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Tying Knots With Light
thedreadedwiccan points out a summary of a recently released physics paper about tying knots with light. A pair of researchers showed that a relatively new solution to Maxwell's equations allows light to be twisted into stable loops. They are designing experiments to test the theory now, and it could have a big impact on fusion technology. The paper's abstract is available at Nature, though a subscription is required to see the rest. Quoting:
"In special situations, however, the loops might be stable, such as if light travels through plasma instead of through free space. One of the problems that has plagued experimental nuclear fusion reactors is that the plasma at the heart of them moves faster and faster and tends to escape. That motion can be controlled with magnetic fields, but current methods to generate those fields still don't do the job. If Irvine and Bouwmeester's discovery could be used to generate fields that would send the plasma in closed, non-expanding loops and help contain it, 'that would be extremely spectacular,' Bouwmeester says."
Anybody who is anybody saw the flux capacitor in what 1984 - this is old work. the flux capacitor had loops and curves etc.
If Irvine and Bouwmeester's discovery could be used to generate fields that would send the plasma in closed, non-expanding loops and help contain it, 'that would be extremely spectacular,' Bouwmeester says."
Bouwmeester continued by saying that light is, "way cool" and the ability to tie knots with it would be, "totally freaking awesome".
Or maybe the scientists are running around in circles? The goal is to figure out a way to bottle up plasma (for fusion energy harvesting). Since the magnetic bottle has not proven to be viable.
Please tell me this is getting me closer to owning a light saber. PLEASE!!!
Even so, why do I think this is not actually going to work? Because for the last fifty years, fusion power has been constantly just twenty years in the future, that's why. The authors don't claim a solution to fusion containment, they are talking about possible new ways of trapping photons or creating condensates.
From scarped cliff or quarried stone she cries "A thousand types are gone, I care for nothing, no not one."
wow, loops.... watch them untie damn it. but no really, thats a bad ass discovery, if only we could find an application for it
The real question is was a silver hammer necessary?
The (slashdot) summary really does miss some of the key points, and emphasize the "fusion containment" aspect, which I doubt anyone takes seriously as a use of this. One of the points that I think is key is the whole subject of homotopy groups (which I've really just learned about).
Maxwell's equations (and the wave equation, the Helmholtz equation in momentum space, etc.) have a family of solutions characterized by various parameter values. When you first start learning physics, you typically only allow real-valued wavevectors, which leads to only propagating waves and so on. Later on, you start to realize (as did George Green around 150 years ago, and Newton realized experimentally) that allowing for complex wavenumbers is more appealing mathematically (because it allows for more complete solutions), and actually leads to physically realizable solutions that propagating waves just don't give you. The effect of passing from real to complex wavenumbers is, on the face of it, crazy, but easily understandable once the analysis is carried out, and simple to visualize on an Argand diagram.
However, homotopy groups (if I understand it correctly) say that there may be other solutions to such equations (in nonlinear/dispersive media) which one can't get to from just simple replacements of real with complex numbers, and so forth---these divisions are the "families" of solutions. There just isn't a simple projection from one family of solutions to another, and the solutions of from one may bear no resemblance to the solutions from other famililes. This means that there may, in sufficiently complicated systems, be physically realizable behaviors which a system may fall in to, which aren't describable by the "usual" solutions of the equations. Of course, Maxwell's equations work wonderfully in all situations I've ever heard of (no concession to the "Electric Universe" wackos!), so perhaps nature, for some reason, won't allow other families of solutions to make themselves known on any scale I know of.
1. How do you bend light without passing it through matter or using a grav field that will crush the experiment?
2. If they can bend light, why are we using electron beams for crt's?
3. If you could build loops of light can they be modulated to store information and read it back again?
I'm pretty sure this was already covered in Spiderman 3 - hopefully things turn out better this time around.
These science publishers are as evil or worse than the RIAA/MPAA with this paywall BS. To paraphrase, science is too important to be left to those that can pay 40 bucks per paper. I can't understand why Google, who wants to "organize the world's information", has not done anything to prevent the world's most valuable information from being inaccessible.
Because I don't need flying cars. I want Jedi weaponry in my lifetime.
That is all.
Help stamp out iliturcy.
Pass me some fiber optic line and I'll make you one.
Its been awhile since I've had anything with Vector Calculus, but doesn't a stable loop of light violate Maxwell's Equations in some way? Divergence of B = 0, Div of E = p/epsilon, Curl of E = dB/dt. Seems like a stable knot might not fit with that. Anyone more math savvy know?
If it is possible it probably appears in nature.
Why aren't they simply published on the internet, instead of some silly place that asks $18 for a pdf?
FRA: STFU GTFO
Great, all we need is another method to tie knots. Imagine if they made something to untie knots with light! Now that would be commercially viable! XD
I like light, I'm just not sure if I'm ready for that kind of commitment.
Were do you get that magnetic fields bend light? Not with Maxwell, not in a vacuum. Any reference to the contrary will be read!
Please correct me if I'm wrong, but I have a basic understanding of homotopy.
I guess you view a solution as a certain kind of map on R^3 that obeys Maxwell's equations and then use homotopy to deform one map into another, all the while respecting Maxwell. Then, one element of the homotopy group would correspond to one family of solutions which may all be transformed one into another via homotopy. Knowledge about the group formed (which has to come from the kind of topological space that Maxwell's equations define) must imply the existence of other families of solutions (e.g., multiplying two known solutions together in the homotopy group to get a new one).
What I'd like to know is how do Maxwell's equations define the topology on the image of the solution maps. Any help?
Hell, there are no rules here-- we're trying to accomplish something. --Thomas A. Edison
Unfortunately the figures, equations, and tables came out as "Unfortunately we are unable to provide accessible alternative text for this. If you require assistance to access this image, or to obtain a text description, please contact npg@nature.com".....if someone can suggest where I should upload the PDF, I'd do that too.
======
Letter
Nature Physics 4, 716 - 720 (2008)
Published online: 31 August 2008 | doi:10.1038/nphys1056
Linked and knotted beams of light
William T. M. Irvine1,2 & Dirk Bouwmeester2,3
Abstract
Maxwell's equations allow for curious solutions characterized by the property that all electric and magnetic field lines are closed loops with any two electric (or magnetic) field lines linked. These little-known solutions, constructed by Rañada1, are based on the Hopf fibration. Here we analyse their physical properties to investigate how they can be experimentally realized. We study their time evolution and uncover, through a decomposition into a spectrum of spherical harmonics, a remarkably simple representation. Using this representation, first, a connection is established to the Chandrasekharâ"Kendall curl eigenstates2, which are of broad importance in plasma physics and fluid dynamics. Second, we show how a new class of knotted beams of light can be derived, and third, we show that approximate knots of light may be generated using tightly focused circularly polarized laser beams. We predict theoretical extensions and potential applications, in fields ranging from fluid dynamics, topological optical solitons and particle trapping to cold atomic gases and plasma confinement.
Introduction
The concept of field lines whose tangents are the electric or magnetic field is typically used to visualize static solutions of Maxwell's equations. Propagating solutions often have simple field-line structures and so are not usually described in terms of field lines. In the present work, we study a propagating field whose defining and most striking property is the topological structure of its electric and magnetic field lines.
An intriguing configuration for field lines is to be linked and/or knotted. Two closed field lines c1(tau), c2(tau) are linked if they have non-vanishing Gauss linking integral3, 4, 5, 6,
Unfortunately we are unable to provide accessible alternative text for this. If you require assistance to access this image, or to obtain a text description, please contact npg@nature.com
whereas for a single field line c(tau) the self-linking number, L(c,c), is a measure of knottedness. The linking integral L can also be computed visually by projecting the field lines onto a plane and subsequently counting the crossings in an oriented way3. For example, the lines in Fig. 1a have linking number 1, but do not form a knot, whereas the blue and orange field lines in Fig. 4 below are knotted and linked to each other. In the case of magnetic or electric fields, averaging the linking integral over all field-line pairs together with the self-linking number over all field lines gives rise to the magnetic and electric helicities4, 5:
Unfortunately we are unable to provide accessible alternative text for this. If you require assistance to access this image, or to obtain a text description, please contact npg@nature.com
where B:=nablatimesA and E:=nablatimesC in free space.
Figure 1: Construction of the Hopf fibration.
Figure 1 : Construction of the Hopf fibration.
aâ"c, Left column: A torus can be constructed out of circles (fibres) in such a way that no two circles cross and each circle is linked to every other one. a,b, Each circle in such a configuration wraps once around each circumference of the torus. c, By nesting such tori into one another, the whole of three dimensional space, including the point at Unfortunately we are unable to provide accessible alternative text for this. If you require assistance to access this image, or to obtain a text description, please contact npg@nature.com (U
http://pdfmenot.com/view/http://pdfmenot.com/store_local/996c794f28d65c93d38d6cb60ff50d2f.pdf
When will Air Jordans have light-based shoelaces?
Airplane Photos, Airline News, Planespotting Guides
For those not in the know with Maxwell's equations, here's the Wikipedia for them.
Light propagates so it is not a true loop, but more like the idea of a vibrating string from string theory. Does this mean nature mimics its self from small scale to large scale since the solar system is similar to an atom? Probably not, but it is a nice idea to think about.
Stable loops of light in plasma. I wonder if this might be related to ball lightning?
Bantam Dominique roosters crow a four-note song. Once you've heard it as "Happy BIRTHday" you can't NOT hear it that way
The novel "Infinite Jest" mentioned something called annular fusion, which involved optics somehow. This article involves optics (in a sense) and fusion. Was David Foster Wallace about twelve years ahead of this curve?
Go be enlightened; there's no excuse not to be.
There's no reason not to have a user agent header, just as there's no reason not to have a 'Server' header. User agent sniffing, on the other hand, is one of the many, many, many things that we have because the internet is an amalgamation of non-standardized crap. Sites do it because they can't just send standards-compliant data, because browsers don't all render it the same. (See: box model bug.) You can't say "fuck those people", because they're the vast majority of the internet (at least, until quite recently); if you're making a public-facing website, to almost everyone who comes there, your site is broken. This is, needless to say, not an option if you want visitors.
The fundamental problem is that writing standards-breaking browsers doesn't come back to bite the authors of said browsers; they have no incentive not to do it, and in fact, if they're being anticompetitive, they have an incentive to make it even worse.
It's rather miraculous that the internet works at all.
Laws do not persuade just because they threaten. --Seneca
Let's cut to the important question... Can this tech be applied to make better light saber toys??
Hmm, fusion. There are certain invariant physical constants in the universe:
1. No matter your temporal coordinates, you are always 50 years away from usable fusion power.
2. The current version of any Microsoft Office product always takes the same amount of time to load.