[dipayankar]

This is the problem with String Theory. It is a very beautiful picture, but is only a picture as of now... The problem of this duality can be solved only if we can somehow prove /disprove String Theory...

Originally Posted by Graybeard Dip .... I'm not sure and would only be guessing. However I see part of the problem From 1 .. 'e' appears to be the charge in the inverse square law of Electricity. The force between two charges separated by a distance is (e1 x e2) / r^2. eg: the further apart they are (r = distance) the less the force acting between them because r^2 is the divisor ... From 39 .... That was because of a basic limitation in our abilities in physics; We are generally able to compute what happens only when the charge, e, is much less than one. (What this means I don't know) From 40 ...... Duality, though, exchanges e with 1/e and it is not possible to have both e and 1/e be much less than 1. The problem here is that duality of a particle describes its particle/wave function. But in String Theory duality describes the uncertainity of Spacetime (see From 37 ... and externally the 'monopole' problem) Altho I don't understand the reasoning, e needs to be less, much less than 1. But with String Theory duality both 'e' and '1/e' are used and they both need to be less than 1. If 'e' is less than 1, then 1/e will be greater than 1. How they solved this in the 3 years prior to 1998 Phuck knows .. Everything I am saying here may be an absolute load of crap, so don't take it too seriously .. LOL I will ask Dave if he can have a go at explaining it for us .... cool bananas ... greg

[Graybeard]

Yes Dip ... when you read it as Witten describes it, its so good it should be right.

I don't understand how they resolved the 'e' and '1/e'.

I don't really get Daves BTW either.

Originally Posted by Dave BTW: (e1 x e2)/r^2 is only valid for forces that are independent; electrons with the same quantum qualities will simply stick together.

I am sure I am missing something, wouldn't the 2 electrons repel each other ??

greg ????

[dipayankar]

My gut feel is that an extreme sub atomic distance, gravity will turn attractive and hence keep the electrons together....

Originally Posted by Graybeard Yes Dip ... when you read it as Witten describes it, its so good it should be right. I don't understand how they resolved the 'e' and '1/e'. I don't really get Daves BTW either. I am sure I am missing something, wouldn't the 2 electrons repel each other ?? greg ????

[dleviwing]

Greg;
Here’s a SA article you may find interesting.
http://www.sciam.com/article.cfm?chanID=sa003&articleID=000DC7CC-9D0B-1C5E-B882809EC588ED9F

[Graybeard]

Originally Posted by Scientific American, Apr, 23 - 2001 They discovered that Wigner crystals form when the electrons are tightly compressed in a plane (see top image).

Dave .. In the 2 illustrations given with the article they show the 'bulls-eye' in a flat plane. Is this correct, or should it be considered as a 'slice' of a spherical arrangement ? Like shells within shells , each ring is a sphere.

cool bananas ... greg

[Graybeard]

Its OK ... I think I found the answer HERE

From the same link above it says

Originally Posted by Wiki There is a single dimensionless parameter characterizing the state of a uniform electron gas at zero temperature, the so-called Wigner-Seitz radius rs = a / ab, Where a is the average inter-particle spacing and ab is the Bohr radius. Quantum Monte Carlo simulations indicate that the uniform electron gas crystallizes at rs = 106 in 3D and roughly rs = 35 in 2D.

Is this referring to an explanation for the 'e' and '1/e' problem that Witten refers to ?

Originally Posted by Graybeard quote Ed Witten 39.. But it seemed well out of reach to determine if it was really true. That was because of a basic limitation in our abilities in physics; We are generally able to compute what happens only when the charge, e, is much less than one. 40.. Duality, though, exchanges e with 1/e and it is not possible to have both e and 1/e be much less than 1. 41.. To test, or use, duality one has to somehow get beyond the traditional limitation of small e. And thats what happened in the last three years, (this written in 1998) with broad implications for our understanding of Standard Quantum Field Theory and String Theory.

But in a 'Quantum Dot (and / or Wigner Crystals) do 'e' and '1/e' approach each other ? Here

Originally Posted by Wiki Quantum dots containing electrons can also be compared to atoms: both have a discrete energy spectrum and bind a small number of electrons. In contrast to atoms, the confinement potential in quantum dots does not necessarily show spherical symmetry. In addition, the confined electrons do not move in free space, but in the semiconductor host crystal. The quantum dot host material, in particular its band structure, therefore plays an important role for all quantum dot properties. Typical energy scales, for example, are of the order of ten electron volts in atoms, but only 1 millielectron volt in quantum dots. .....

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cool bananas ... greg

[dipayankar]

How do we practically use quantum dots???

Originally Posted by Graybeard Its OK ... I think I found the answer HERE From the same link above it says Is this referring to an explanation for the 'e' and '1/e' problem that Witten refers to ? But in a 'Quantum Dot (and / or Wigner Crystals) do 'e' and '1/e' approach each other ? Here . cool bananas ... greg

[Graybeard]

Originally Posted by dipayankar How do we practically use quantum dots???

They are used in nano-technology, research for QM computing, and research applications

Here is an example. It also appears that this research may be indirectly helping String Theory.

Here is another ... the worlds smallest radio

cool bananas ... greg

[dipayankar]

Thanks Greg... I am thrilled. It seems we are already enroute our ToE...

Originally Posted by Graybeard They are used in nano-technology, research for QM computing, and research applications Here is an example. It also appears that this research may be indirectly helping String Theory. Here is another ... the worlds smallest radio cool bananas ... greg