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.
Interesting throughout.
by Alex Tabarrok on September 18, 2013 at 11:31 am in Science | Permalink
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.
Interesting throughout.
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What does this say for TGS?
That were reaching past the low hanging fruit?
Or that economists should not make predictions about innovation (or about the future)? They are guaranteed to be backward looking, and economists basically no competence to judge what is happening in other fields. (I am assuming that there can be no innovation in economics).
It’s called Crack.
It is what I have always suspected!
Hey hey, ho ho, locality and unitarity have to go!
If I’m not mistaken, Newton preferred the medium of geometry.
come on, this was discovered years ago.
http://www.newyorker.com/reporting/2008/07/21/080721fa_fact_wallacewells
Not at all the same thing.
As Bourjaily put it: “Why are you summing up millions of things when the answer is just one function?” “We knew at the time that we had an important result,” Parke said. “We knew it instantly. But what to do with it?”
This is the way science progresses, but sadly none of these guys will make money off this invention, since it’s math.
So an analogy: the Feynman diagram of particle physics is something like the infinite series of a fraction X infinity, while the new geometric way is simply plugging x into the infinite series formula: 1/(1-(1/3)) = 1.5
You see the same thing with Fourier Series, Fourier transforms, and so forth, none of these path breaking math inventions (not discoveries, but inventions) being patentable, sadly.
Why sadly? Do you have information that the pace of physics has been too slow relative to the boost that IP protection of mathematical formulae would give? In your answer, make sure to account for those dissuaded from using the formula, and improving it, by the cost of access.
You are asking me to prove a negative. Do you have information that slavery was economically inefficient (it wasn’t)? That promoting labor over machines in pre-20th century China was bad (it wasn’t)? That in medieval India and the Byzantine empire, and for that matter pre-communist Russia, the rigid use of wage and price controls, and the use of serfs or caste members, was bad (it wasn’t, look how long these regimes lasted)? But clearly there was a better way than the status quo, it’s just difficult to prove (like a math proof!) So, what is your prior? Mine is property rights and ownership induces a greater incentive. Yours is that ‘inventors invent’, as evidenced by these guys (they did not care about stinking incentives), and the status quo is fine. As for software patents, they are a recent innovation (post 1970s) and only applicable largely in the USA not Europe or worldwide. I would like to see the government step in and give prizes for mathematicians who invent such formulas, then dedicate the formulas to the public. That was make the ‘cost of access’, the second part of your question, zero. Another way of zeroing costs is to make the cost of litigation less by making patent courts more efficient, and inducing penalties for the losing parties (i.e., patent trolls)
Applying IP in pure mathematics seems much worse to me than applying it in software, which, in my opinion, is already bad enough. (I would not call them innovation but scourge. The idea might have been fine, but it is completely unworkable in the real world. The total count of stupid patents like “blinking cursor” goes into millions.)
Everything in pure mathematics stands on previous work of other people. Pure mathematics is hard enough on its own. I can’t imagine that a math researcher would have to burden himself with patent research at the same time.
Moreover, understanding contemporary scientific results in pure math is not possible for anyone outside the field. How would then the patent office decide which ideas are new enough? Such a patent office would either grant nonsensical patents, or would have to employ a sizable group of pure mathematicians, whose creative capability would be wasted by a bureaucratic job.
Last but not least: having studied pure algebra and number theory for a PhD, I know a lot of career mathematicians. These people live in a different world, and they have different incentives than businessmen. Money isn’t high on their motivational ladder; fame among peers, yes, but not wealth.
I agree on the practical and short term drawbacks of my approach. But if you read this, consider this: (1) don’t confuse the short term with the long term; I realize today nobody in pure math does it for the money or cares about patents, but what about 100 years from now, with my proposal? People respond to incentives. Build a better mousetrap, and it will be ripped off and commercialized by savvy businessmen with other people’s money. Own a valuable piece of real estate in a major US city, that you inherited, and you live on Easy Street. Sad, no? But true all over the world. (2) what about a committee of experts, such as those that award the Field Prize in math, to give, retroactively, a reward to inventors of pure math discoveries, with the provision that their discoveries are forever royalty free? I’m not suggesting we adopt today’s patent system to pure math; (3) what about those quants on Wall Street who do math for the money? Not everybody invents for the love of inventing (though granted it seems many do). Thanks for reading.
I think it might be patentable along the lines of Method for the Rapid Calculation of Particle Interactions. It’s a software patent.
Now whether there’s a market for this patent is a complete different question. Who would use it, other than theoretical physicists? And how would you catch infringers?
Someone feel free to help me, please: I scanned this enormously interesting article without seeing word one about wave function collapse: surely the advent of this fresh approach has some significant bearing.
Does this mean that justly-celebrated wizard Richard Feynman actually set quantum conceptualization back a few years? (Id est: what is the “quantum outcome” or “quantum expression” of a Feynman diagram in terms of this fresh assessment?)
Hugely interesting article, thanks, Alex.
To answer the first question: the article has nothing to do with “wave function collapse”, by which I am guessing you mean the “measurement problem” that affects the philosophical interpretation of quantum theory. Though it is a large part of the popular-level explanations of the theory (Schroedinger’s cat, many-worlds, etc), the conceptual/philosophical discussions relating to it do not affect the vast majority of technical applications of quantum physics. The article is about a significant technical advance in computing certain quantities in quantum field theory and particle physics, uncovering a previously unknown mathematical structure; but it has no bearing at all on the philosophical questions surrounding the theory.
As for the second question, the answer is again no. Feynman diagrams were a huge step forward at the time they were invented, and quantum field theory would have progressed much slower without them. This development builds upon them and finds a new unifying formula for some of the computations they have been used for, but it would have been impossible to discover it without this grounding 60 years ago.
Thank you, Alejandro (says this amateur science fictionist and science satirist).
Attempting to take further advantage of your capacity for patient articulation, Alejandro: is the amplituhedron at all related to the math used to generate Mandelbrot sets and Julia sets?
To add to Alejandro: Wavefunction collapse is a particular interpretation of Schrodinger’s approach to classical quantum mechanics. This article describes an advance in quantum field theory, which generalizes and supersedes Schrodinger’s (non-relativistic) equation.
And thank you, Neal, truly . . . . but now I need to learn how the amplituhedron relates to the growing block universe notion of time, since I’m persuaded Fermi’s paradox confirms that the future does not exist: when it’s not something, it’s always something else.
And Neal: as you seem no less well-informed than Alejandro and comparably articulate: the amplituhedron gives a boost to Yang-Mills superstring theory, or so suggests the Wikipedia entry already up and running. Any specific tests that could be performed at the LHC for support? (To my pedestrian mind the entire acclaim of the amplituhedron consists of its ability to predict outcomes of particle collisions.)
Thanks, one and all.
“…challenges the notion that space and time are fundamental components of reality…”
Pfft. Immanuel Kant coulda told you that. Space and time are merely pure a prioi intuitions, not attributes of things as they are in themselves. And I’ll shoot anyone who disagreees with a gas pistol.
I see whatcha did there, you dirty Kantian. Go back to Koenigsberg.
In economics Gilboa and Schmeidler have proposed allowing probabilities of possible expected events to sum to less than one to allow for unquantifiable uncertainty.
How much less than one will they allow? Or is that another unquantifiable.
I think they specify a range in their patent. 🙂
Surely the Physics Sentence Of The Day is “Using Feynman diagrams is like taking a Ming vase and smashing it on the floor.”
This reminds me of Geometric Algebra, which I thought very interesting and powerful, though reading about it made my head hurt.
“Algebra is but written geometry, and geometry is but figured algebra.” (Sophie Germain)
I do agree with her view.
So we discovered a new mathematical technique that vastly simplifies the calculations of quantum particle interactions.
Does this increase or decrease your estimate of our universe being a simulation?
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