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A key sentence in TWF #232 
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#1
May2806, 09:26 PM

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PF Gold
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this may have been emphasized at Usenet SPR, I didnt check. I will flag it here in case anyone overlooked it.
=====quote Baez TWF #232==== Second, suppose we let two particles collide and form a new one:
exp(p") = exp(p) exp(p') since little loops going around the two incoming particles can fuse to form a loop going around the outgoing particle. Note that we're getting conservation of the groupvalued momentum, not the Liealgebravalued momentum  we don't have p" = p + p' So, conservation of energymomentum is getting modified by gravitational effects! This goes by the name of "doubly special relativity"... ====end quote==== I will see if the paste version copies OK 


#2
May2806, 09:42 PM

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PF Gold
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this comes in
http://math.ucr.edu/home/baez/week232.html pretty far down the page more discussion currently here http://math.ucr.edu/home/baez/README.html which currently describes Baez seminar talk http://perimeterinstitute.ca/activit...&SeminarID=749 and colloquium at Perimeter http://math.ucr.edu/home/baez/quantum_spacetime/ ===================== the reason I wanted to highlight that passage from #232 is that the fundamental law of momentum conservation is a MULTIPLICATION of group elements and it is only ADDITIVE TO FIRST ORDER so what Newton told us about conservation of momentum, that it was an additive (Lie algebra) thingthat is only a first order approximation of the real multiplicative (Lie group) conservation law or so this example suggests might be, which is kind of odd, and something I guess we should know about 


#3
May2806, 11:32 PM

P: 169

However, I'm also trying to make it clear that only in 3d spacetime can we think of the momentum of a point particle as Liealgebravalued. So only in this case can we switch to using groupvalued momentum. That's because in 3 dimensions, Minkowski spacetime is a Lie algebra! You first get an inkling of this when you learn about the "cross product" in linear algebra. The cross product is a special way to make 3d space into a Lie algebra, which doesn't work in other dimensions. A similar trick works for 3d spacetime.... But for 4d spacetime, we need a different trick! That's what my papers with Crans, Wise and Perez are about. We need to switch from point particles to strings! A string is just the right thing to have a momentum density valued in a Lie algebra, so we again can  and must!  switch to a group when we turn on gravity. (Topological gravity, that is  in other words, BF theory. I'd like to get this to work for fullfledged gravity, but 4d gravity is, of course, tough.) 


#4
May2906, 08:34 AM

P: 271

A key sentence in TWF #232
So Professor Baez, you're back in physics now?



#5
May2906, 08:52 AM

Astronomy
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PF Gold
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to me that it was rather the best possible sort of mathematics that is, inventing something new in the realm of logic and formal ideas that physicists can USE if they want to, and also people can just have fun with if they don't want to not a thought out reaction on my part. but it seems to be a fit of sleepwalking mathematical inventiveness that comes at the right time to let some physicist fly get out of his bottle if he wants toand he can stay in if he doesnt. (I mean the inventiveness you need to raise the show to 4D) 


#6
May2906, 10:25 AM

PF Gold
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#7
May2906, 02:09 PM

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PF Gold
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Have you seen that David Corfiel posted a discussion between himself and Professor Baez on this and other topics at his blog: http://www.dcorfield.pwp.blueyonder....ngingrig.html. Just a couple of mathematicians noodling around with the ideas that fascinate them, but how enlightening! And we have it here too! Wow! 


#8
May2906, 02:10 PM

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PF Gold
P: 8,147

Have you seen that David Corfiel post a discussion between himself and Professor Baez on this and other topics at his blog: http://www.dcorfield.pwp.blueyonder....ngingrig.html. Just a couple of mathematicians noodling around with the ideas that fascinate them, but how enlightening! And we have it here too! Wow! Also check out the stuff at TWF 233. 


#9
May2906, 02:41 PM

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the conversation is long and rich in intuitionas far as I could tell from the initials it is JB talking much of the time. not to actually "give up" on TWF 233, I should say that I have checked it out and find it not the easiestI get more out of 232 and also little chunks of this Corfield blog. So I will print out the corfield and go read it in a more comfortable chair 


#10
May2906, 04:32 PM

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PF Gold
P: 8,147

I remember the instructer trying to explain this to me in a course in Lie Algebras my first year of grad school. "But I was one and twenty; no use to talk to me." 


#11
May2906, 05:11 PM

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housman is technically good, but the despair bothers me
we are practically in the cockpit with something very interesting, aren't we? the focus of my confusionwhere I completely say DUH! right nowis this i understand that you can have a worldline in 3D and it can be a conical singularity persisting thru time and the deficit angle can be the mass now he says that to generalize this to 4D we need a "worldpipe" or a "worldhose"which should be a VERY familiar idea to many of us and this is swept out by a ring and instead of mass of a point you have TENSION of the ring and this makes something like a whole sheet of conical singularity persisting thru time and this Y diagram that we have in this thread becomes a "Ypipe" this is what I want to think about before taking an afternoon nap. It was a nice holiday weekend here. hope all's well in the Midwest ============= BTW just today, in Utrecht, Alejandro Perez was giving a talk to Loll's seminar exactly about this stuff: quantization of branes coupled to beeftalk had the same title as the Baez/Perez paper 


#12
May2906, 05:51 PM

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PF Gold
P: 8,147

As Feynmann said in a slightly different context; "There's plenty of room at the bottom." 


#13
May2906, 06:00 PM

Astronomy
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PF Gold
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being in the garden these days gives me an idea that Category theory is historically like the appearance of the flowering plants. All it does really is SPEED UP THE RATE OF MATHEMATICAL INVENTION. you just set up a new mechanism, namely insects that fly around, or you set up a functors to be the embodiment of analogy, and it speeds up the rate of evolution. in the end, perhaps it could have happened the old slow way too, maybe and then there are people such as Kea who I suspect just like the flowers 


#14
May2906, 06:08 PM

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#15
May2906, 07:22 PM

P: 169

Greg Egan had some nice questions about this "groupvalued momentum" business, which I was able to answer in part. However, I think there's still some work to be done to dig out the full meaning of this concept  some calculations, thought experiments, and so on.
Egan wrote: John Baez wrote:I replied: Greg Egan wrote: 


#16
May2906, 07:34 PM

P: 169

Most of the time I really want to do math, stuff involving ncategories and the like. But I have these grad students, Jeffrey Morton and Derek Wise, who are eager to work on quantum gravity. So, we had to dream up a project for them to work on, and this "strings in 4d BF theory" was what we cooked up. If all goes well, this will hook up to Freidel and Starodubtsev's work on treating 4d gravity as a BF theory plus a perturbation term, which is supposed to lead to a spin foam model for quantum gravity. In fact the G = 0 version of this spin foam model seems to be related to some work of Kea's! Then, with more luck, we will see strings and also particles showing up in this spin foam model. (I was an idiot, I saw where the strings fit in but not the particles!  Freidel pointed that out after Baratin's talk last week. But, if I'd seen the particles, I might not have seen the strings.) Dreams, dreams... It might work; it probably won't. But, luckily, all that really matters is Jeff and Derek will have nice theses. If I think about it this way, it takes the pressure off, and I can just have fun. It's important to have fun. 


#17
May3006, 03:19 AM

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PF Gold
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Why BF? There are other approaches that appear equally promising to me. That took me by surprise  I didn't know you favored BF. PS, I really like category theory.



#18
May3006, 01:57 PM

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PF Gold
P: 8,147




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