Slashdot Mirror
Physicists Discover Geometry Underlying Particle Physics
New submitter Lee_Dailey sends this news from Quanta Magazine:
"Physicists have discovered a jewel-like geometric object that dramatically simplifies calculations of particle interactions and challenges the notion that space and time are fundamental components of reality. 'This is completely new and very much simpler than anything that has been done before,' said Andrew Hodges, a mathematical physicist at Oxford University who has been following the work. The revelation that particle interactions, the most basic events in nature, may be consequences of geometry significantly advances a decades-long effort to reformulate quantum field theory, the body of laws describing elementary particles and their interactions. Interactions that were previously calculated with mathematical formulas thousands of terms long can now be described by computing the volume of the corresponding jewel-like "amplituhedron," which yields an equivalent one-term expression."
"They also claim to have found a "master amplituhedron" with infinitely many faces in infinitely many dimensions which should now be as important as the circle in two dimensions. ;-) Its volume counts the "total amplitude" (?) of all processes; faces of this master jewel harbor the amplitudes for processes with finite collections of particles."
http://motls.blogspot.co.uk/2013/09/amplituhedron-wonderful-pr-on-new.html
No idea what that means, but doesn't it sound cool?
It looks like Wolfram was onto something in A New Kind of Science with his approach to replacing complex equations with simple rules.
I'd say Plato (perhaps Pythagoras) was onto something when he basically said that math is the fundamental everything of everything. Yep, the guy was wrong on the details, but what damn fine intuitions he managed to have 2400 years ago. No matter what we do we always end up referring back to him...
Conservatism: (n.) love of the existing evils. Liberalism: (n.) desire to substitute new evils for the existing ones.
IANAPOM (I am not a physicist or mathematician), but from what I could gather from the article, it sounds like this isn't a new model that approximates the old, more complicated one, but rather a massive simplification of the existing one that produces provably identical results in all cases. To drastically oversimplify using my extremely limited understanding while putting it in terms I can wrap my brain around, it sounds like when you first learn about the arithmetic series in calculus (e.g. the summation of i from 0 to n). At first, the only way you can approach it is by actually adding 0 + 1 + ... + (n-1) + n, but eventually you learn that you can skip that whole process if i starts at 0 and use n*(n+1)/2 to reach the result with far less work, and then you're shown how to derive that formula yourself.
It sounds like something similar here. They previously had to calculate the results of every single Feynman diagram and then sum them together to reach a final result, which would involve billions upon billions of calculations for even a very simple particle interaction. Now, however, rather than having to calculate all of the component parts and summing them, they've derived a formula that produces the same answers with far less work.
Again, I may be way off, but that's the takeaway I had from the article.
This doesn't necessarily invalidate Feynman's approach. His problem was that he assumed a limitless supply of graduate students to calculate the various reaction path probabilities.
Have gnu, will travel.
But I'm hoping we never actually prove that souls exist. That's one door I'd prefer to remain closed. If science determined that souls exist, then we'd be figuring out ways to harness souls for energy. And then that'd bring up the whole question of what else is out there in that sphere of reality--and I'd really rather not draw a Nyarlathotep-analogue's attention.
Here's to hot beer, cold women, and Glaswegian kisses for all.
and that they weren't suggesting that they reflected reality (although they did).
What's interesting there is we say it reflects reality because it makes the calculations easier. Other than the math and mental models being easier to grasp, there really is no good reason to say the earth goes around the sun* rather than the sun going around the Earth. We just all decided that the calculations being easier trumps the very intuitive model that the sun circles the Earth. You can construct a perfectly rational model of the Universe from the non-inertial frame of reference that holds the Earth as stationary. It's just full of epicycles etc..
It's a fairly rare achievement for mass society to replace the naively simpler model of the stationary Earth.
*for the sake of argument, lets not get into them both orbiting a common barycentre; the argument extends to that as well anyway.
A religious person is foolish for believing in something they can't see that doesn't help them consistently and accurately predict things they can observe.
Quantum computation won't make a dent in any NP-HARD problem.
The fact that nature (basically THE quantum computer) can fold a complex protein in a fraction of a second seems to demonstrate that at least some of these problems are solvable by QC in P time.
Is this because the problem wasn't NP-hard to begin with (but it sure seemed that way)?
Or don't we yet have the right QC algorithms to do this (it's a growing field)?
Or maybe nature cheats and doesn't solve the same problem (but finds some local minimum in the energy landscape)?