8 ms·

Physicists Prove Surprising Rule of Threes

129 points by digital55 12y ago

datenwolf 12y ago
I wonder if this principle can also be applied to nucleons. Protons and neutrons are each made up of 3 quarks. And there are some troubles in pinning down the radius of the proton. If Efimov scales apply to nucleons, this would imply that there are multiple scales in which quarks can arrange depending on the outside potential. This could explain the differences of measured proton radius depending on the used experimental setup. But I'm just wildly speculating here.
- Panoramix 12y ago
  This trick only works for bosons *Edit: I think. At any rate, these depths of physics are quite complex and not very intuitive, and this kind of discovery shows it is very easy to overlook things. A giant discovery could be looming in the horizon...
  - anigbrowl 12y ago
    In the lab. The paper contemplates the possibilities for nucleons too - it's just harder for spin particles: http://www.uibk.ac.at/exphys/ultracold/projects/levt/efimov/SovJNucPhys12.589.efimov.pdf http://www.uibk.ac.at/exphys/ultracold/projects/levt/efimov/...
  - evanb 12y ago
    Sort of. There are some tricks you can play with fermions (eg. align all of their spins) to get very analogous effects.
- evanb 12y ago
  It applies (in very rough approximation) to groups of nucleons, which is where it was first discovered. People observed that the nucleon/nucleon scattering length was surprisingly long for what they considered natural nuclear scales (or equivalently, that the deuteron was very weakly bound). The circumstance where the Efimov effect is mathematically exact is when the scattering length is infinite. Fermions in this circumstance are described as unitary. Sadly, the Efimov effect has nothing to do with the proton size puzzle. Source: IAANuclearPhysicist.
pavel_lishin 12y ago
Interesting that they referenced 22.7 falling out as similar to pi, since 22/7 is one of the simpler approximations of pi.
- zorbo 12y ago
  Completely coincidental, I'm sure.
  - manicdee 12y ago
    Then you represent the number in base 23 to a few billion decimal places and find the signatures of the creators of this version of the universe.
  - wlievens 12y ago
    Obivously, since base 10 is arbitrary.
pessimizer 12y ago
I swear I'm not trolling, just ignorant, but could a workable theory of local hidden variables be based on this?
- danbruc 12y ago
  I am pretty sure this is not related to local realism. I would naively imagine the situation as follows (not having read anything related in detail and not being a physicist). The forces between particles become very weak with growing separation but never become zero. Now imagine throwing two ping-pong balls into a pool making ripples on the surface similar to the force field or the probability of presence of the particles. There will be a interference pattern and you can probably find a valley where you can place a third ping-pong ball and it will sit there more or less stable. Now finally imagine every pair of ping-pong balls forming the valley for the third ping-pong ball. This may of course be incredible far off from what really happens - just making up images.
  - araes 12y ago
    I like the ping pong balls over the surface of a pool, that's a neat analogy. However, I am also not a physicist, but my impression is that this is something closer to how a http://en.wikipedia.org/wiki/Lagrangian_point http://en.wikipedia.org/wiki/Lagrangian_point (in particular, the L4 or L5 lagrange point) works. In fact, I think the size difference thing they describe in the article is probably very similar to how gravity, and relative object positions work out based on their mass ratios. Kind of an equilateral force balance, with a self stable state that things will naturally gravitate towards if the background energy level is low enough. Course, then that makes me wonder if there's a 4-body version with a stable tetrahedron formation?
  - tiglionabbit 12y ago
    This should create many such points. At least two.
- jakebian 12y ago
  Why would this offer any threat to the no-local-HVM proofs by Bell?
ipsin 12y ago
The Efimov constant is only approximately ≅ 22.7. It would be a little surprising to have a physical constant end in exactly 0.7, since it would imply that there's something special about base 10 and bases that are a multiple of 10. Section 3 of this paper talks about the actual transcendental equation that provides the constant. http://rsta.royalsocietypublishing.org/content/369/1946/2679.full http://rsta.royalsocietypublishing.org/content/369/1946/2679...
- infogulch 12y ago
  Thank you! I was thinking the same thing about the constant being exactly representable in base 10.
- 3rd3 12y ago
  Rational numbers tend to have easily recognizable patterns in their fractional digits in all bases (at least as long the numbers aren't too big), so it wouldn't imply there is something special about base 10. In fact, you can always choose the base as q for a rational number p/q and get rather simple fractional digits.
  - ipsin 12y ago
    It's not repeating digits I'm talking about, though, it's termination. If it were exactly 22.7, that's 227/10. The question would be "Why is the denominator 10?"
    - akiselev 12y ago
      Because you used the denominator "10." If the constant is precisely 22.7 then it can be represented in any other base with just as much precision, you'd just use a different format for the number before and after the decimal point.
      - thaumasiotes 12y ago
        You're not paying attention to the comment you're pretending to reply to. From above: > It's not repeating digits I'm talking about, though, it's termination. 227/10 will not terminate in any numerical base which isn't a multiple of ten. Combining this with the idea that no numerical base should be privileged over another, we can rephrase this to say that it's surprising for a physical constant to be a rational (but not integral) number. It's not surprising for a physical constant to be an integer because we really believe that integers have special qualities. It's not surprising for a physical constant to be irrational because that's just the way numbers are. If it's rational but not integral, you want to justify the denominator somehow.
thomasahle 12y ago
“Although we didn’t see an infinite number of them, there’s pretty strong evidence when you see three in a row,” - What a physicist thing to say :P
- sp332 12y ago
  One time, Feynman was giving a lecture to some middle-school kids. He used the date of some battle as an example, but he got it a bit wrong and the kids immediately corrected him. He laughed and said "Hey! 3 significant digits is pretty good for a theoretical physicist!"
- ctdonath 12y ago
  3, 5, and 7 are prime, therefore 9 is prime.
  - graycat 12y ago
    No: 11 is prime. 13 Is prime. So 9 is just an exception!
    - D-Coder 12y ago
      "Experimental error."
      - graycat 12y ago
        Terrific!
    - GotAnyMegadeth 12y ago
      A teacher asks a group of students to prove that all odd numbers above 1 are prime numbers. After a short while the students begin arguing about the best proof. Mathematician: "We should use proof by induction, I can show 3 is a prime number by listing all of it's factors, and then from there I can show that 2n + 1 is prime ..." Scientist: "What? that doesn't make any sense. What we need is experimental data. Let's collect enough points, 3, 5, 7, 9, 11, 13. Six points should do, now look, the general trend is that all of them are prime. We have one anomaly, but it's probably just caused by a random fluctuation in..." Engineer: "Nah, all this theory is pointless, we only need to know if they are prime in the real world. Let's just take a few and see if they work for our purposes. 3 - prime, 5 - prime, 7 - prime, 9 - nearly prime, 11 - prime, surely that's good enough." Computer scientist: "While you lot have been wasting your time arguing I have been writing a program that will do all the work for us" All of the students gather around the CS's computer and watch as he presses go. Computer: 3 is prime 3 is prime 3 is prime 3 is prime 3 is prime 3 is prime 3 is prime 3 is prime 3 is prime 3 is prime 3 is prime 3 is prime 3 is prime 3 is prime 3 is prime 3 is prime
ph0rque 12y ago
Quite fitting... “What you see is three groups, in three different countries, reporting these multiple Efimov states all within about one month,” said Chin, who led one of the groups. “It’s totally amazing.”
- gpvos 12y ago
  How far were these groups spaced apart?
Evgeny 12y ago
More than 40 years after a Soviet nuclear physicist proposed an outlandish theory that trios of particles can arrange themselves in an infinite nesting-doll configuration, experimentalists have reported strong evidence that this bizarre state of matter is real. I think it's quite awesome that Vitaly Efimov lived to see his theory being proved (or, at least, to see strong evidence in its favor). It always makes me sad when I read about scientists who made great discoveries just to be laughed at until their days end, and then their theories are proved after they are dead. A classic example is Alfred Wegener, who postulated continental drift just to be ridiculed., but of course there are many, many others. http://en.wikipedia.org/wiki/Alfred_Wegener http://en.wikipedia.org/wiki/Alfred_Wegener Another, even more tragic story is that of Ignaz Semmelweis, who not only pioneered antiseptic procedures in hospitals, but, to my mind, proved their effectiveness beyond any reasonable doubt, was rejected, and died tragically. http://en.wikipedia.org/wiki/Ignaz_Semmelweis http://en.wikipedia.org/wiki/Ignaz_Semmelweis

129 points by digital55 12y ago

I wonder if this principle can also be applied to nucleons. Protons and neutrons are each made up of 3 quarks. And there are some troubles in pinning down the radius of the proton. If Efimov scales apply to nucleons, this would imply that there are multiple scales in which quarks can arrange depending on the outside potential. This could explain the differences of measured proton radius depending on the used experimental setup. But I'm just wildly speculating here.

Panoramix 12y ago
This trick only works for bosons *Edit: I think. At any rate, these depths of physics are quite complex and not very intuitive, and this kind of discovery shows it is very easy to overlook things. A giant discovery could be looming in the horizon...
- anigbrowl 12y ago
  In the lab. The paper contemplates the possibilities for nucleons too - it's just harder for spin particles: http://www.uibk.ac.at/exphys/ultracold/projects/levt/efimov/SovJNucPhys12.589.efimov.pdf http://www.uibk.ac.at/exphys/ultracold/projects/levt/efimov/...
- evanb 12y ago
  Sort of. There are some tricks you can play with fermions (eg. align all of their spins) to get very analogous effects.
evanb 12y ago
It applies (in very rough approximation) to groups of nucleons, which is where it was first discovered. People observed that the nucleon/nucleon scattering length was surprisingly long for what they considered natural nuclear scales (or equivalently, that the deuteron was very weakly bound). The circumstance where the Efimov effect is mathematically exact is when the scattering length is infinite. Fermions in this circumstance are described as unitary. Sadly, the Efimov effect has nothing to do with the proton size puzzle. Source: IAANuclearPhysicist.

pavel_lishin 12y ago

Interesting that they referenced 22.7 falling out as similar to pi, since 22/7 is one of the simpler approximations of pi.

zorbo 12y ago
Completely coincidental, I'm sure.
- manicdee 12y ago
  Then you represent the number in base 23 to a few billion decimal places and find the signatures of the creators of this version of the universe.
- wlievens 12y ago
  Obivously, since base 10 is arbitrary.

pessimizer 12y ago

I swear I'm not trolling, just ignorant, but could a workable theory of local hidden variables be based on this?

danbruc 12y ago
I am pretty sure this is not related to local realism. I would naively imagine the situation as follows (not having read anything related in detail and not being a physicist). The forces between particles become very weak with growing separation but never become zero. Now imagine throwing two ping-pong balls into a pool making ripples on the surface similar to the force field or the probability of presence of the particles. There will be a interference pattern and you can probably find a valley where you can place a third ping-pong ball and it will sit there more or less stable. Now finally imagine every pair of ping-pong balls forming the valley for the third ping-pong ball. This may of course be incredible far off from what really happens - just making up images.
- araes 12y ago
  I like the ping pong balls over the surface of a pool, that's a neat analogy. However, I am also not a physicist, but my impression is that this is something closer to how a http://en.wikipedia.org/wiki/Lagrangian_point http://en.wikipedia.org/wiki/Lagrangian_point (in particular, the L4 or L5 lagrange point) works. In fact, I think the size difference thing they describe in the article is probably very similar to how gravity, and relative object positions work out based on their mass ratios. Kind of an equilateral force balance, with a self stable state that things will naturally gravitate towards if the background energy level is low enough. Course, then that makes me wonder if there's a 4-body version with a stable tetrahedron formation?
- tiglionabbit 12y ago
  This should create many such points. At least two.
jakebian 12y ago
Why would this offer any threat to the no-local-HVM proofs by Bell?

ipsin 12y ago

The Efimov constant is only approximately ≅ 22.7. It would be a little surprising to have a physical constant end in exactly 0.7, since it would imply that there's something special about base 10 and bases that are a multiple of 10. Section 3 of this paper talks about the actual transcendental equation that provides the constant. http://rsta.royalsocietypublishing.org/content/369/1946/2679.full http://rsta.royalsocietypublishing.org/content/369/1946/2679...

infogulch 12y ago
Thank you! I was thinking the same thing about the constant being exactly representable in base 10.
3rd3 12y ago
Rational numbers tend to have easily recognizable patterns in their fractional digits in all bases (at least as long the numbers aren't too big), so it wouldn't imply there is something special about base 10. In fact, you can always choose the base as q for a rational number p/q and get rather simple fractional digits.
- ipsin 12y ago
  It's not repeating digits I'm talking about, though, it's termination. If it were exactly 22.7, that's 227/10. The question would be "Why is the denominator 10?"
  - akiselev 12y ago
    Because you used the denominator "10." If the constant is precisely 22.7 then it can be represented in any other base with just as much precision, you'd just use a different format for the number before and after the decimal point.
    - thaumasiotes 12y ago
      You're not paying attention to the comment you're pretending to reply to. From above: > It's not repeating digits I'm talking about, though, it's termination. 227/10 will not terminate in any numerical base which isn't a multiple of ten. Combining this with the idea that no numerical base should be privileged over another, we can rephrase this to say that it's surprising for a physical constant to be a rational (but not integral) number. It's not surprising for a physical constant to be an integer because we really believe that integers have special qualities. It's not surprising for a physical constant to be irrational because that's just the way numbers are. If it's rational but not integral, you want to justify the denominator somehow.

thomasahle 12y ago

“Although we didn’t see an infinite number of them, there’s pretty strong evidence when you see three in a row,” - What a physicist thing to say :P

sp332 12y ago
One time, Feynman was giving a lecture to some middle-school kids. He used the date of some battle as an example, but he got it a bit wrong and the kids immediately corrected him. He laughed and said "Hey! 3 significant digits is pretty good for a theoretical physicist!"
ctdonath 12y ago
3, 5, and 7 are prime, therefore 9 is prime.
- graycat 12y ago
  No: 11 is prime. 13 Is prime. So 9 is just an exception!
  - D-Coder 12y ago
    "Experimental error."
    - graycat 12y ago
      Terrific!
  - GotAnyMegadeth 12y ago
    A teacher asks a group of students to prove that all odd numbers above 1 are prime numbers. After a short while the students begin arguing about the best proof. Mathematician: "We should use proof by induction, I can show 3 is a prime number by listing all of it's factors, and then from there I can show that 2n + 1 is prime ..." Scientist: "What? that doesn't make any sense. What we need is experimental data. Let's collect enough points, 3, 5, 7, 9, 11, 13. Six points should do, now look, the general trend is that all of them are prime. We have one anomaly, but it's probably just caused by a random fluctuation in..." Engineer: "Nah, all this theory is pointless, we only need to know if they are prime in the real world. Let's just take a few and see if they work for our purposes. 3 - prime, 5 - prime, 7 - prime, 9 - nearly prime, 11 - prime, surely that's good enough." Computer scientist: "While you lot have been wasting your time arguing I have been writing a program that will do all the work for us" All of the students gather around the CS's computer and watch as he presses go. Computer: 3 is prime 3 is prime 3 is prime 3 is prime 3 is prime 3 is prime 3 is prime 3 is prime 3 is prime 3 is prime 3 is prime 3 is prime 3 is prime 3 is prime 3 is prime 3 is prime

ph0rque 12y ago

Quite fitting... “What you see is three groups, in three different countries, reporting these multiple Efimov states all within about one month,” said Chin, who led one of the groups. “It’s totally amazing.”

gpvos 12y ago
How far were these groups spaced apart?

Evgeny 12y ago

More than 40 years after a Soviet nuclear physicist proposed an outlandish theory that trios of particles can arrange themselves in an infinite nesting-doll configuration, experimentalists have reported strong evidence that this bizarre state of matter is real. I think it's quite awesome that Vitaly Efimov lived to see his theory being proved (or, at least, to see strong evidence in its favor). It always makes me sad when I read about scientists who made great discoveries just to be laughed at until their days end, and then their theories are proved after they are dead. A classic example is Alfred Wegener, who postulated continental drift just to be ridiculed., but of course there are many, many others. http://en.wikipedia.org/wiki/Alfred_Wegener http://en.wikipedia.org/wiki/Alfred_Wegener Another, even more tragic story is that of Ignaz Semmelweis, who not only pioneered antiseptic procedures in hospitals, but, to my mind, proved their effectiveness beyond any reasonable doubt, was rejected, and died tragically. http://en.wikipedia.org/wiki/Ignaz_Semmelweis http://en.wikipedia.org/wiki/Ignaz_Semmelweis