Knots and Quantum Theory - Edward Witten

Edward Witten
Institute for Advanced Study
December 15, 2010
A knot is simply a tangled loop in ordinary three-dimensional space, such as often causes us frustration in everyday life. Knots are also the subject of a rather rich mathematical theory. In the last three decades, it has unexpectedly turned out that rather deep aspects of the theory of knots are best understood in the context of 20th and 21st century developments in quantum physics. In this talk, Edward Witten, Charles Simonyi Professor in the School of Natural Sciences, attempts to explain what quantum theory has to do with knots. He starts at the beginning in a talk that should be accessible to anyone who has ever puzzled over a particularly vexing mess of string.
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[@mikevaldez7684]

His lecture flows like poetry and was like listening to the great tales of Brothers Grim or Andersen. I loved every minute. I hope he gives many more like this

[@mikevaldez7684]

Beautiful, beautiful exposition by a truly brilliant mind. The "why" is everything in mathematics--it's the holy grail of rewards

[@user-kq2lk6uj3v]

"You'll love my knots" -- Edward Witten

[@kamilziemian995]

Good and simple talk.

[@brendawilliams8062]

Thankyou for your lecture.

[@NothingMaster]

Elementary, but establishing an elegant and useful connection.

[@lunatuna5203]

World reknown physicist - does powerpoint in the original MS Paint.

[@benpietrzykowski9216]

I don’t understand a thing but enjoy this level of intellect

[@jazw4649]

If you want to destroy my sweater, pull this thread as I walk away. ~ Weezer

[@aboundproductions6036]

Witten is pretty witty, I wish he went into stand-up comedy instead of mathematics.

[@zarkarimi]

why would you wish that ?!

[@columbus8myhw]

Didn't you describe HOMFLY instead of Jones?

[@KineHjeldnes]

Does anyone know the title of the paper Witten wrote about self-crossing path of a particle?

[@KaliFissure]

I suggest that the figure 8 knot is the best model for out total topology but that trefoil is best to model only EM fields

[@Myrslokstok]

YT is amazing Witten must be that special high schoolstudent.

[@psi.squared9448]

I love how he evades questions about string theory and the state of phisics

[@joemagarac405]

No, when asked directly about it at 46:25, he answers directly. No evasion at all.

[@edgeworthyeconomics]

41:20

[@davidwalker5054]

The only thing i have in comon with him is i dont understand the quantum world

[@TheNorgesOption]

Oh wow, this might be a frame of reference bias. Let us say we detect a particle, can therefore say that particle is in this particular location? However is it in that location to another observer traveling at relativistic speeds or close to a event horizon? My understanding is no it is not (:). So when talking about the path of a particle (or a sting in this case) and its detection, we also have to include all possible frames of reference. When we use that method, the collapse would then be expressed as a wave again. We then would include random fluctuations in the quantum fields, which would then cause the particle to be detected in different locations. This is related to the waves produced by the string which produces the particle. So that a detection is merely the point of the exchange of energy between two particles, not the determination of the particle’s location. If that is the case, there is really no need to define the path of the particle much less define the location of the string.

[@SpotterVideo]

Quantum Entangled Twisted Tubules: When we draw a sine wave on a blackboard, we are representing spatial curvature. Does a photon transfer spatial curvature from one location to another? Wrap a piece of wire around a pencil and it can produce a 3D coil of wire, much like a spring. When viewed from the side it can look like a two-dimensional sine wave. You could coil the wire with either a right-hand twist, or with a left-hand twist. Could Planck's Constant be proportional to the twist cycles. A photon with a higher frequency has more energy. (More spatial curvature). What if gluons are actually made up of these twisted tubes which become entangled with other tubes to produce quarks. (In the same way twisted electrical extension cords can become entangled.) Therefore, the gluons are actually a part of the quarks. Mesons are made up of two entangled tubes (Quarks/Gluons), while protons and neutrons would be made up of three entangled tubes. (Quarks/Gluons) The "Color Force" would be related to the XYZ coordinates (orientation) of entanglement. "Asymptotic Freedom", and "flux tubes" make sense based on this concept. Neutrinos would be made up of a twisted torus (like a twisted donut) within this model. Gravity is a result of a very small curvature imbalance within atoms. (This is why the force of gravity is so small.) Instead of attempting to explain matter as "particles", this concept attempts to explain matter more in the manner of our current understanding of the space-time curvature of gravity. If an electron has qualities of both a particle and a wave, it cannot be either one. It must be something else. Therefore, a "particle" is actually a structure which stores spatial curvature. Can an electron-positron pair (which are made up of opposite directions of twist) annihilate each other by unwinding into each other producing Gamma Ray photons. Does an electron travel through space like a threaded nut traveling down a threaded rod, with each twist cycle proportional to Planck’s Constant? Does it wind up on one end, while unwinding on the other end? Is this related to the Higgs field? Does this help explain the strange ½ spin of many subatomic particles? Does the 720 degree rotation of a 1/2 spin particle require at least one extra dimension? Alpha decay occurs when the two protons and two neutrons (which are bound together by entangled tubes), become un-entangled from the rest of the nucleons . Beta decay occurs when the tube of a down quark/gluon in a neutron becomes overtwisted and breaks producing a twisted torus (neutrino) and an up quark, and the ejected electron. The phenomenon of Supercoiling involving twist and writhe cycles may reveal how overtwisted quarks can produce these new particles. The conversion of twists into writhes, and vice-versa, is an interesting process. Gamma photons are produced when a tube unwinds producing electromagnetic waves.

[@johnstfleur3987]

GOOD THOUGHT.

[@UnforsakenXII]

hahahah 42:00 Finding excuses to waste time because you can't think what else to do. Oh boy!

[@taliesinbeynon]

Frankly that did not strike me as a clear explanation of how to calculate the Jones polynomial.

[@sallylauper8222]

Witten is one of those people about whom you hear that he's a genius, he's smart, he's not gay, etc. Based only on the fact that they can't understand a word he says. Aloto people like that are pure fakers. Witten is a rare critter. Everybodies afraid of him, but I think even few doctorate mathematicians or physicists understand him. Perhaps I'm just projecting. Witten IS a genius, in the worst sense of the word.

[@harrywilson1660]

Theoryn

[@TheMemesofDestruction]

38:10 -- Nani?

[@willjennings7191]

When you go down to the sub-atomic level with knot theory, several other theories of physics become more mathematically consistent than Witten's own work.

[@travisfitzwater8093]

From the standpoint of one pole there is only a monopole which would be the other Pole and vice versa what that means I will leave it up to the consideration of the reader

[@johnstfleur3987]

"I HAVE HUMBLY PROVEN ATLEAST SUPER DUPER STRING THEORY, THUS YAHWEH MUST EXIST."(JC)

[@zbubby1202]

This introductory statement perplexes me: it is impossible to know, given a knot, if it can be untangled. How so? A series of operations took place to render the knot in the first place. Theoretically those operations could be performed in the inverse to undo it. Then I thought about one-way functions....

[@schmetterling4477]

Yes, it is always possible to know if a knot can be untangled, but the problem is NP-complete, so that's not all that helpful for even fairly simple knots, I am afraid.

[@n-da-bunka2650]

This is all very simple... it's just the number of times the lines cross over or under each other. Interesting that we would need complex math for something so very simple but the logic is only functional if the lines are contiguous

[@brendawilliams8062]

It makes me think of a button threaded on a loop of string. Winding the loop makes a spinner on a rubber band.

[@johnstfleur3987]

I AM L.

[@jakethemistakeRulez]

Why do they always have someone that nobody wants to hear talk do some long annoying introduction.

[@nabilmalouf1575]

If you survive introduction, then you deserve hearing the following