + 1/ ( 1 + 1/ ... an infinite recursion based on the number 1 is somewhat interesting and could be insightful.
- dc2k08 17y ago
  I can recommend a book called: The Golden Ratio: The Story of Phi - the World's Most Astonishing Number. It gave me a bit of bit of a Phi fetish. It appears like a kernel of existence.
- dandelany 17y ago
  Not when the number is irrational. What's most interesting to me is that phi often occurs in recursive systems, so it's discovery often implies natural recursion.
- Sukotto 17y ago
  The thing about the golden number is that it really does appear just about everywhere. That's one of the reasons it's so cool.
- ams6110 17y ago
  In the quantum realm, doesn't looking for something make it appear?
  - eru 17y ago
    It may work the other way round --- if you don't look it doesn't appear. But you can't just make any stuff appear.
- jordanb 17y ago
  Well, the set of all numbers is infinite, so you would wouldn't expect to find just any number appear in a lot of different contexts by chance. Some numbers do tend to show up over and over again. That makes those numbers special. φ is such a special number. But there are a lot of special things about 3 though too: It's an integer (which is a pretty special property for a number to have, considering there are an infinite number of real numbers between each integer). What's more, it's a very small integer (the fourth smallest) and it's the second smallest prime number. In fact, we could say that 3 is a very special number, in the scheme of things, and has lots of reasons to show up in particular contexts. Now φ being the golden ratio is pretty much all that's unique about it. Otherwise, it's just one of the uncountably infinite set of real numbers between 1 and 2. So if you find φ show up some place, almost surely you're dealing with the golden ratio. The same is true of π. It's just some real number that happens to be the ratio of a circle's circumference to its diameter. I've heard of mathematicians working on problems and having π appear in their calculations, and then suddenly realizing that they're working on a harmonics problem. The fallacy of numerology is getting attracted to numbers that have lots of reasons to show up in various problems (usually small integers, like 3) and then taking whatever one of their many properties is most convenient and treating it as an iron link to whatever they're trying to prove.
teeja 17y ago
More on Golden Ratio in math: Wolfram: http://mathworld.wolfram.com/GoldenRatio.html http://mathworld.wolfram.com/GoldenRatio.html Geometry: http://www.cut-the-knot.org/do_you_know/GoldenRatio.shtml http://www.cut-the-knot.org/do_you_know/GoldenRatio.shtml which includes the beautiful identity φ : 1 = 1 : (φ - 1)
- deleted 17y ago
  [deleted]
Confusion 17y ago
This is just numerology. You can find all kinds of 'special' numbers anywhere, if you just try enough 'special' numbers on enough of 'anywhere'. This has no special significance at all.
- dmix 17y ago
  Yes, I've seen Pi as well. Good Movie. But I think they put a little more thought into it before publishing it in the Science journal.
  - Confusion 17y ago
    I haven't seen Pi. I've studied physics. My point is that the fact that the 'golden ratio' is indirectly involved here, is completely irrelevant. The point is the E8 symmetry. Mentioning the golden ratio is just a grab for attention from laymen and it draws attention away from the actually interesting things, as well as giving those laymen the impression that what physicists do is numerology.
stcredzero 17y ago
This headline is actually a key point revealed in the last issue of Echo: http://en.wikipedia.org/wiki/Echo_(comic_book) http://en.wikipedia.org/wiki/Echo_(comic_book) Huge technical advances were made possible by reworking the mathematics of General Relativity and quantum mechanics using base-Phi.
yread 17y ago
This http://math.ucr.edu/home/baez/week289.html http://math.ucr.edu/home/baez/week289.html is what John Baez has to say about this
Adam_jake 17y ago
I am pleased that the truth has prevailed. Nature is now accused of trying to undermine Mohamed El Naschie deliberately. This accusation is not frivolous. How else can we explain the blind vicious attack by certain doubtful blogs on the golden mean work of El Naschie and how Quirin Schiermeier the journalist working for Nature utilized these vicious attacks to write a completely unacceptable article in Nature. Then came the heavenly justice when a German professor von Storch complained on his blog that the Nature article of Schiermeier deliberately misquoted him. He was gentle enough to say that the harm was not great. However in principle the harm could have been great. No one has the right to smear the reputation of anyone whether deliberately or recklessly due to irresponsible journalism. Now to the burning scientific question. How does the golden mean enter into quantum mechanics. The answer is as simple as it is ingenious. Mohamed El Naschie reformulates quantum mechanics in spacetime following the same concepts used by Richard Feynman as well the classical work of Einstein. Since the building blocks of spacetime are his elementary random Cantor sets and because these random Cantor sets possess the golden mean as a Hausdorff dimension, the golden mean slips into the fundaments of quantum mechanics. Nothing that quantum mechanics is the most fundamental theory upon which science is based, the golden mean could rightly be described as the basis of science. From this reasoning the ideas which Ed Nash expressed in his previous comment follows effortlessly.

63 points by slater 17y ago

pohl 17y ago

There's a very good Ted Talk on E8. I don't understand how the appearance of Phi suggests E8 (if someone here understands this, please explain), but the first thing that came to mind was whether Garrett Lisi knows about this news yet: http://www.youtube.com/watch?v=y-Gk_Ddhr0M http://www.youtube.com/watch?v=y-Gk_Ddhr0M http://en.wikipedia.org/wiki/E₈ http://en.wikipedia.org/wiki/E₈

Devilboy 17y ago
I understand that most particle physicists don't really take Lisi's work very seriously. Does this discovery lend more weight to his E8 theories?

tibbon 17y ago

I want to look into this more, but I have to wonder- if you look hard enough for a number/ratio to appear, won't you find it almost everywhere? Seems kinda like a fortune teller asking you to look for the number '3'. I am not a mathematician, so I also have no idea what I'm talking about- just gut instinct.

pohl 17y ago
That's a good question. I would imagine the probability to vary a great deal by what particular number one is looking for. That is, I would expect it to be very easy to find small integers, but extremely unlikely to accidentally find a very large prime number. I suspect it would be much harder to find (1 + sqrt(5)) / 2 everywhere you look than to find 3.
snorkel 17y ago
The value 1.618... is not as interesting as its recursive fraction form which happens to be = 1 + (1 + 1/ ( 1 + 1/ ( 1 + 1/ ... an infinite recursion based on the number 1 is somewhat interesting and could be insightful.
dc2k08 17y ago
I can recommend a book called: The Golden Ratio: The Story of Phi - the World's Most Astonishing Number. It gave me a bit of bit of a Phi fetish. It appears like a kernel of existence.
dandelany 17y ago
Not when the number is irrational. What's most interesting to me is that phi often occurs in recursive systems, so it's discovery often implies natural recursion.
Sukotto 17y ago
The thing about the golden number is that it really does appear just about everywhere. That's one of the reasons it's so cool.
ams6110 17y ago
In the quantum realm, doesn't looking for something make it appear?
- eru 17y ago
  It may work the other way round --- if you don't look it doesn't appear. But you can't just make any stuff appear.
jordanb 17y ago
Well, the set of all numbers is infinite, so you would wouldn't expect to find just any number appear in a lot of different contexts by chance. Some numbers do tend to show up over and over again. That makes those numbers special. φ is such a special number. But there are a lot of special things about 3 though too: It's an integer (which is a pretty special property for a number to have, considering there are an infinite number of real numbers between each integer). What's more, it's a very small integer (the fourth smallest) and it's the second smallest prime number. In fact, we could say that 3 is a very special number, in the scheme of things, and has lots of reasons to show up in particular contexts. Now φ being the golden ratio is pretty much all that's unique about it. Otherwise, it's just one of the uncountably infinite set of real numbers between 1 and 2. So if you find φ show up some place, almost surely you're dealing with the golden ratio. The same is true of π. It's just some real number that happens to be the ratio of a circle's circumference to its diameter. I've heard of mathematicians working on problems and having π appear in their calculations, and then suddenly realizing that they're working on a harmonics problem. The fallacy of numerology is getting attracted to numbers that have lots of reasons to show up in various problems (usually small integers, like 3) and then taking whatever one of their many properties is most convenient and treating it as an iron link to whatever they're trying to prove.

teeja 17y ago

More on Golden Ratio in math: Wolfram: http://mathworld.wolfram.com/GoldenRatio.html http://mathworld.wolfram.com/GoldenRatio.html Geometry: http://www.cut-the-knot.org/do_you_know/GoldenRatio.shtml http://www.cut-the-knot.org/do_you_know/GoldenRatio.shtml which includes the beautiful identity φ : 1 = 1 : (φ - 1)

deleted 17y ago
[deleted]

Confusion 17y ago

This is just numerology. You can find all kinds of 'special' numbers anywhere, if you just try enough 'special' numbers on enough of 'anywhere'. This has no special significance at all.

dmix 17y ago
Yes, I've seen Pi as well. Good Movie. But I think they put a little more thought into it before publishing it in the Science journal.
- Confusion 17y ago
  I haven't seen Pi. I've studied physics. My point is that the fact that the 'golden ratio' is indirectly involved here, is completely irrelevant. The point is the E8 symmetry. Mentioning the golden ratio is just a grab for attention from laymen and it draws attention away from the actually interesting things, as well as giving those laymen the impression that what physicists do is numerology.

stcredzero 17y ago

This headline is actually a key point revealed in the last issue of Echo: http://en.wikipedia.org/wiki/Echo_(comic_book) http://en.wikipedia.org/wiki/Echo_(comic_book) Huge technical advances were made possible by reworking the mathematics of General Relativity and quantum mechanics using base-Phi.

yread 17y ago

This http://math.ucr.edu/home/baez/week289.html http://math.ucr.edu/home/baez/week289.html is what John Baez has to say about this

Adam_jake 17y ago

I am pleased that the truth has prevailed. Nature is now accused of trying to undermine Mohamed El Naschie deliberately. This accusation is not frivolous. How else can we explain the blind vicious attack by certain doubtful blogs on the golden mean work of El Naschie and how Quirin Schiermeier the journalist working for Nature utilized these vicious attacks to write a completely unacceptable article in Nature. Then came the heavenly justice when a German professor von Storch complained on his blog that the Nature article of Schiermeier deliberately misquoted him. He was gentle enough to say that the harm was not great. However in principle the harm could have been great. No one has the right to smear the reputation of anyone whether deliberately or recklessly due to irresponsible journalism. Now to the burning scientific question. How does the golden mean enter into quantum mechanics. The answer is as simple as it is ingenious. Mohamed El Naschie reformulates quantum mechanics in spacetime following the same concepts used by Richard Feynman as well the classical work of Einstein. Since the building blocks of spacetime are his elementary random Cantor sets and because these random Cantor sets possess the golden mean as a Hausdorff dimension, the golden mean slips into the fundaments of quantum mechanics. Nothing that quantum mechanics is the most fundamental theory upon which science is based, the golden mean could rightly be described as the basis of science. From this reasoning the ideas which Ed Nash expressed in his previous comment follows effortlessly.