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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."
To elaborate, models are only as good as their power to explain and predict. So if those models improve (explain/predict more, get simpler) over time, so much the better.
Just because a mathematical model simplifies certain calculations, does not mean that the actual underlying physical geometry matches the theoretical model.
That's not really a problem if all you want to do is simplify the mathematics. Besides which, that was pretty much the reason that early astronomers weren't branded as heretics; they just said that a heliocentric model made the calculations easier, and that they weren't suggesting that they reflected reality (although they did).
All direct observations to date point to a 3D universe.
Well no shit Sherlock. It's rather hard to observe dimensions that your eyes can't see and your mind can't design instruments to detect. Oh... and, you know, time?
*sigh* With your track record of getting +4 for talking out of your backside, what's the point?
"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?
This is basically what particle colliders do. Imagine that We lived in a 2D universe like a sheet of paper. The particle collider smashes atoms and we observe the splash it makes. From the splashes around the collision, we see that things seem to have appeared out of nowhere, but if We assume that there is actually a 3rd dimension, we can perceive that the particles/energy didnt just appear, but traveled on an unseen dimension. That is what a particle collider does, if You can wrap Your head around it, but in our 4D length/width/height/moment range of observation.
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.
No idea what that means, but doesn't it sound cool?
I wonder how much this math simplification (?) will allow us to accelerate physical systems emulation, not to mention approaching general AI. The upper bound for emulation of the human brain in the absolute worst case scenario, the one that supposes consciousness arises from individual particles interacting rather than from a higher level of organization such as synapses signaling, was thought to become computable by the old method in about 100 years (if Moore's law holds until then). I'd love to know how many performance doublings this one will allow us to cut from that. The Singularity is one step closer! :-)
Also, computing proteins folding is probably going to get a serious performance boost too. If this proves to really work genetic engineering is going to enter a new phase.
Conservatism: (n.) love of the existing evils. Liberalism: (n.) desire to substitute new evils for the existing ones.
Logic. Logic is the firmament. Without it, math is just man's scribblings.
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.
The brain is not a machine, it's a chemical factory. If you can't even tell that difference then you should probably shut up.
"Do you believe in souls?"
define soul.
When talking about good art , or love, or friends, that feeling is often called soul.
If you mean a incorporeal being, then no.
" You're already an AI running"
by definition, that's false.
You also make the false assumption that AI = singularity. It does not. For some interpretation of singularity to do not need AI.
I don't know which definition you are using.
If you think you will upload your brain and then YOU will be in the computer, you are wrong.
A copy of you will exist on the system. One that diverges from the meat bag version immediately.
Lets say you just uploaded you memories and responses into a machine, are you telling me the next day you don't mind if someone puts a gun in you mouth and pulls the trigger?
Unless you think 'who you are' can be moved from your brain into the machine becasue it's all part of an incorporeal being. You don't believe in incorporeal beings, do you?
The Kruger Dunning explains most post on
The amplituhedron, or a similar geometric object, could help by removing two deeply rooted principles of physics: locality and unitarity.
...And unitarity holds that the probabilities of all possible outcomes of a quantum mechanical interaction must add up to one.
I'm probably being very naive attempting to understand this article that has probably already been massively dumbed down, but, how can the probabilities of all possible outcomes of an interaction not add up to one? Surely they add up to one by definition, otherwise they are not probabilities? For example outcome X having a probability of 1/3 means, on average, you can multiply the number of times you observe the interaction by 1/3 and get the expected number of times you would see outcome X. If the probabilities in your statistical trials didn't add up to 1, doesn't that mean adding up the numbers of individual outcomes observed would give a number bigger (or smaller) than the total number of interactions observed? Obviously it cannot mean that, as that fails basic arithmetic.
I can imagine tossing a fair coin - heads has probability 0.5, tails 0.5, total 1. So now how about a 3 sided coin without unitarity? Let's say the probability of heads is still 0.5, tails 0.5 but it has a third side, bodies that also has probability 0.5 of occurring. That sounds mathematically impossible. It could be a mind-reading coin, where you pick heads and find that then occurs on half your coin tosses. Later you pick tails, and that occurs on half your coin tosses, but when you pick bodies, that also occurs on half of those coin tosses. OK, I give up! Can anyone who really understands unitarity enlighten me please? Is this anything like the uncertainty principle?
Your ad here.
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)?