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The Rule of Three Proved By Physicists
An anonymous reader writes "In 1970, Russian physicist Vitaly Efimov developed mathematical proof (PDF) that any three-particle substance, referred to as a trimer, will scale up or down in size by a factor of 22.7 and that if the particles are not all of the same type, 'the scaling factor of 22.7 decreases according to the particles' relative masses.' In 2006, physicists in Austria proved that Efimov's trimers can be created in laser-cooled environments. And now, in 2014, physicists in Austria, Germany, and the U.S. have physical proof that Efimov's trimers do indeed scale by a factor of 22.7 if they are comprised of the same particles or a lower ratio relative to their particles' masses if they are comprised of a mixture of different particles (abstract 1, abstract 2, abstract 3). 22.7 — a.k.a., the rule of three — now appears to be as significant as pi."
left out
CLI paste? paste.pr0.tips!
No.
Pi is the volume of the box around the quarter pizza I just ate.
"Each 22.7-times larger Efimov state is also 22.7-squared times weaker, requiring the optical trap to be cooled even further to allow the new state to form. Grimmâ(TM)s group perfected its techniques and detected the state at the very edge of experimental limits."
"Meanwhile, the two other groups managed to observe three consecutive Efimov states by taking advantage of a footnote in the theory: When a trimer is built from a mixture of different particles rather than an identical set, the scaling factor of 22.7 decreases according to the particlesâ(TM) relative masses. In other words, nesting dolls made of atomic mixtures become closer in size, enabling more of them to be observed within the experimental window."
cool sure, but ""The law is a geometric progression of evermore-enormous trios of particles, spanning in a theoretically infinite sequence from the quantum scale to (if the particles were cold enough) the size of the universe and beyond. âoeAlthough we didnâ(TM)t see an infinite number of them, thereâ(TM)s pretty strong evidence when you see three in a row,â Chin said.""
yeah sure, universe size yeah why not if we have 3 smallest and every sequence is weaker...
world was created 5 seconds before this post as it is.
The volume of a pizza of radius z and height a is pi*z*z*a.
Well, it's closer to 22.6942....
It could be just a coincidence. Going from 22.7 to 22/7 is quite a leap. Correct me if I'm wrong.
Not much of a leap on my keyboard, / being next to . so an easy typo to make...
"Wait. Something's happening. It's opening up! My God, it's full of apricots!"
Boy am I going to look so smart in Trivia Pursuit now
22.7 is 2*10^1+2*10^0+7*10^-1. .7 is no longer going to be a 7 after the decimal point, 7*10^-1. Note that you multiply it by TEN to get the 7 in the denominator of 22/7. In another base, you'd be multiplying by something other than 10, so you wouldn't get 7.
If you express the same quantity in a bar other than ten, the
--TheOrangeSquid Is it any wonder things seem so awry? We swim in a sea of confusion and don't have to think to survive
http://rsta.royalsocietypublishing.org/content/369/1946/2679.full
If you check section three, you'll be able to compute that the number in question is 22.6943825963666951931....
Maybe I'm as dumb as a rock but this article doesn't make much sense to me. Maybe a bit more info about trimers would have helped.
That 22.7 number is going to get numerologists going. Remember, that in ancient times 22/7 was a common approximation for pi ...
Americans are too fond of pi , so they are never going to embrace being trimmer
The adorable thing about people with Asperger is that they really think they've made a contribution when they state the obvious. (This is offset by how angry they get when they don't understand something and have a tantrum over how WRONG others must be.)
Damit, Coffee, all, over, my, keyboard! :p
At first I thought they were talking about this:
http://en.wikipedia.org/wiki/Planescape#Rule-of-Three
I want to see Slashdot Ypsilon. With that name it had better be some real Daliesque shit.
Strange, I get 22.6943825953666951928... As supporting evidence, a Google search for 22.69438259536 gives some hits, but not for 22.69438259636.
Yes but consider this: $ \omega\infty\int\hbar $
Proof that having a threesome is not only okay, but proved to be fucking awesome by none of than science!
Is it really 22.70000000 or is there some interesting splatter of digits beyond? I didn't see any more specific number in the article.
Interesting! You are right about the 5, but your last digits are also wrong...
s_0 = 1.0062378251027814890640668123429012308420481556643372852718021332089137814435579...
which gives:
22.69438259536669519286021713693337651029896890130319136482608...
Why is this relevant?
What does it teach us that a normal person could understand?
Please explain to us why someone should care about this.
- Zav - Imagine a Beowulf cluster of insensitive clods...
I thought this was about celebrities dying in threes.
People do not have "Asperger". They have "Asperger's", or "Asperger's Syndrome".
Asperger alone means nothing.
You should know this.
- Zav - Imagine a Beowulf cluster of insensitive clods...
OK. That right there is why "Funny" mods deserve karma.
The Efimov state is the most elementary effect in few-body physics, the researchers said, but there are countless others that seem to influence the arrangements of small numbers of atoms: four-, five- and six-body interactions and so on.
I'm fine with it as long as they don't use water molecules and they keep the number of particles below nine.
Considering the number of people making this connection, I would submit that this explanation is effectively "not obvious." I await your impending tantrum.
Look again. The last digits given by your parent match what you have.
People do not have "Asperger". They have "Asperger's", or "Asperger's Syndrome".
Asperger alone means nothing.
You should know this.
Thanks for confirming the parent's point.
half life 3 confirmed
"22.7 — a.k.a., the rule of three — now appears to be as significant as pi."
22/7 approximates pi.
Iiiinteresting...
Not really. To truncate the series there, it would be properly noted as ...29...
Thanks for the funniest thing I'll probably read all day. :)
The cesspool just got a check and balance.
Sorry this is off topic, but why the fuck does beta (fuck beta btw) always cut off the titles of posts? You can see the whole title when you click reply, but it's cut off otherwise. Either fix this or warn about the length that will be displayed.
So a 200-foot praying mantis is still a possibility as long as it's scaled up some power of 22.7. Got it.
the preceding comment is my own and in no way reflects the opinion of the Joint Chiefs of Staff
yay! i'm going to memorize as many digits as i can of the Rule of Three!
i could live a little longer in this prison
To truncate with rounding, yes. Lazy truncation, however...
APK quotes people (including myself) without context and should not be trusted. Just thought you should know.
is a good approximation for pi.
That that is is that that that that is not is not.
.. on why this is significant?
I thought the proof was verified decades ago. Perhaps you wanted to say "evidence" instead?
Ezekiel 23:20
This needs to be a t-shirt.
And by posting this, I guarantee that it already is.
"in 2014, physicists in Austria, Germany, and the U.S. have physical proof that Efimov's trimers do indeed scale by a factor of 22.7 if they are comprised of the same particles or a lower ratio relative to their particles' masses if they are comprised of a mixture of different particles (abstract 1, abstract 2, abstract 3)"
Ah, proto-culture and the triumvirate. When do I get my hovercycle?
There must always be a master, an apprentice, and the apprentice's secret apprentice.
is most likely transcendental. According to Efimov's original paper, the magic value "22.7" (we shall M) is given exactly by e^(pi / |s0|), where s0 is a pure imaginary solution (very close to i) of an equation (9) he derives earlier and is related to the three-body problem (there are an infinite number of real solutions s1,s2...). If you define s0 = i x where x is real, then (by converting from trig to hyperbolic trig) it can be shown that the number M is given by e^(pi / x), where x is the positive real solution to:
0 = (8 / sqrt(3)) sinh( pi * x / 6) - x * cosh( pi * x / 2)
If you copy/paste the right-hand side into the WolframAlpha website, you will see that the curve has exactly two non-zero solutions, approximately (+-) 1.00624. You can ask for more digits, and it will give you x=1.0062378251027814891..., which means to eight digits, M = 22.694382595... This equation above is a transcendental equation whose non-zero solutions are neither rational nor algebraic, and very likely M itself is also transcendental. Proving these sorts of things, however is very difficult. The best we can hope for is that the number can be expressed as an infinite expansion whose terms have a nice form which converses rapidly. A few more clicks on Wolfram Alpha and I'm sure someone will work it out.
Further, if the density of the pizza is p, the Earth's mass times the gravitational constant is u, and the pizza's distance to the center of the Earth is l, the force on that pizza is p*i*z*z*a*p*u / l*l.
I'm more concerned about the Rule of Two. When Obama goes, who is there to take his place?
I want to delete my account but Slashdot doesn't allow it.
Our knowledge tends to be high in the middle of the spectrum.
When we try to grasp the entire Universe, we end up looking at pixels of info. We know little and speculate much.
Similarly, at the smallest scales we have to resort to atom smashing to learn a bit and speculate a lot.
This theory suggests that life is LEGO-like after all. Once we know this underlying pattern, we can look for it, and we can use it to build better models of stuff very large and very small.
I would add that these results are consistent with my own theory.
I come here for the love
Only if you treat it as a point mass.
Pretty sure I first saw that joke on a t-shirt.
Indeed, there appears to be something of a selection at least one of which appears to miss the joke.