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  #31  
Old 05-06-2011, 03:35 PM
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Originally Posted by system7 View Post
I don't suppose Prof Susskind has had an easy life pursuing a topic that was in the doldrums for many years, and he probably needed a strong ego and a few bottles of wine to get over the early criticism or indifference of his work. But I like String Theory, because it combines geometry and symmetry with a simple particle model of strings/loops or perhaps a torus. I hope it works out.
Time will tell.
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Back on-topic, we seem to have 3 dimensions of extended space, 6 dimensions of looped space along with a dimension of time and an extra spatial dimension that is strangely different but important right now in 11D M-Theory. It's all coming along quite nicely!
Is there a theory with more than 11 dimensions? like 20?
I can imagine how complicated transformations are needed to apply physics laws on 9+ dimentions. Hopefully computers come to the rescue...

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Nerdmaster, you'd be interested to know that our Digital Filtering teacher at IC was Prof Anthony Constantinides. A brilliant maverick of a teacher with hugely entertaining strong views and a liking for wine after lunch. In fact most of us signed up for his obscure course on optimum network theory just for the fun of it.
I have heard of him before but never realised that he has 250 papers!
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  #32  
Old 05-07-2011, 10:56 AM
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I've been following the lectures on String Theory, which I currently visualise as being like bubble rings in the case of the Spin 2 graviton, which rely on a spin to stay stable:



I'm not sure I buy the 26D theory, which attempts to keep the harmonic oscillator ground state at -1 energy through 24 degrees of freedom:


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26D theory only seems to work with Bosons like Mesons. 11D may be enough, but I'll need more lectures to follow the details.

The maths is quite impressively far ranging, including Beta functions in scattering theory, and the lovely conformal mappings preserving features, and even the Z-Transform I used in digital filtering. Also at heart are the Planck units in terms of the speed of light, the gravitational constant and Planck's constant of action:



These describe the size of strings and even possibly the mass of the lightest possible Black Hole.
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  #33  
Old 05-07-2011, 11:34 AM
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System7, who the hell are you?
Are... are you a wizard?
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  #34  
Old 05-07-2011, 09:09 PM
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...

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  #35  
Old 05-08-2011, 04:16 AM
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26D theory only seems to work with Bosons like Mesons.
So it is not correct.
A theory has to predict and describe as many examples as posible (not just one).

(26 dimentions are so many!)
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  #36  
Old 05-08-2011, 01:39 PM
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I'm not saying 26D theory is wrong, but it seems a rather artificial trick to use 24 dimensions to fudge the numbers you want on the ground state (or zero-point energy) of the oscillating ring. The trick is to tame the ground state to avoid creating negative mass, which is the unlikely Tachyon faster than light particle. The maths is right in a sense, just that maybe the physical model is wrong. Time will tell.

I was mulling over Brian Greene's simplistic model of a rolled-up small looped dimension today, and perhaps there are 7 small ones:



It's a poor model in some ways, but consider the big dimensions we live in are really loops too, as big as the universe. Is there a transform that will put the big and the small circles on an equal footing? In fact there is, and it's called a Conformal Mapping. In Ryde High Street on the Isle of Wight I pass this skillful painting on a sphere every day at the Orrery Cafe...



You could regard it as equivalent to reflection in a mirrored sphere, and it preserves angles while changing circles and straight lines about!

In fact anyone who has done electromagnetism will be on familiar ground here. The electric field and the potential are always at right angles in this dipole situation. It is not hard to convert this diagram to represent magnetism, or wrap it round a sphere so the central vertical line becomes the equator, and the charges move to the poles. It is also the mathematics of analog and digital filters. The only parameter that matters in this diagram is the interval/distance between the two charges.



So here is a way to equalise the small and large dimensions into a consistent geometry. In fact Conformal Mapping is a hugely powerful method, that can convert an s-channel Feynman collision diagram with a short-lived particle into a t-channel scattering with an exchange particle. All that matters is the duration of the temporary particle. The maths is unchanged!
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  #37  
Old 05-10-2011, 12:52 PM
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I guess I lost you guys with the last post, so perhaps (beyond the observation that Leo Susskind does exactly the sort of conformal mapping I was talking about by doing the String Physics in his lecture course at high Z momentum which shortens space and time...) we gotta just move on here.

We've been doing Particle Physics with spheres seems like for ever, but Strings suggest the Torus is a better candidate for sub-atomic particles:



The maths of the Torus is quite simple, and it's quite interesting that you can transform it into two spheres or circles by taking a slice in another plane. Someone just has to discover a simple bit of geometry that throws out the Fundamental Constants like Planck's Constant, the speed of light an' stuff and we are home and dry!

I am currently interested in the conformal mapping that that gives to adjacent sphere's reflections that equate to 1, 1/3, 1/5, 1/7 etc. in the odd terms of the Euler Zeta function.



It may be good, it may be rubbish! But interesting!
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  #38  
Old 05-14-2011, 05:04 AM
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I know a lot of you are following this with bated breath, so time to move on...

In Lecture 8, Leo Susskind discusses some basic math of conformal transformations:
http://www.youtube.com/watch?v=s43SM...56448F&index=8



The important ones are really the natural log (the integral of 1/n) and the Z+1/Z-1 mappings which transform circles and rectangles.

In Lecture 9, he then explains why the quantised angular momentum (n times Planck's Constant h bar) goes to hell on the surface of a sphere as the closed string gets bigger:



He lost me on the Ricci Tensor bit through unfamiliarity with General Relativity, but in essence things work nicely on a torus, which compactifies two dimensions:



This surface allows a string to move around freely in the compactified dimensions with an energy related to 1/R, or to wind around a dimension with an energy proportional to R and the number of windings. Nice! And the maths is not too hard.
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  #39  
Old 05-14-2011, 10:19 AM
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Nothing much to add, except that I got 95% for my Physics assessment and I'm feeling like a smarty pants.

I have no intention of even having close to your knowledge on this subject however, system7. That was enough, no more of this crazy stuff for me.
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  #40  
Old 05-14-2011, 10:32 AM
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Congratulations, James! Quantum Electrodynamics (QED) is a subject that always baffled me, though I have a vague notion of what it calculates.

In fact Quantum Chromodynamics (QCD) is best done in the Standard Model using a packet of M&Ms evidently. Not crazy at all!


http://forums.xkcd.com/viewtopic.php?f=59&t=70953

So far this model also finds the M,W,E and 3 particles in the packet...but it works. I am wondering if Fruit Polos might help me in my String researches.
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